tag:blogger.com,1999:blog-10435978265990851222024-03-10T01:05:52.898-08:00McSquaredA teacher's real-time journey into Web 2.0Unknownnoreply@blogger.comBlogger184125tag:blogger.com,1999:blog-1043597826599085122.post-44785057581183959762020-07-17T07:43:00.002-07:002020-07-17T07:47:51.301-07:00Routines for Synchronous Courses at LEARNTwo years ago<a href="https://audrey-mcsquared.blogspot.com/2018/05/learns-self-paced-blended-learning-year.html" target="_blank"> I wrote about how we at LEARN </a>had reorganized our synchronous courses (what we call Real Time, or RT), to accommodate students who wanted to study in a self-paced, mostly asynchronous format (what we call Self Paced Blended Learning, or SPBL). Both RT and SPBL students are in blended courses, it's just that the RT blend has a much greater synchronous component and the SPBL blend is much more asynchronous.<br />
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I suspect that, in the coming school year, as a result of the pandemic, many teachers will actually be doing a blend of RT and SPBL - in other words, a blend of two blends. Whereas we meet with our RT students every single day, and our SPBL students only once a week, they'll probably be somewhere in between. I don't know how to do that, but I figured I could at least follow up the SPBL post with this one about how we've been organizing our Real-Time courses.<br />
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<span style="font-size: large;">Real-Time Daily Routine:</span><br />
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We each have a regular schedule of our classes, just as anyone in a brick and mortar school would. I see the same kids everyday in my 9:00 class, my 10:00 class, etc. We hold our classes in Zoom. We ask our students to join the Zoom room via our LMS (Sakai), because we use it not only for content storage, but also as a bulletin board, with announcements and reminders that we want them to see on their way into class. So on December 2 (in the before time) this is what they saw on their way into class:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTNWxFVsNAGXJXzqs4d0SviH0xDcw3SEYg3bFvsbe1aewkGpaIY-0roqa8vdKUs6V8jjT0-4Jlg5rGwwIW5Ej1Yf4FFCr4Ahjv2SMN7qRrF-zMx7mcR_3wMCbEvjtsNSW9Ow-we_536KA/s1600/sakai.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="694" data-original-width="504" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTNWxFVsNAGXJXzqs4d0SviH0xDcw3SEYg3bFvsbe1aewkGpaIY-0roqa8vdKUs6V8jjT0-4Jlg5rGwwIW5Ej1Yf4FFCr4Ahjv2SMN7qRrF-zMx7mcR_3wMCbEvjtsNSW9Ow-we_536KA/s640/sakai.JPG" width="464" /></a></div>
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<i><span style="color: #0b5394;">Note: I'm jumping into a part of the year where the kids are all pretty familiar and comfortable with the routine - but typically we spend the first month or two getting them there, by introducing the tools slowly, and giving them lots of opportunities to tell us how things are going etc.</span></i></div>
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On Dec 3 there was a reminder of what's due right now, today's secret word, and a shot of a tweet from one of the students (we use Twitter a lot with our students). Off they then go to class by clicking on the Zoom tab at the left. Our classes are 50 minutes long, and I happen to see all my students everyday, although that's not the case for all of our courses, of course that depends on the number of credits the course has. What happens in class is covered below in "Resources organization".</div>
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<span style="font-size: large;">Other routines:</span></div>
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Students can access other important links via the tabs on the left in Sakai, such as Voicethread, Gradebook, etc. It's a one-stop shop.</div>
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We make a weekly work guide and share it with the admins of each school, as well as of course with the students. More about that later.</div>
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Most student work, digital or paper, is handed in via dropbox or email. It's then returned via individual student google drive folders. The exception would be if the work was done in a Desmos or Classkick activity, in which case the work and the feedback live there.</div>
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For tests, we use paper and pencil. We send the test to their brick and mortar school, where it's printed, and they then write it supervised by someone at that end, who then faxes the papers to us.</div>
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We take attendance, contact parents, tutor, and fill out report cards like usual. Our students write the same final formal June exams like everybody else in Quebec, excluding this year of course. </div>
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<span style="font-size: large;">Resources organization: </span><br />
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The rest of the routine is more easily explained by looking at the resources, and how they're organized on Sakai.<br />
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Since we don't all organize our resources exactly the same way, I'll just show how I do it - basically I organize things by week, but I'll show you a whole unit as an example.<br />
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<span style="font-size: large;">A Unit:</span><br />
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Here's how the Optimization unit looked for one of my courses, called Math SN5. At the beginning of each week, I upload all the necessary resources within a folder. I add it to the top of the pile, which is why it's in descending order:<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqTrJo_C9vy_65MHN4N-t0Jql0NfyNVhtjO_NdyLow_xeKNUMGDZ0wcAFdrrglWBAgE79t_JZfExWgtG3HznRdyUK6sTRzFtmQkh3st46sCJAFBS4p2l_Qa8oyJVqT10SX9C8dBeUKY3s/s1600/synchronous+1.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="106" data-original-width="324" height="130" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqTrJo_C9vy_65MHN4N-t0Jql0NfyNVhtjO_NdyLow_xeKNUMGDZ0wcAFdrrglWBAgE79t_JZfExWgtG3HznRdyUK6sTRzFtmQkh3st46sCJAFBS4p2l_Qa8oyJVqT10SX9C8dBeUKY3s/s400/synchronous+1.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Week number and topic</span></td></tr>
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<span style="font-size: large;">A Week: </span></div>
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Inside each folder is everything that's needed for that week, including the weekly work guide, all the Voicethreads (and their offline counterparts for those with no internet at home), accompanying notes to complete, links to activities, assignments etc. There are some additional items that would only appear as the week progresses, for example, the recorded live lessons (archies) for anyone who was absent, solutions to various assignments etc. Here's what week 14 looked like:</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMkUbh-7WAsE-1CGrtiYRLr9PJkPSvC8od4uz4FeVd6sSMJRnZsVPX0bjf9znXLDP6BiqNKbKWNEXRed1iqB_GPU0naK-7ImqjbNvvw8_GH-g24lfwhgVzmlbsG3fBf36tEGBZfRyss0g/s1600/synchronous+2.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="419" data-original-width="361" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMkUbh-7WAsE-1CGrtiYRLr9PJkPSvC8od4uz4FeVd6sSMJRnZsVPX0bjf9znXLDP6BiqNKbKWNEXRed1iqB_GPU0naK-7ImqjbNvvw8_GH-g24lfwhgVzmlbsG3fBf36tEGBZfRyss0g/s640/synchronous+2.JPG" width="548" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">The view inside one week's folder</span></td></tr>
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Of all these documents, probably the work guide is the most important. I keep circling back to it as the week goes on, because sometimes, pretty much always, things change. In case the screenshots are too hard to read, here are the links to the googledocs for <a href="https://docs.google.com/document/d/1LtWL-dYZpQ4F1DljhnrAWjAXIgFtBKobjjpz5Y7zIjw/edit?usp=sharing" target="_blank">Week 13</a>, <a href="https://docs.google.com/document/d/1vURrmJHMi_nr6V_oBdKpgfAlN0QbUMW_uph_VYPlvAw/edit?usp=sharing" target="_blank">Week 14</a>, <a href="https://docs.google.com/document/d/1IA0Jo0RdZepwK2pDtDh0znMqV6ohbZQJ3JTtxcNt-PE/edit?usp=sharing" target="_blank">Week 15</a>:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglx0GIxKNoph5xpDYwZSd-prZKq9dzOLWXs0z63EUgjP4qSHIlN8XTsardfzxfM_bOgEdqFZlJ8BYuiSCbEl1cZ3ZkRzbV_zVvTvcguJD88tj0NaQl9SycAH9qn89cG_exsTVtNK7CjLk/s1600/synchronous+w13.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="642" data-original-width="524" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglx0GIxKNoph5xpDYwZSd-prZKq9dzOLWXs0z63EUgjP4qSHIlN8XTsardfzxfM_bOgEdqFZlJ8BYuiSCbEl1cZ3ZkRzbV_zVvTvcguJD88tj0NaQl9SycAH9qn89cG_exsTVtNK7CjLk/s400/synchronous+w13.JPG" width="325" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFeiz-AeAICtGSTKu9OOw3yMr_K4V0FcuHVRduBxExES2AKNEaWYhWgwzjtNpBxyM5_PzMVdmbaRFHxIs8f99TlvRGPXpm_SeXKBULgxkIJDxhM2mw6AGQX4FfabPxMCTkdrF3vbPWy-U/s1600/synchronous+w14.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="626" data-original-width="397" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFeiz-AeAICtGSTKu9OOw3yMr_K4V0FcuHVRduBxExES2AKNEaWYhWgwzjtNpBxyM5_PzMVdmbaRFHxIs8f99TlvRGPXpm_SeXKBULgxkIJDxhM2mw6AGQX4FfabPxMCTkdrF3vbPWy-U/s640/synchronous+w14.JPG" width="404" /></a></div>
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As you can see, the work guide includes important announcements, (like upcoming tests or assignments), what's happening during and between classes (like voicethreads), and what needs to be handed in by the end of the week. Obviously, the synchronous part happens during class, and the asynchronous part between.<br />
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<span style="font-size: large;">A Class:</span><br />
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What's the routine in class? I need to show my "lesson slides" to explain. Each day, I create what I call lesson slides, using powerpoint. These slides have everything I need in order to do what's on that day's list. I then share my screen and just click through the slides, pausing as needed if they're going to be writing something over a slide. It saves time, makes things flow during class, but it also helps me make sure I don't forget to do anything I wanted to do. That happens...a lot.<br />
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<span style="text-align: center;">Here is a collection of different types of slides that I might have (not all from the same day, but all from this unit). I've put callouts in yellow so you get some background for each type of slide (<a href="https://docs.google.com/presentation/d/1AcbN3Lb7_RyXwntJIuA8CotkEht4YZyE2QlMVXFj6p0/edit?usp=sharing" target="_blank">here's the link in case it's hard to read</a>):</span><br />
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<iframe allowfullscreen="true" frameborder="0" height="389" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/e/2PACX-1vSz-g-3QWgKUIJ299Ei6tS_RCNt2pxjATnTrP28Y-XpECbHdGv3cc0Hq2fickWh3NWxmcjbI9pEKjyd/embed?start=false&loop=false&delayms=3000" webkitallowfullscreen="true" width="480"></iframe><span style="text-align: center;">
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So the types of slides that happen everyday are: Title, Today, & Tonight. Everything else depends on the list for that day.<br />
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But amongst these slides, perhaps the most important is the title slide. I use it to display the date and a picture that either they've sent me, or, if I've run out of those, one of mine. It might be about my garden, or about the topic we're doing, the season, or something that's happening in the world. We spend the first few minutes talking about that picture, whatever it is. Protip: They love sharing about their pets, as well as food they've made, which I discovered after the shutdown and we were all baking like crazy. This helps a lot to overcome the fact that we're all so far apart, and likely would never meet face to face. It humanizes the whole experience! It's also made it possible for me to create a movie at the end of each year, that's just a run-through of the title slides, but which tells the story of our year together. This year's nearly broke my heart:<br />
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<iframe height="480" src="https://drive.google.com/file/d/16zgNBjFuzyAHMaxRm3qzdNMU7seyE_lo/preview" width="640"></iframe>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-17150505807260935022020-07-14T04:47:00.000-07:002020-07-14T04:47:48.768-07:00What Happened in My Class After the ShutdownMar 13 was the day the Quebec government announced a complete shutdown of Quebec's schools due to the 2020 pandemic. At LEARN's Virtual Campus, that didn't <i>necessarily</i> mean much would change for us, or our students. Theoretically, we could all still attend classes, (as long as there was internet), because we've been used to doing it all online for a long time. The reality was of course that many students stopped attending due to poor connectivity at home, and various other reasons. We did finish our courses, minus any kind of formal assessments, as per our directives, although we did provide our students with practice tests & exams, which were entirely optional.<br />
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Our extreme-outlier (until this year that is) situation gave us an immeasurable advantage over all the teachers who were literally thrown into emergency long-distance teaching. We had the luxury of already being thoroughly familiar and comfortable with the online environment, as did our students, so we were able to kind of roll with it by making adjustments for the reduced attendance and reduced expectations. I realize that I was enormously privileged in this regard, and I want to use that privilege in the only way I know - sharing.<br />
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No tests and no final June exam meant I had more time during class to do three things:<br />
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<li>Cover the actual course material better and deeper than I was ever able to previously</li>
<li>Cover topics that weren't on the course but were related/cool</li>
<li>Do fun stuff just for fun</li>
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Today I'll start blogging about it all, starting with a few things I did under the heading...</div>
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<span style="font-size: large;">Covering the course better:</span><br />
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1. Composites and Operations on Functions<br />
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When the shutdown happened, we were almost finished the trig function unit. In the past when I've finished this unit I've always wanted to spiral back to operations on functions, and composites of functions, to experiment with them using those beautiful trig curves. Boom. Wish granted. I put together this <a href="https://teacher.desmos.com/activitybuilder/custom/5e721e3dc59e631cf6969993" target="_blank">Desmos activity on Operations on Trig Functions</a> and this one on <a href="https://teacher.desmos.com/activitybuilder/custom/5e7ca0054eccd20c8942dac2" target="_blank">Composites of Trig Functions</a>, and here are a few shots of what my brilliant students did (anonymizer is on, & for most, original two functions are in blue & green, result in red):<br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Operations: Students were given 2 trig functions and they<br />decided which operation to do on them</span></td></tr>
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<b><i><span style="font-size: medium;">Lo and behold, g</span><span style="font-size: medium;">ardening and teaching intersected!</span></i></b></div>
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At the end of the operations activity, we looked back at a problem that they'd done way back in October, involving multiplication of an exponential function and a trig function. At that time, they didn't know anything about either of those functions. But they did know how to use straight arithmetic to multiply, point by point, two functions (in blue and green) and graph the result (in red):<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj81r4EjpRQUIIA20OqF5dbBUW0X-3eYOOvUIXKICM3cXd2jz2xc1EAHMmlluRdzaO4pFlLMnA4r0o9-ZEb4pL-R_zY9oq6lECr_VLhX_NJCnugdS17lkM6BpUyBR46ENvxPc4QKnjyc8E/s1600/con+1.1+nbr+6+solutions.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="393" data-original-width="685" height="228" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj81r4EjpRQUIIA20OqF5dbBUW0X-3eYOOvUIXKICM3cXd2jz2xc1EAHMmlluRdzaO4pFlLMnA4r0o9-ZEb4pL-R_zY9oq6lECr_VLhX_NJCnugdS17lkM6BpUyBR46ENvxPc4QKnjyc8E/s400/con+1.1+nbr+6+solutions.JPG" width="400" /></a></div>
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I remember that back in October, there was great consternation about this question and its solution, even amongst those who understood HOW to do it this way. They were uneasy about it, because this arithmetic method seemed so haphazard, inelegant, and no way to construct the graph of a function - don't we usually use an algebraic rule, which by the way what even would this one be?!? Worry not, I said, all shall be revealed. In previous years, that was a lie, because I never remembered or had time to circle back to it. But this year we had time, and since it was now June, and they were much more sophisticated mathematicians, they now had an opportunity to figure out the rule of the red curve, right on the last slide of the activity. Here is what one student figured out:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkWINV0wTgph_Zv8ffRO-m6m24aSkvRMG2KrweoAnPN8t2kPaLfHBgnLYVNguq9E6FjvPphEd1qZZddKbmq88ThmYIRaN7pQzCza8M1hjV7bCo30WroVdMbsQrYdTWVVE2s97RVgwx1lo/s1600/student+ans.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="492" data-original-width="1006" height="195" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkWINV0wTgph_Zv8ffRO-m6m24aSkvRMG2KrweoAnPN8t2kPaLfHBgnLYVNguq9E6FjvPphEd1qZZddKbmq88ThmYIRaN7pQzCza8M1hjV7bCo30WroVdMbsQrYdTWVVE2s97RVgwx1lo/s400/student+ans.JPG" width="400" /></a></div>
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The view from my teacher dashboard made me feel like a gardener who'd planted a seed and whose patience has finally paid off with fruit. Next year, I plan to plant a lot more seeds and harvest a lot more fruit! I also think it might be fun to have them work backwards - eg here's the result of a composite, what were the two functions?<br />
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2. Function Properties:<br />
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This is a topic I'd always circled back to each time we'd added another function to the pile. I already had a Desmos cardsort activity for this, but <a href="https://teacher.desmos.com/activitybuilder/custom/57ffec5c735113820ccc8d64" target="_blank">this year's version</a> had one extra slide at the end. I gave them a bunch of graphs, and asked them to sort them using their own secret headings, which the rest of the class, myself included, would then try to detect:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrVdv_3npr8YJF37qBoxwr78iKj-8l-jurU17IOPIupAxlvfpopNmT9cEAr1ufYblkmTX4YOgQCjF1WanRPGh88_FJ2eIVBnQQqCkOcv4rD13_EJjIfA-usmxXxWUhBFfTQolQFFmrZb0/s1600/fnpropscardsort1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="737" data-original-width="977" height="301" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrVdv_3npr8YJF37qBoxwr78iKj-8l-jurU17IOPIupAxlvfpopNmT9cEAr1ufYblkmTX4YOgQCjF1WanRPGh88_FJ2eIVBnQQqCkOcv4rD13_EJjIfA-usmxXxWUhBFfTQolQFFmrZb0/s400/fnpropscardsort1.JPG" width="400" /></a></div>
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In order for everyone to see the mystery sortings, I was originally going to share each of their screens myself, from my trusty dashboard, for I am the teacher, and I am so powerful and techy. But since there were so few kids there, I asked them to, one at a time. Each student shared their screen so we could all (myself included) try to guess what criterion they'd used to sort. This turned out to be fun and challenging - I wasn't able to guess some of them. I tweeted about some of them <a href="https://twitter.com/a_mcsquared/status/1263503270112346112?s=20" target="_blank">here</a>, but if you're not keen on twitter, here are some screenshots (if you want to see the answers though, they're in the tweet!)</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0bS5KlKtEKooxUAcg_nOtp2DpmlCGTKX2-0utH2F9mW8QvGYV5LEwgh0FizC5ITS_bFsTBTHgVQShVX7VOBZT1tIp2x3CA41jkthzVpuMEm52gSupGfX0T7lWvCJtVBxE1TBFLhYiRPU/s1600/sort1.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="674" data-original-width="569" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0bS5KlKtEKooxUAcg_nOtp2DpmlCGTKX2-0utH2F9mW8QvGYV5LEwgh0FizC5ITS_bFsTBTHgVQShVX7VOBZT1tIp2x3CA41jkthzVpuMEm52gSupGfX0T7lWvCJtVBxE1TBFLhYiRPU/s400/sort1.JPG" width="337" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Mystery sort #1</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJJ-Jaj42Hhw9-QMQU080KE9n0vl3BsppimYlbLAqE6nkVe872EC64dRekjiJp-csICEGv5v_TcqZFtQrIbIH1jSuuw3TxqGNMjzLf-OhNharQccGmuxgj2o5cWHhs6szLAOOU4S2sJ1g/s1600/sort2.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="687" data-original-width="732" height="375" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJJ-Jaj42Hhw9-QMQU080KE9n0vl3BsppimYlbLAqE6nkVe872EC64dRekjiJp-csICEGv5v_TcqZFtQrIbIH1jSuuw3TxqGNMjzLf-OhNharQccGmuxgj2o5cWHhs6szLAOOU4S2sJ1g/s400/sort2.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Mystery sort #2</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlIReUrHmBATE75u3Gtizx5n_29m-WYjDpv4ze7-ba3nXV_Gqj66gVf-UlmzYXRYeiidq226Vr_9tcN8-AsTPCajH8YYZuWxADMIFbE4XxrUuc4VvSqZe3Qe8G4JjQKbRq9Nxhx3B8wpg/s1600/sort3.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="673" data-original-width="803" height="335" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlIReUrHmBATE75u3Gtizx5n_29m-WYjDpv4ze7-ba3nXV_Gqj66gVf-UlmzYXRYeiidq226Vr_9tcN8-AsTPCajH8YYZuWxADMIFbE4XxrUuc4VvSqZe3Qe8G4JjQKbRq9Nxhx3B8wpg/s400/sort3.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Mystery sort #3</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfwbGjz15nYDgD4o7jGN6VPI2exCjJ_caD91B_YmnVXFEztLyoO5IBZ2ZDzaHWrfP1BePugSSwUVeT-V_WixqzAljbHf6YCLVYd83MMDYiN-dYdqwSEewJNOdmJVA7Y1VqcXdTRYLZhdw/s1600/sort4.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="545" data-original-width="743" height="292" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfwbGjz15nYDgD4o7jGN6VPI2exCjJ_caD91B_YmnVXFEztLyoO5IBZ2ZDzaHWrfP1BePugSSwUVeT-V_WixqzAljbHf6YCLVYd83MMDYiN-dYdqwSEewJNOdmJVA7Y1VqcXdTRYLZhdw/s400/sort4.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Mystery sort #4</td></tr>
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<span style="font-size: medium;"><i><b>Math and humanity intersected!</b></i></span></div>
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I don't know that this activity deepened their math understanding any more than usual, but it stood out to me for other reasons. Getting each student to take turns sharing their screens was powerful. It's so important to establish presence in the online classroom, so that the experience is as human as possible. That goes for students as much as teachers. I'll be getting them to do that a lot more from now on. Also, putting them in the driver's seat, and putting myself in the same boat as them, where I'm as in the dark about the answer as the rest are, models what I'm always saying to them - we're all teachers and we're all learners in this classroom. But as for the math, next time I do this, I'll crank it up a notch by tossing in some additional functions, and getting everyone to sort them according to the current student's scheme. And they won't all be graphs - I'll toss in some other representations while I'm at it. I might as well deepen the math while I'm humanizing!</div>
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3. Ellipses:</div>
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I gave them <a href="https://www.geogebra.org/m/wNJAvJR5" target="_blank">this GeoGebra, created by the brilliant Jennifer Silverman</a> (@jensilvermath) so they could draw ellipses and experiment with the impact of changing string length and position of the pins:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiR-6pezEZEMQO0vQEnZN6BrRTFo2z1TIsA6Ht67jNKT4hyphenhyphenz2CRD2M-WT_lJ29ffSjJu8NhfoyyQH0anQYMj4O871jOIKXjVBhBpGILbITtwCjrjP5OqYTfbH6tQ1JMNAZ5jQebFXKvNtA/s1600/ellipse+jennifer.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="645" data-original-width="538" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiR-6pezEZEMQO0vQEnZN6BrRTFo2z1TIsA6Ht67jNKT4hyphenhyphenz2CRD2M-WT_lJ29ffSjJu8NhfoyyQH0anQYMj4O871jOIKXjVBhBpGILbITtwCjrjP5OqYTfbH6tQ1JMNAZ5jQebFXKvNtA/s400/ellipse+jennifer.JPG" width="332" /></a></div>
I used to just toss my students into this activity without much scaffolding, but this time, because I had fewer students, I structured it a lot better. I gave them all one specific thing to change at a time, say, string length only. I asked one to share their screen, so that the rest watched and discussed what about the ellipse is changing, as well as what isn't changing. The next student to share their screen had a different aspect to vary, eg move one pin only. This made for a much more orderly math discussion, and at the same time was great for creating that group cohesion.<br />
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Next I edited Jennifer's to look like <a href="https://www.geogebra.org/m/fua3xwrt" target="_blank">this</a>: </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6Q3QFpb7wsJxdDmfHQOxlJOEN7IP65r_g0ZJDIEOvOF1C-xz-B0wVh4NOukIgCsKGPYCcHcXKUWsLcCzjlNWSt-JtPqko3P7Y8Rkd20JiUdwKFXwWeOwFpj66Ioix-REsITfn81Fg7K4/s1600/ellipse1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="482" data-original-width="904" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6Q3QFpb7wsJxdDmfHQOxlJOEN7IP65r_g0ZJDIEOvOF1C-xz-B0wVh4NOukIgCsKGPYCcHcXKUWsLcCzjlNWSt-JtPqko3P7Y8Rkd20JiUdwKFXwWeOwFpj66Ioix-REsITfn81Fg7K4/s400/ellipse1.JPG" width="400" /></a></div>
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Now everyone had to draw the same ellipse. At this point in the learning cycle, they did not know how to find the locations of the foci, but they did know how long the string had to be (major axis), so the only part they had to trial and error was where to put the pins. But - again, via sharing and discussing, they were able to pin down a few things - pins had to be horizontally oriented, and equidistant from the center C.</div>
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All of this I had done in previous years, except as I said for the scaffolding, but this year, thanks to the pandemic, I discovered Classkick, so once they'd learned about the rule of an ellipse, I made <a href="http://app.classkick.com/#/assignments/AXGsUKk3Q8idLfeK31sk4Q" target="_blank">this in-class activity</a>:</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfOwdCThOb-pQLiHHe8hhwIcE6UVTYVAPYlio9dv7wLU9V7hhdQuVl1cJ_ZBilJjmRCbfsUpYCK4fhvmQacZFUQ7Lh4XJMKJ0ePTUClPdvkkVF4_R4ElzKQxYdC37MIwQB1pgcLFF-dQQ/s1600/classkick1.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="233" data-original-width="577" height="161" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfOwdCThOb-pQLiHHe8hhwIcE6UVTYVAPYlio9dv7wLU9V7hhdQuVl1cJ_ZBilJjmRCbfsUpYCK4fhvmQacZFUQ7Lh4XJMKJ0ePTUClPdvkkVF4_R4ElzKQxYdC37MIwQB1pgcLFF-dQQ/s400/classkick1.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">The original Classkick slides</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXtzCL71ZbzzPFmUgUUZrc19mMu0bgfNbntf29kWbynYTCq3eV8Hyzattp8fYvt77C537-p6o3EDesZwktUfn1vf5dZ4LM_OBaIGfT_URPEqfuQYrGpeDE3p8uIK4uotRZ__MKvVdEaRA/s1600/classkicknicholas.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="630" data-original-width="717" height="351" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXtzCL71ZbzzPFmUgUUZrc19mMu0bgfNbntf29kWbynYTCq3eV8Hyzattp8fYvt77C537-p6o3EDesZwktUfn1vf5dZ4LM_OBaIGfT_URPEqfuQYrGpeDE3p8uIK4uotRZ__MKvVdEaRA/s400/classkicknicholas.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Sample student work (stickers are part of my feedback)</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjH2kpOpxWqTpWstfuGh64C-va8FUJ86asWjshL8U7HOvgive7i6c1aMbc2MLLuodtE2lbjf-sdx5qSpywoyvv2upkpeL_-FSdwdWkpCqu9BP9TCtZWSob9Jr_PF9HNipcR4mtDduhyeiw/s1600/classkickjacob.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="567" data-original-width="498" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjH2kpOpxWqTpWstfuGh64C-va8FUJ86asWjshL8U7HOvgive7i6c1aMbc2MLLuodtE2lbjf-sdx5qSpywoyvv2upkpeL_-FSdwdWkpCqu9BP9TCtZWSob9Jr_PF9HNipcR4mtDduhyeiw/s400/classkickjacob.JPG" width="351" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Sample student work</span></td></tr>
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Classkick was a huge find this year, and if it hadn't been for the pandemic, I might not have known about it. I happened to see a tweet about it from Michael Pershan (@mpershan), who, in his new online classroom situation, wanted to find a way to see his students' work and give feedback quickly. He'd researched many tools and found Classkick.</div>
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I have been teaching online for 12 years, I've seen all the things, and this one really turned my head. It's similar to Desmos activities in that from my teacher dashboard, I can watch all my students' writing and actions emerge live, either all students at once or only one of them. But in addition, in Classkick, I can give many different kinds of feedback, including audio (AND STICKERS OMG), and my students can respond to that feedback, either in a chat sidebar, or by writing directly on the screen. Talk about humanizing! It's pretty much like walking around the room as kids work at their desks, except I can see and do so much more than if I were there. There are advantages to this online environment!</div>
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Finally, I returned to Jennifer's original GeoGebra, sort of, with <a href="https://www.geogebra.org/m/advpfesq" target="_blank">this two-part activity</a>, once they knew all the secrets of the ellipse, the geometric ones and the algebraic ones:</div>
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Screenshots: </div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvNtjLFtdevlu5x4kk53GQwrgctnEi-uSF9PRjVwmvsRHwjBqSSWMgMZc75ktbJ6pS5umfLujZMvqQQAI4nO4Yn7hkSrsidzrDn7Z7u7_tbi9OIqJPDhUfF1FxUCukG_gxwyKzKNZS3vs/s1600/ellipse2.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="623" data-original-width="689" height="361" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvNtjLFtdevlu5x4kk53GQwrgctnEi-uSF9PRjVwmvsRHwjBqSSWMgMZc75ktbJ6pS5umfLujZMvqQQAI4nO4Yn7hkSrsidzrDn7Z7u7_tbi9OIqJPDhUfF1FxUCukG_gxwyKzKNZS3vs/s400/ellipse2.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Part 1: Students draw the ellipse by typing in an algebraic rule</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJi-neuzAS_zsoM-JCm9xQOefo7_JbXl3zDlxgUl58d2QfzBsMIv9pNPMRE4jvD1xw0oQNy9UkwzvN_5QYaSAJiWxASxz0oPr2apgYs3VfsHT0t_LUOIjWxpSsQQg3HllN_dKp5IWMrJQ/s1600/ellipse3.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="624" data-original-width="701" height="355" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJi-neuzAS_zsoM-JCm9xQOefo7_JbXl3zDlxgUl58d2QfzBsMIv9pNPMRE4jvD1xw0oQNy9UkwzvN_5QYaSAJiWxASxz0oPr2apgYs3VfsHT0t_LUOIjWxpSsQQg3HllN_dKp5IWMrJQ/s400/ellipse3.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Part 2: Students draw the same ellipse by calculating string length and pin positions</span></td></tr>
</tbody></table>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: large;"><b><i>All the things happened here. A deeper math dive, group cohesion, </i></b><b><i>gardening, </i></b><b><i>humanity.</i></b></span></div>
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<br /></div>
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<span style="font-size: large;">Future posts about my pandemic classroom experience shall include:</span></div>
<ul>
<li><span style="font-size: large;">Topics that weren't part of the course but related/cool:</span></li>
<ul>
<li>Polar coordinates (<a href="https://teacher.desmos.com/activitybuilder/custom/5b34f444966ba63686182cb8" target="_blank">thanks to Mrs McCarthy for this</a>!)</li>
<li>Binomial expansion</li>
<li>Sum and difference of cubes</li>
<li>Partial Fractions</li>
<li>Sequences</li>
</ul>
</ul>
<ul>
<li><span style="font-size: large;">Fun stuff just for fun:</span>:</li>
<ul>
<li><a href="https://teacher.desmos.com/collection/5e9f1c532141e50b06c4688b" target="_blank">All of Joel Bezaire's (@joelbezaire) Storytimes:</a></li>
<ul>
<li>Proof that the square root of 2 is irrational</li>
<li>Pascal's Triangle</li>
<li>Erathosthenes & the circumference of the earth</li>
<li>The seven bridges of Konigsberg</li>
</ul>
<li>Desmos Challenge Creator:</li>
<ul>
<li> <a href="https://teacher.desmos.com/activitybuilder/custom/580ab469f249fd03067d331f" target="_blank">Parabola Slalom</a></li>
<li><a href="https://teacher.desmos.com/activitybuilder/custom/5807c540f270d2e305d42c0b" target="_blank">Laser Challenge</a></li>
</ul>
</ul>
</ul>
<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-35499265193279966472020-02-05T13:01:00.000-08:002020-02-06T07:38:26.228-08:00Mentally Prepping Students for Exams When it comes to high-stakes assessments, I feel the biggest part of my job is to prepare my students mentally, as opposed to mathematically. I know, there's a lot of overlap, in fact it probably is mostly overlap. But I think that without that affective aspect of preparation, it really doesn't matter how good they are at mathing.<br />
<br />
It's stressful writing these things, and the biggest stress-busting window of opportunity is only open before the exam. As in sportsball games, a great deal of the result is really determined during practice and preparation. Since I teach high school students, that part is my job too. It's not enough that I do a good job teaching stuff, or that I spend a period or two reviewing stuff - I have to accompany them on their mental preparation as well.<br />
<br />
<span style="font-size: large;">What I want to do BEFORE the exam is to actively, in a structured and gradually empowering way, help them:</span><br />
<ul>
<li>practice retrieving information</li>
<li>organize all that math info in their minds to enable retrieval</li>
<li>know what to expect on the day of the exam</li>
<li>become fluid with certain types of questions that are likely to be on the exam (note - if I'm the author of the exam I probably give a lot away here - if anyone's paying attention it can pay off for them big time)</li>
<li>try questions that they've never seen before but for which they nevertheless have all the tools they need</li>
<li>come up with strategies to handle questions like the aforementioned</li>
<li>practice pacing themselves</li>
<li>develop independence and confidence</li>
</ul>
There are, of course, some kids who don't need me to do this, who always do well and don't even need to spend much time studying, but my instincts, and my results, tell me that those students are in the minority. Most either don't know how to digest and use large amounts of info, or aren't motivated to spend the time preparing. They're my students too, and I refuse to simply shrug my shoulders and write them off as not having what it takes. If it's motivation they're lacking, that's also my job.<br />
<br />
And if there are students whose only preparation takes place during class with me, I at least want to make sure that time counts for SOMETHING.<br />
<br />
<span style="font-size: large;">What I did this year: Outside of class</span><br />
<br />
<b>Review VoiceThreads:</b> Review started outside of class. I didn't want to spend class time going over the basics, so for that I made review VoiceThreads. <a href="https://voicethread.com/myvoice/thread/13630305/82805062/76733617" target="_blank">Here's a sample for the optimization unit.</a><br />
<br />
These asynchronous reviews covered the procedures, examples, vocabulary, notation, and summarized all the stuff they've seen before, which is theoretically already in their notes. Some kids will have already looked that over, or won't even need to, but again, they're in the minority, so for the rest, I do this. This way, the kids who are ready to practice don't have to sit and listen to me blather endlessly during class, but the kids who need the refresher have it there. Do they all do it? Nope. But it's there for those who are motivated and who need it. Am I doing too much? That's another blog post. Also no. These are kids and this is a hard course.<br />
<br />
Sidenote: For the reviews on functions, my voicethreads gradually form a sequence as the year goes on, because I keep adding to each one as we study new functions. I use a structure I call the Wheel of Functions. Here's the most recent one, with 4 functions in it:<br />
<br />
<iframe allow="camera https://voicethread.com; microphone https://voicethread.com; fullscreen https://voicethread.com;" allowfullscreen="" allowusermedia="" frameborder="0" height="337" src="https://voicethread.com/app/player/?threadId=13630266" width="585"></iframe>
<br />
It's a kind of scaffolding that I think makes it easier to see connections, to get the big picture, and compare the properties of different functions. This hits the organizing of large amounts of info, which helps with the retrieval practice.<br />
<br />
<b>Review Packages: </b>It's not enough to consume of course - math is about doing, so the next thing they get is review packages, which are made up of actual exam questions. I realize this is what most people do. (Organizing a decade or so of these questions and keeping track of which ones I've used...that's a whole other thing...) These are to be handed in, so everyone has to at least try these questions. I give a mark, but it's based on 3 things only: Handing it in on time, trying every question, and showing all reasoning for each question. So even if you're not ready to correctly do these questions, you can get a good "mark" because you're starting to prepare yourself. Does everyone do this? Pretty much. It's either a wake-up call to start working (in a shock-therapy kind of way) or it's a good indication of where to focus one's attention. At the very least it hits the knowing-what-to-expect benchmark.<br />
<br />
<span style="font-size: large;">During class: Snappers, Zingers, and Deep Dives</span><br />
<br />
A combination of quick-to-answer and not-so-quick questions that everybody gets to try:<br />
<br />
<b>Snappers:</b> You have to walk before you can run. I start a class with 4-5 easy questions (Eg which function needs 2 templates OR Simplify the rule y = 10 + 3^2x OR write this as a constraint) that they can answer in 1-2 minutes, then send me their answer by private message, and if they don't know the answer, then that's what they pm me. Once I've heard from all, we immediately go over it, then if needed we do another one just like it, immediately. End result: retrieval practice, exposure to the very least of what's expected, motivation - they are super motivated and capable to get it right the second time, encouragement, practice with pacing, also sets up next day's review. Also - hopefully this causes some to take to those review voicethreads if they haven't already!<br />
<br />
<b>Zingers: </b>When it's closer to exam time, fewer questions. Same structure as snappers but these take a little more time. These questions may just take longer because there are more steps, or they may use some of the ideas we went over in the snappers. Again, if needed, do another one right away. End results: Exposure to next level, more pacing practice, more fluidity, also communicates subtly that maybe they should pay attention to the exact things I'm reviewing now because there's probably a good reason I'm focusing on it...<br />
<br />
<b>Deeper dive:</b> These I weave in between the snappers and the zingers.This is where we really get into it:<br />
<ol>
<li>Revealing hidden layers - like that fact that in this course, we end up solving systems of equations very often, even though it's not actually part of the course. We solve a system to:</li>
<ul>
<li>express a vector as a linear combination of other vectors</li>
<li>to find two missing parameters of a function</li>
<li>to find the coordinates of the vertices of a polygon of constraints. It's everywhere.</li>
</ul>
<li>Reviewing certain types of multi-step questions that typically show up, like piecewise functions. We took another look at actual test questions that they've already done, along with the full solutions, and if time, give them another one to try right then and there.</li>
<li>Trying those questions they've never seen before, and for which they have all the tools</li>
<li>Going over strategies to deal with those questions they've never seen before, to identify the tools they need to mobilize</li>
</ol>
<div>
<span style="font-size: large;">Overall: Variety Really Matters</span></div>
<div>
<br /></div>
<div>
I try really hard to fit as much variety in the voicethreads, review packages, snappers, zingers, and deep dives as possible so that by the time the exam happens, their brains have truly been stretched and warmed up for the race. Those that did it all are really ready, and those that did only the minimum have at least a chance.<br />
<br />
Today they wrote their exam, and tomorrow they write the second.<br />
<br />
Fingers fervently crossed.</div>
Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-1043597826599085122.post-62863099023681161162020-02-05T06:08:00.000-08:002020-02-05T06:08:21.681-08:00Exponent MindfulnessIn preparation for our exponential/logarithmic function unit, I decided to try something I called Exponent Mindfulness. Mindfulness because that's an initiative the team I work with has been working on, and exponents because being able to not only evaluate expressions involving them, but recognising numbers as powers, is the key to this whole unit. After all, working exponents out backwards is what logs are all about.<br />
<br />
First we spent a week on Exponent Boot Camp, in which I review WHAT the exponent properties are, and also WHY they are, including negative exponents, rational exponents, and rational bases with positive and negative exponents. That covered the first part - evaluating expressions with all kinds of bases and exponents.<br />
<br />
On this day, however, it was all about going the other way, developing those exponent lenses. After warming up with a few evaluation examples, I put 16 on the board and asked how can we write this number as a power? The answers I got were as expected:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhT5DsHfI_J1lUjb6bUo9_MXnsiRnB3wrPEtc4ec1ev_wwjscI3gMauq2pkGeaq_ad7O6RrGtfxyQSqcemGYteeaK4dDeFE3Dxy4-ZMuj5HBvarUWaLewzkvjMZuF1OuHJEvXwKn38RSfU/s1600/exponent+mindfulness+1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="648" data-original-width="870" height="297" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhT5DsHfI_J1lUjb6bUo9_MXnsiRnB3wrPEtc4ec1ev_wwjscI3gMauq2pkGeaq_ad7O6RrGtfxyQSqcemGYteeaK4dDeFE3Dxy4-ZMuj5HBvarUWaLewzkvjMZuF1OuHJEvXwKn38RSfU/s400/exponent+mindfulness+1.JPG" width="400" /></a></div>
Then I asked - that's it right? No other possibilities? Waited and asked about the possibility of a negative exponent. Here's where things got interesting. Even though everyone was fine moments ago with how to figure out a fraction to a negative exponent, the idea that you can get 16 from a negative exponent suddenly seemed to be mind bending. (It's always more fun to give your students the answer and ask them to come up with the question.)<br />
<br />
Anyway, so I showed them this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEZFPcQ1dnl_5S1L1zm7Tjlj5jJaBcvHn0i4hEve-VqB_hv0ReQdayJH3EPDGFmnZZ_ONqfPIvKigxRNeOLom0bWCVOBKA2oP7qRSb4xpMvjsEK-3O_curO_rZPUli-vuIN4VPZaWncqA/s1600/exponent+mindfulness+2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="625" data-original-width="848" height="293" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEZFPcQ1dnl_5S1L1zm7Tjlj5jJaBcvHn0i4hEve-VqB_hv0ReQdayJH3EPDGFmnZZ_ONqfPIvKigxRNeOLom0bWCVOBKA2oP7qRSb4xpMvjsEK-3O_curO_rZPUli-vuIN4VPZaWncqA/s400/exponent+mindfulness+2.JPG" width="400" /></a></div>
<br />
<br />
We spent a few minutes working out each of these, just to re-convince everyone that these were in fact all equal to 16.<br />
<br />
Back to 16, and I asked again, "That's it now, right? No other possibilities?"<br />
<br />
My students know me well enough to know that answer to that. So we moved on to rational exponents:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4uBy6edLQvpZ5RLkvL3xQlod7T0XJskrUC1DarL_OjE9QG39hE2JIP0I8PrPx58pL39B_ZG8H8McaEmsedw8MKubqZj8lfJmPau4sTPp80pXK3sQM90bJMCnshP9SNB1SMuduvaaANs4/s1600/exponent+mindfulness+3.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="631" data-original-width="854" height="295" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4uBy6edLQvpZ5RLkvL3xQlod7T0XJskrUC1DarL_OjE9QG39hE2JIP0I8PrPx58pL39B_ZG8H8McaEmsedw8MKubqZj8lfJmPau4sTPp80pXK3sQM90bJMCnshP9SNB1SMuduvaaANs4/s400/exponent+mindfulness+3.JPG" width="400" /></a></div>
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I got a few really great answers added here, like 65536^(1/4) and 1048576^(1/5).</div>
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Me: So that's it right?</div>
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Students: Nope, that's never it is it?</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyErzrur-rTSI0jjnVuiRxTJDq6ZYvCcHj6wQCU9OINX7u-VddSIv4RXIoVNKEtASua2pS-EPR3MP83FgBTs4YNikW6IWIk7Tb_-j3bet0ecwYA1ApGXfIs1H6cDhoIg2Uqb3zcz2xyRU/s1600/exponent+mindfulness+4.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="624" data-original-width="854" height="291" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyErzrur-rTSI0jjnVuiRxTJDq6ZYvCcHj6wQCU9OINX7u-VddSIv4RXIoVNKEtASua2pS-EPR3MP83FgBTs4YNikW6IWIk7Tb_-j3bet0ecwYA1ApGXfIs1H6cDhoIg2Uqb3zcz2xyRU/s400/exponent+mindfulness+4.JPG" width="400" /></a></div>
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So now that we all knew that there were in fact infinitely many ways to express a number as a power, I asked everyone to write a power on the board that equals 81, specifying that you can't use one that's already there. That went really well. Definitely you should do this again next year Future Audrey.</div>
Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-1043597826599085122.post-40610821287181027922019-10-08T11:42:00.004-07:002020-02-06T05:00:15.953-08:00Marrying Zoom to VNPSI've been very keen to adapt Peter Liljedahl's vnps to my live online classroom (which is in Zoom), and I've come up against a lot of obstacles, but today it felt like it's finally taking hold.<br />
<br />
<span style="font-size: large;">The fantasy, or the ideal situation for a vnps class session (which I experienced and fell hard for at OAME 2019):</span><br />
<br />
<ul>
<li>The students are put into random groups of 3 and stationed at whiteboards around the room.</li>
<li>The teacher gives each group of 3 one problem to work out on the whiteboard.</li>
<li>Only one person in each group writes on the whiteboard, and does not speak, and the other 2 speak and do not write.</li>
<li>Once they're done, they call the teacher over, who gives feedback and another question for them to do, but this time the roles shift.</li>
</ul>
The benefits are astounding, and for a much more complete list see Peter Liljedahl's or anyone's writing about #vnps (vertical non-permanent surfaces). For example, students feel safe in their group because it doesn't fall on any single person to know what to do. They also feel safe within the room due to the low-level hum of talkers talking, which is somewhat noisy but not chaotic. They're more physically active than if they were working things out sitting down. The nature of the whiteboards and pens makes it easy to write/discuss/change their minds about what to do. The teacher can see all of them quickly and deliver just-in-time feedback.<br />
<br />
<br />
<span style="font-size: large;">The reality of my online environment:</span><br />
<br />
I meet my students at the same time everyday, but not in the same physical space as any of them. They're scattered all over Quebec, mostly in the computer rooms of their schools, most of which are in somewhat remote parts of the province. Some of them are completely alone in their school when they're with me, and some of them are with other students at their school. Others are home schooled.<br />
<br />
Anyway, in my Zoom setting, there are BIG challenges to this. Not all of the students are in the same room with other students. Even if they are, they have to leave their computer (and hence the Zoom room) to go to the whiteboard in their actual room, so we might not be able to see/hear each other anymore. And how do I see their work and give feedback?<br />
<br />
At first I had to check with all the schools to see if everyone had access to a whiteboard. Most but not all did. Then I had to think of how they'll show me their work. I had thought of Rocketbook or Twitter dm, but today the answer turned out to be SO MUCH easier. They just turned on their webcams and aimed them at their whiteboards!<br />
<br />
I cannot express how exciting it was to see my students gathered around the problem, talking, erasing, checking back with me. I know f2f teachers are probably thinking - we call that Tuesday. Or everyday.<br />
<br />
There is still an issue with communication between me and them when they're at the board - at one school all the students could keep their headsets on while at the board, but others couldn't.<br />
<br />
At any rate, for those students who are not alone in their school, who do have a whiteboard and webcam, things are moving. Next - to find the closest approximation for students who are alone in their setting and/or don't have access to a whiteboard or a webcam. For now, they've been using the Zoom whiteboard, which means struggling to write legibly with the pen tool, typing their wonderful math thoughts in the chat tool, all the while sitting in front of a computer screen - in other words getting virtually none of the benefit.<br />
<br />
But this was a truly awesome start.Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-1043597826599085122.post-31479611977380051322019-08-13T09:37:00.000-07:002020-02-06T05:06:43.875-08:00Day 11: More DiagrammingI had my first meeting yesterday with the wonderful Mr. Chow, and holy wow you guys you need to talk to Jay. Not only did he answer my questions, and fix things that needed fixing (in my head and in my CL) but he helped me move ahead in my diagramming - this is not to say that what you're about to see is officially sanctioned by him, only that he gave some encouragement on an idea I had. If there is a mistake in it (<b>which I already know there is</b>) it's mine.<br />
<br />
<div style="text-align: left;">
So here's where I am now in my diagramming. I've added the possible data types that could fill the first and last fields in a script. Since those possible data types depend on which component is involved, I've made a slideshow, with each slide corresponding to a specific type of component, eg note, input, or graph. The possibilities for the source data type of an input component are not the same as those for a graph, for example.</div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
This is meant to help get a sense of how the CL is structured, but not go into much detail (yet) about what individual terms like "initialLatex"mean. For example, I don't yet know what "initialLatex" actually does, only that it's something that would go into the field I've labelled "<span style="background-color: cyan;">Sink Data Type</span>", so that tells me it's something to do with a component into which something is being injected. <b>(Maybe it's something that is to be displayed in an input to prompt students? No idea.)</b> This at least helps me not get overwhelmed when I'm reading someone else's script.</div>
<br />
<div style="text-align: center;">
<iframe allowfullscreen="true" frameborder="0" height="375" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/e/2PACX-1vTg8MhPVcKAzIad5CbxWRddY7YBqf2w42DiyCFsAdg_29C_LWCB2bl309DvyS1TjQ/embed?start=false&loop=false&delayms=3000" webkitallowfullscreen="true" width="480"></iframe></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: left;">
The mistake is in the "To put a script into the gearbox of" part. I'd previously felt pretty sure that the script always goes into the gearbox of whatever component is the sink. But, for example, in the cardsort (last slide), according to <a href="https://teacher.desmos.com/activitybuilder/custom/5d52e23f2d630f2d825c7e10" target="_blank">this sample from Jocelyn's collection</a>, the script is in the gearbox of the actual title of the screen. So I need to think on that for a bit. Also I need to add "title" as a component.</div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
Also, I haven't worked in yet how to show that once you've selected a certain data type for your sink, your choices for the source data type are further filtered down, because they must match. For example, if your <span style="background-color: cyan;">sink data type</span> is "number", your <span style="background-color: lime;">source data type</span> can't be "content", but it could be "numericValue". </div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-80164796005105420332019-08-13T06:55:00.005-07:002019-08-13T06:55:54.523-07:00Day 10: First Attempt at a How-To-Computation-Layer DiagramI created and shared my first attempt at a CL diagram on twitter, and Jay Chow (thank heaven for Jay Chow y'all) replied:<br />
<blockquote class="twitter-tweet">
<div dir="ltr" lang="en">
Lines 1 and 2 👌🏽<br />
Title for line 3 confuses me slightly. The format looks like you’re just creating a sink that requires an identifier (cell reference, function name, etc), but the title implies that we are creating both a variable in CL and a sink into the component. take to DM?</div>
— Jay Chow (@mrchowmath) <a href="https://twitter.com/mrchowmath/status/1158403024995246081?ref_src=twsrc%5Etfw">August 5, 2019</a></blockquote>
It turns out that it's not quite accurate to say that third example defines a variable. I had misinterpreted this example from the CL doc:<br />
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I had thought that the variable m was being defined in this line, but after checking out the "try it" I realized that m had been defined within the graph, so it wasn't accurate to say that it was defined right here.</div>
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So for now I'm sticking with the ones that I know are good:<br />
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So now....I tried making up random CL things to see if they worked. Got something to work yay! I'm still not sure of when we need variables and when we don't but I think for now I'll just assume we always do and keep defining them. They need to be defined in the same place as the script that's referring to them. It's still in draft mode but <a href="https://teacher.desmos.com/activitybuilder/custom/5d3da124a2e2cb668c2d4e7b" target="_blank">here is where I'm playing around</a>.<br />
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<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-9368792797533421002019-08-05T06:15:00.000-07:002019-08-05T07:00:21.269-07:00Day 9: Maybe I Should Just Stick to Dragging and DroppingI'm still watching the <a href="https://drive.google.com/file/d/14sHOLnvYvoixMyZZHPSdnwHroiLoXTSl/view" target="_blank">first of Jay chow's webinars</a>. One thing I know for sure is that having the ability to pause & re-watch is huge. (Hello flipclass.)<br />
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I'm trying to get my head around that example on screen 16:</div>
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It's easy enough to get it to automatically graph whatever rule the student types in, but I wonder:</div>
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<b>How could I get it to only graph once the submit button is pressed? It doesn't seem to fit the When-otherwise scenario. Taking Jay's advice on writing it out in english first: When input2 is submitted then inject input2 into the graph otherwise do nothing. </b><i>For the do nothing - just make the otherwise part "Type in the equation of the line that goes through these points." </i><b> I tried typing "when" and seeing what the error code told me. It said it was expecting otherwise, but then when I put that in it said it wasn't expecting that...</b></div>
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Went back to trying exactly what Jay was doing with the T variable, and I got it to work. Unpacking the whole variable idea again. We needed T in the graph so that as it increased in value (which is done by moving the T slider to the right), the domain of the function f being graphed got wider, so the curve appears slowly from left to right. Clear, very clear. And we needed to connect that T value with the CL by calling a variable <i>by the same name</i>, so that however much that variable T is in the CL, that's how much T in the graph is. So in effect, changing the value of the variable T is equivalent to moving the T slider. And if we want to increase the value of the T variable in the CL, we make it equal to the number of seconds since the submit button was pressed. Got it.</div>
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Tracing the path of T - it starts having a value on submit, which gets sent to the graph, then overrides the value of T on the slider.</div>
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Jay says: "The basic structure of CL is we create something (the sink) FROM something (the source)." This is a good way to think of it.</div>
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Screen 20: Noticing something that has happened before. I am certain I've typed exactly what Jay typed but I'm getting these brackets (I've highlighted in grey) immediately after the timeSincePress</div>
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It doesn't seem to be a problem though, and the error was due to me mistyping timeSincePressed - shouldn't have had the -ed at the end.</div>
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I tried to make the second "when" include the current coordinates but it didn't work. Sigh.</div>
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Back to Jocelyn's collection. I'm going through it again from the beginning, one by one, to see if I can recreate them.</div>
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On example 2, the correct script was simpleFunction(table1.cellContent(1,2),"x") which also works without the x at the end. But I don't get why we don't have to put .latex anywhere like we did for example 1. The only difference between this one and example 1 was that there are 3 functions to type instead of 1, so we're using a table this time.</div>
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Maybe it IS better if I just drag and drop other peoples' stuff....</div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-43075581658384575762019-08-02T09:17:00.000-07:002019-08-07T08:18:19.122-07:00Day 8: OHHHH SO THAT'S WHAT TIMESINCESUBMIT IS FOR!!!!Next, I'm going to look at <a href="https://drive.google.com/file/d/14sHOLnvYvoixMyZZHPSdnwHroiLoXTSl/view" target="_blank">Jay Chow's Webinar 1</a> and the accompanying Desmos activities. Audrey's on a roll, baby!<br />
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I've decided that, for now, I'll abandon my so-far strategy of looking at the DA in preview mode and trying to unpack the CL before peeking at it, and instead I'm going to just watch Jay's webinar and let him unroll these things. He's a really great CL-er and he's made a lot of webinars, so he knows what he's doing.<br />
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Comment on how he is doing the webinar: First there are some screens for us to interact with, after which I see that Jay is using the screens of a DA as a presentation in and of itself - he's sharing his screen (and of course he has turned on the Anonymizer to make a safe environment), and clicking through the DA screens. I like that. Imma do that!<br />
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<span style="font-size: large;">Screens 1-4:</span><br />
<span style="font-size: small;">We are asked to input something and nothing happens as a result. I think I see where this is going. </span><br />
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At 9:38, Jay makes the case for using CL by contrasting activities without CL and with CL. (we just did 4 screens without and immediately felt the need for CL - Also this reminds me of how Christopher Danielson (@trianglemancsd) presented CL last year at the Desmos Fellows weekend (cohort 3). He said - I'm going to make you unhappy, then I'll show you something that will make you happy.)<br />
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Without:<br />
When your students type in the input it's a static entity<br />
Action buttons don't work<br />
Things don't work together<br />
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The first example we are trying to add CL to is one in which we want the student to input an expression that evaluates to 4, hit the submit button, then get feedback. The feedback will depend on whether or not it's correct.<br />
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Around screen 14, I see Jay using the snapshots feature, also while he is sharing his screen. I've never used that feature, so it's nice to see it in action.<br />
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Aha at 25:01 I was wondering why the input expression hadn't been evaluating as it usually does - because it's been disabled with the built-in disableEvaluation, behind the input component. The full script is disableEvaluation: true. And that's why the gearbox for the input component is green, that's the script in there.<br />
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37:35 I see the effect of the ${} - it turns static text into dynamic text. No variable needed. Jay recommends we write out in english what we want to do BEFORE we write any script. Very good idea.<br />
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Next example screen 16: Students see a graph with 2 points on it and they are to type the equation of a line that goes through those two points, submit, and get feedback.<br />
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At around 47:00 Jay is using someone's suggestion to do two things - put the typed equation into the expresion list on the graph, and then graph it. <b>I thought that as soon as an equation is in the expression list, it's automatically graphed? Why do we need to ask it to graph it? </b><i>This turns out to be that we want the graph to be revealed slowly, as a result of additional interaction from the student. See "Whoah" below.</i><br />
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Also, I see a lot of auto-complete happening as letters are typed - very helpful.<br />
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To make a function, use the built-in function thingy? In the graph gear, the sink is indeed function: ("f") but the name f has already been typed into one of the graph boxes. Needed to label the input and use latex as source type.<br />
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At 52:04 script at this point is<br />
<blockquote class="tr_bq">
function("f"): input2.latex</blockquote>
but there is an error message:<br />
<blockquote class="tr_bq">
Sink "function" expects a function but got a string.</blockquote>
So input2 is currently being interpreted as a string, even though the source data type is latex. I'm not sure why that is happening. But based on examples I've seen from <a href="https://teacher.desmos.com/collection/5cacb59a0847cb0c70183e13" target="_blank">Jocelyn's collection</a>, I bet it needs simpleFunction maybe? <i>Yup.</i><br />
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Now it's:<br />
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function("f"): simpleFunction(input2.latex)</blockquote>
Jay: "I'm gonna make that function from the latex...in this case it's gonna look for x"<br />
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So I'm noticing a new level here - in input2.latex, we still have the syntax sourcelabel.sourcedatatype but it's in brackets that go with the built-in function called simpleFunction. And we need this built-in because otherwise the source (called input2, which remember is the equation typed in by the student) will be interpreted as a string (text), and the graph sink doesn't accept that type of data.<br />
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This made me go back to the CL doc and look up Graph. Question -<b> what do the subheadings "Sources" and "Sinks" mean here? That these are all the types possible when the graph is a source? Or all the types possible for the graph's sources when the graph is a sink? </b><br />
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Back to Jay. Next step is to stop it from graphing until submit has been clicked, so we'll need to use that input2.submitted thing. Last time we used that, it was part of a when-otherwise structure.<br />
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<span style="font-size: large;">WHOAH.</span><br />
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So it's not at all like last time. It's that as soon as the student clicks submit, the curve is slowly revealed as the seconds tick by. To do this:<br />
1. A variable T (for time) had to be introduced into the graph, and its values restricted to x < T , which means that as you move the T slider, the graph is slowly revealed from left to right. (This was later tweaked to x < T - 10 to make the graph start showing at -10 instead of starting at the origin.)<br />
2. To link the CL to the T in the graph, a variable T had to be defined in the CL. The variable was defined in one of the familiar ways like this:<br />
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number("T"): timeSinceSubmit </blockquote>
which kind of makes the submit button a source for the variable T. As soon as that button is pressed, a timer is started at 0, so there's now a variable T whose value is 0, and as the timer continues, the value of T increases. This makes the line start graphing on the left, and slowly be completed. So a student doesn't know right away if they're right, but they can pretty much predict, and even change their answer if they want.<br />
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I HAVE BEEN WONDERING WHAT THE HECK THAT TIME-SINCE-SUBMIT WAS ALL ABOUT FOR OVER A YEAR!!! It makes animation happen as soon as a student clicks the submit button wut!!!<br />
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Stopping at 58:00 because I need to step outside and look at how this learning has unfolded so far. My ultimate goal is to help others learn this, so I need to figure out what worked for me.<br />
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<span style="font-size: large;">How I’ve learned so far:</span><o:p></o:p></div>
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Read, looked at examples, re-read, tried things, and re-re-read, all the while documenting observations and questions on my blog. Some of the questions got answered in the same day, in which case I wrote the answer in italics next
to the question. Those that didn’t, I bolded (thanks for that idea @geonz.) Some
of those bolded questions I remembered on later days and went back and
answered, but others I picked up later after deliberately re-reading my posts. The bigger ones, I just put a note on “answered in later post”
and put that whole thing in a subsequent post.</div>
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<o:p></o:p></div>
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Next I watched Jay Chow's webinar. As I watched, many questions were answered, (what
are ${} for ? – it changes something from static text to dynamic text, just
like objects in GeoGebra) and many observations were confirmed (when you select
latex in an input it automatically displays the math expression properly and
evaluates it without any need for CL – also found out how to turn it off!).<o:p></o:p></div>
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But here's what I noticed about how I learn:</div>
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<span style="font-size: large;">I needed to have already asked those questions or
observed those things in order for them to have meaning for me as I watched the
webinar. </span><br />
<span style="font-size: 13.5pt; line-height: 115%;"><br /></span></div>
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<span style="line-height: 115%;">That probably makes me...human.</span><o:p></o:p></div>
<b><br /></b>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-19138704755982121662019-08-01T09:35:00.003-07:002019-08-01T09:35:56.759-07:00Learning CL Day 7: CoolcoolcoolFirst I'm going back over my previous posts to check for unanswered questions, which I already went back and bolded a few days ago so I could find them easily.<br />
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<span style="font-size: large;">On day 1:</span> I wondered about the word script in this line:<br />
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content: note3.script.greeting</blockquote>
and it reminds me of something I wondered about yesterday, and that is the seeming interruption of the sequence sinktype: label.sourcetype with words like script, or simpleFunction.<br />
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<span style="font-size: large;">On day 2:</span> I wondered about the example under the heading "Sources" involving latex and variables, and I remember starting to feel very anxious right around then. Here's what I said:<br />
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content: "<br />
You entered: ${l}<br />
which evaluates to: ${v}"</blockquote>
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Earlier in the script the variables v and l are defined:</div>
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v = exp5.numericValue<br />
l = exp5.latex</blockquote>
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and both those variables belong to exp5, which is the name of the input. So does this mean the exp5 is the source here? I typed 4^2 into the input and it got injected into the note AND the input. <b>Soooooo the input is the source and the sink here?</b></div>
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Now I think I know a bit more about what was happening there. So hmmm. What gets typed into the input (labelled exp5) is displayed in two places - obviously right in exp5, but also in the note. So it seems true that the input (exp5) is both a source and a sink. But whatever gets typed is also a source for the note, which explains why the script is behind the note's gearbox. But now I'm wondering what is making the 4^2 to be displayed properly AND get evaluated right in the input box? <i>I did an experiment and deleted the note completely, which means there is no longer any CL or script. I typed 4^2 and this happened:</i><br />
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Which tells me that the lovely folks at Desmos take care of that without any CL being necessary. As soon as you select f(x)math for a note, it interprets what you type as latex, and it evaluates it. </div>
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I know that I knew that already on some level, but NOW I REALLY KNOW IT.</div>
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<span style="font-size: large;">On day 3: </span>This is where I first encountered simpleFunction. Hopefully today its placement in the script will start making more sense.<br />
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All the other days had no open questions, so I'm ready to move on.<br />
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I feel like I need to re-read the <a href="https://teacher.desmos.com/computation-layer/documentation" target="_blank">CL doc</a>, because I had stepped away to try other things out and immerse myself in examples. Time to go back and un-overwhelm myself, and to get a better handle on that secret sauce: Variables.<br />
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<span style="font-size: large;">Variables:</span><br />
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So you can call a variable anything I guess, and you define it by what's on the other side of the equals sign. You can have something in quotations, like:<br />
<blockquote class="tr_bq">
greeting = "hello, world!"</blockquote>
Or it can be whatever's in another component (which is the source for that variable), which has a label, like:<br />
<blockquote class="tr_bq">
v = exp5.numericValue</blockquote>
in which case we need to also specify the data type of that component (or source) that we want to extract, because there are other types, like:<br />
<blockquote class="tr_bq">
l = exp5.latex</blockquote>
You can also define a variable right inside the script for a sink, without any equals sign, but using brackets and quotations, like this:<br />
<blockquote class="tr_bq">
number("m"): exp1.numericValue</blockquote>
which was in the guess-the-slope-of-this-line example, but in order for things to work, the variable m had to be in the graph itself, as y = mx. So one way or another, there has to be an equals sign involved in the definition of a variable.<br />
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Another new word I see in this section is "keyword", in this example:<br />
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<b>I wonder if "keyword" has a specific meaning in the CL syntax world?</b><br />
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<b>Also I still feel unsure of when a variable is needed, and when it's not.</b><br />
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<span style="font-size: large;">Functions:</span><br />
<br />
Aha. "We have a few built-in functions for interpreting sources and converting between data types." Perhaps this is where those seeming interruptions (script, simpleFunction) come in. From the examples, it looks like these built-in functions go into the script after the equals, then are followed by brackets, which contain the expected sourcelabel.sourcetype. <b>However, all the examples are variable definitions, so I'm wondering if these built-ins can be invoked for sinks as well?</b><br />
<b><br /></b>
<span style="font-size: large;">Conditionals:</span><br />
<br />
This seems more familiar, maybe because I've recently been putting a lot of Conditionals in my GeoGebras, which uses the If-then-else structure, equivalent to when-otherwise. Did the Try it preview first. The student enters a number in the input, and a message, entirely text, no numeric part, is immediately displayed in the notes above it. But what message is displayed depends on the number input. So let's see if I can predict any of the the script:<br />
<br />
The source is the input box, so that must be labelled exp1 or something.<br />
There must be a variable defined for whom the source is exp1, like n = exp1.numericValue .<br />
f(x)math must be selected on the input<br />
There must be script in the note's gearbox something like content."text message" and there must be a few when lines for different values of n.<br />
<br />
Checking: The input is labelled "number" instead of note1, ok.<br />
I got the variable definition syntax right.<br />
f(x)math is indeed selected.<br />
I was right about the content dot part and the whens. Yay! Also, the various text messages are enclosed in quotation marks, and a built-in "isUndefined(n)" is also there to display nothing when whatever was typed in wasn't a number.<br />
<br />
Getting somewhere, coolcoolcool!<br />
<br />
Tomorrow, I'll start watching <a href="https://drive.google.com/file/d/14sHOLnvYvoixMyZZHPSdnwHroiLoXTSl/view" target="_blank">Jay Chow's webinars.</a><br />
<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-67258508066053124252019-07-31T09:34:00.003-07:002019-08-01T08:08:20.257-07:00Learning Desmos CL: Day 6I just took another look at Andrew Knauft's tweet and I didn't even realize before now that it had a variable in it - in fact it SAYS "variable assignment". My brain doesn't register stuff until I've come around to it I guess. Variables are, I think, the secret sauce.<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxCHvi9QG80Tzu6JU4nDXDFOKPXYLnrv99fOCr47LFOgRLMddvx3-eimfIsCEUYTfed2x2Vwpo7z5Ao2lMTPiD7AkzCwfTvKmokq8Caokpx_1W6E4Y-dZYHkG2hYfjgwT5wu3yYf5slO4/s1600/cl+andrew.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="506" data-original-width="481" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxCHvi9QG80Tzu6JU4nDXDFOKPXYLnrv99fOCr47LFOgRLMddvx3-eimfIsCEUYTfed2x2Vwpo7z5Ao2lMTPiD7AkzCwfTvKmokq8Caokpx_1W6E4Y-dZYHkG2hYfjgwT5wu3yYf5slO4/s400/cl+andrew.JPG" width="380" /></a></div>
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<br />
I'm going to try this out but first predict what it does. In this activity, a student will be prompted to enter a number in an input component (labelled input1), and once they do, a note will display the message "Your number was" followed by whatever number they input. These two lines of script go together as sink and source, which is one thing that's been sort of confusing me. I thought there always had to be two lines of script, one about each, but up till now, that hasn't always been the case.<br />
<br />
Tried it, didn't work at first because I forgot to check the f(x) Math option in the input, now it works on screen 5 of <a href="https://teacher.desmos.com/activitybuilder/custom/5d3da124a2e2cb668c2d4e7b" target="_blank">this puppy.</a><br />
<br />
So we needed a variable here because not every student will type in the same thing, but we want whatever they do type to be immediately displayed. <b>But why didn't we need one for, say, the guess-the-slope-of-the-line activity? </b>Was it because the slope was being sent to a graph as opposed to a note, and the graph sort of takes care of the variable part of it with the y = ax thing? And also this part of the script <b><span style="color: blue;">number("a"):</span></b> which seems to be defining the variable AND the sink at the same time?<br />
<br />
I notice that in the variable assignment, the structure is similar to a sink assignment, in that, after the equals sign, it names the component that will be the source, and its data type.<br />
<br />
I'll continue looking at <a href="https://teacher.desmos.com/collection/5cacb59a0847cb0c70183e13" target="_blank">Jocelyn's collection</a> now. I've already looked at and blogged about the first 3-4 so far but I'll look again with new eyes. I'll also try a new strategy of looking at the preview first, then figuring out all I can about what the script must have been. Eg 1 preview:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhS4ndKMSD9hzQLKBit2OsPOO1q7b6kNql5sII5RMeTsdU3GRlWEQrjyYdYidMOeN-xVo3PGeMI7mlFXBUVRA6-i7hvPPJymSS-Sjks3fQbXRXeqUPwoC7DdW5v-Gyb80GkpPBnn99yrXM/s1600/cl+joce+eg+1+preview.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="512" data-original-width="895" height="228" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhS4ndKMSD9hzQLKBit2OsPOO1q7b6kNql5sII5RMeTsdU3GRlWEQrjyYdYidMOeN-xVo3PGeMI7mlFXBUVRA6-i7hvPPJymSS-Sjks3fQbXRXeqUPwoC7DdW5v-Gyb80GkpPBnn99yrXM/s400/cl+joce+eg+1+preview.JPG" width="400" /></a></div>
<br />
3 components, a graph, a note, and an input. Whatever is typed into the input immediately shows up on the graph. So the source is the input and the sink is the graph. There must be script in the graph's gearbox. The script must include sinktype: note1.sourcetype. Also since the equation I typed is being displayed properly and not as y = x^2, which is what I actually typed, it must be that what I type is being interpreted as latex, so the f(x)math option must have been selected in the input, and the sourcetype must have been latex. I'm not sure what the sinktype would be. Also in the actual graph there must be something about a variable that is the name of the function being graphed?<br />
<br />
And after checking: In the graph the function has been called f(x), so that's the variable definition. The input has been labelled input1. The script is where I expected it to be, in the graph's gearbox. The script is one line:<br />
<br />
<blockquote class="tr_bq">
function("f"):simpleFunction(input1.latex)</blockquote>
<br />
So the sinktype was <span style="color: #6aa84f; font-weight: bold;">function, </span>it includes the variable f in brackets and quotes so that it references which variable we want going into the sink, and the source type is latex. The only part that surprised me was the simpleFunction part. Why does that have to be there? And since it's after the colon, does that mean it's a sink or a source type? I expected a label to follow the colon, which there is one but not immediately after.<br />
<br />
Back to the CL doc, where I'll look up simpleFunction (again) in the table under Graph.<br />
<br />
I found it but only under function, and under the Sinks part. It says:<br />
<br />
<div class="documentation-table-name" style="background-color: white; box-sizing: border-box; font-family: HelveticaNeue-Light, "Helvetica Neue Light", "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;">
<blockquote class="tr_bq" style="background-color: white; box-sizing: border-box; color: #444444; font-family: HelveticaNeue-Light, "Helvetica Neue Light", "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif; font-size: 14.4px; line-height: 1.3em; padding: 5px 0px; width: 280px;">
<a href="https://teacher.desmos.com/computation-layer/documentation#components:input/graph:sinks:function" id="components:input/graph:sinks:function" style="box-sizing: border-box; color: #222222; outline: none; text-decoration-line: none;">function</a><span class="params" style="box-sizing: border-box;">(<span style="box-sizing: border-box;">identifier: string</span>)</span><span class="" style="box-sizing: border-box;">Sets the output of simpleFunction() to a variable defined in the graph.</span></blockquote>
</div>
<br />
<br />
The accompanying example is:<br />
<br />
<blockquote class="tr_bq">
<span style="font-family: "arial" , "helvetica" , sans-serif;"># Get the latex string from "equationInput" and assign</span><span style="font-family: "arial" , "helvetica" , sans-serif;"># it to f in the calculator.</span></blockquote>
<blockquote class="tr_bq">
function("f"): simpleFunction(equationInput.latex, "x") </blockquote>
<br />
which is virtually identical to the one in Joce's eg except for the "x" part, which I seem to recall is something that if it's not there, is assumed.<br />
<br />
I also looked under "Functions" and found simpleFunction. It says:<br />
<br />
<div class="documentation-table-name dcg-hovered" style="background-color: white; box-sizing: border-box;">
<blockquote class="tr_bq" style="background-color: white; box-sizing: border-box; color: #444444; font-family: HelveticaNeue-Light, "Helvetica Neue Light", "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif; font-size: 14.4px; line-height: 1.3em; padding: 5px 0px; width: 280px;">
<a class="dcg-hovered" href="https://teacher.desmos.com/computation-layer/documentation#functions:simpleFunction" id="functions:simpleFunction" style="box-sizing: border-box; color: #222222; outline: none;">simpleFunction</a><span class="" style="box-sizing: border-box;">Takes a latex string and returns a function which can, for example, be passed into the function sink of a calculator.The first argument is the latex string, and additional arguments are The names of the variables to treat as input variables (defaults to)one-variable function in terms of x if not specified</span></blockquote>
<div style="font-family: HelveticaNeue-Light, "Helvetica Neue Light", "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;">
<br /></div>
<span style="font-family: inherit;">Aha that's where I saw the bit about the x. Anyway, so it appears there are other pre-defined operations, like simpleFunction, that do additional things if you put them into the script. I don't know how to put this into my syntax structure from day 5. Does it always go right after the colon/equals sign? Is it a source or a sink or a datatype or something else altogether?</span><br />
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit;">I really need to come up with some kind of a diagram to help me order things in the script, and I suspect others who are struggling with CL might too.</span></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-68452578285906591312019-07-30T08:00:00.001-07:002019-08-01T08:08:01.840-07:00Learning CL: Day 5It's amazing how many times I have to read, re-read, re-re-read before things start to sink in. (Haha sink get it?)<br />
<br />
Syntax/structure I've gotten so far:<br />
<ol>
<li>Label all components you intend to use as a source eg note1, exp2, table1 etc</li>
<li>Script goes in the gearbox of whichever component you want to be the sink</li>
<li>Script starts with the <b style="background-color: white;"><span style="color: #6aa84f;">data type for that sink</span></b>, which could be a word like content, number, function, cellContent.....etc then that is followed by a colon</li>
<li>Next you put the <b><span style="color: orange;">name of the component </span></b>that you want to be the source eg exp1, note1, table2 etc, followed by a dot</li>
<li>After the dot you specify the<b><span style="color: red;"> </span><span style="color: magenta;">type of data you want to extract from the source</span></b> (bc it could contain more than one type of data) so that could be numericValue, content, latex, cellContent(1,2) etc</li>
</ol>
<div>
So a script starts out talking about the sink, then ends talking about the source. The script says "This is what's going here and this is where I'm getting it from."</div>
<div>
<br /></div>
<div>
To confirm this, I've gone through a few samples of CL from <a href="https://teacher.desmos.com/computation-layer/documentation" target="_blank">the CL doc</a> and from <a href="https://teacher.desmos.com/collection/5cacb59a0847cb0c70183e13" target="_blank">Jocelyn's collection</a>, to trace this pattern. (Some of these examples have um other stuff besides what I've listed above):</div>
<div>
<br /></div>
<div>
<b><span style="color: #6aa84f;">Data type of the sink</span></b> at the beginning of the script, followed by a colon:<br />
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The <b><span style="color: orange;">name of the component</span></b> from which something will be extracted, followed by a dot:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirm0rhIiUaCkEetHdKWL1ICqw2e4l0u1equWgHaVZ9XwsnF8CMCAtTq3mqSeRGifix-k03C7wrX_73X7cJEe0q9T21tdrRahCSx_SiKVx6cjcym9VlY-Rkkl-8rezeyu7wvKC6NzDP6xQ/s1600/CL+lables.JPG" imageanchor="1"><img border="0" data-original-height="535" data-original-width="727" height="293" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirm0rhIiUaCkEetHdKWL1ICqw2e4l0u1equWgHaVZ9XwsnF8CMCAtTq3mqSeRGifix-k03C7wrX_73X7cJEe0q9T21tdrRahCSx_SiKVx6cjcym9VlY-Rkkl-8rezeyu7wvKC6NzDP6xQ/s400/CL+lables.JPG" width="400" /></a></div>
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In the first example, what's in the quotation marks is, I guess, the source. This must mean that no matter what happens, Hello! I'm the computation layer! is what will be displayed. Similar to the third example, in which the variables m and b will only ever take on the values 1.5 and 2.</div>
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Finally, the<b><span style="color: magenta;"> type of data being extracted from the source:</span></b><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBqWMBsC8L5_4cUa0nHm8p9WzeTe3FrdEhIlH-Unl3x2XUuOQRwOIiFeZ_JpwuYq32Zh8RKkow9p3SkzAF_kERNQphmtCHAnyJCL_iRPabyn-XMtl5PesnClZLKaMVebpOMtzjcKrkWEM/s1600/CL+sources.JPG" imageanchor="1"><img border="0" data-original-height="533" data-original-width="733" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBqWMBsC8L5_4cUa0nHm8p9WzeTe3FrdEhIlH-Unl3x2XUuOQRwOIiFeZ_JpwuYq32Zh8RKkow9p3SkzAF_kERNQphmtCHAnyJCL_iRPabyn-XMtl5PesnClZLKaMVebpOMtzjcKrkWEM/s400/CL+sources.JPG" width="400" /></a></div>
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I'm seeing a LOT of examples involving variables, in which instead of a colon, there's an equals sign. There must be something to this variables thing. I don't think you can really do much without variables.</div>
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That's it for today. Back on vacay.</div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-12719673222329515982019-07-29T06:59:00.001-07:002019-08-01T08:07:31.896-07:00Learning CL: Day 4After a brief time away, today I resume my CL journey.<br />
<br />
I started out by re-reading my own posts, and suddenly had the urge to start trying things out myself, starting with <a href="https://teacher.desmos.com/activitybuilder/custom/5d3da124a2e2cb668c2d4e7b" target="_blank">recreating the "guess the slope of the dashed line" activity</a>. Made me see a few things:<br />
<ol>
<li>Why there has to be a y = ax on the graph screen, so that the slope (a) that the student inputs gets sent to that value in the graph.</li>
<li>I allowed the slider to be created, and it didn't seem to make any difference. The y = 0.5x graph shows up no matter what, but the y = ax one only shows up once a value for a has been input.</li>
<li>The script gave a warning because I hadn't checked the f(x) math box on the input. Then I was allowed to use the numericValue part. Not checking that makes the input component a text, so the type wouldn't match.</li>
</ol>
I then did a few more screens with a similar example right away to reinforce all the things:<br />
<br />
number("a"): exp2.numericValue is the script inside in the graph's gearbox. number("a") means that some part of the graph is expecting a number it's calling a, exp2 means it will get that numerical data from a component called exp2, and .numericValue means that the type of data is a number, not text. Worked.<br />
<br />
Just not sure why we need to say number at the beginning and then numericValue again at the end. Going back to the <a href="https://teacher.desmos.com/computation-layer/documentation#about" target="_blank">CL documentation.</a> Under "About the CL Language", it says that "every sink expects a specific type, and every source emits a specific type." So in the examples I made with the graphs, "number" is at the beginning to specify that the graph component is a sink that expects a number. Note: Other words you can have at the beginning of a script are string, or boolean. (What about content, isn't that a possibility too? <i>yes - see the table with the heading "Note"</i><b>)</b><br />
<b><br /></b>
Under "Sources" it says "each component has a different set of sources". So a component can have more than one type of data in it - in the example here two types come from the same component, one being numericValue and another latex.<br />
<br />
It seems that the word "number" at the beginning of the script refers to the sink's data type, and the numericValue at the end refers to the source data type.<br />
<br />
So what comes after the dot is the type of data we are extracting from a component. There are tables with headings "Sources" listing all the things that could come after the dot, and others with the headings "Sinks" listing all the things that could come before the colon.<br />
<br />
I just remembered something Andrew Knauft sent me on twitter:<br />
<blockquote class="twitter-tweet" data-conversation="none">
<div dir="ltr" lang="en">
I managed to find this picture I made way back when. Just a taste of the vocabulary! <a href="https://t.co/AL99O2VTE8">pic.twitter.com/AL99O2VTE8</a></div>
— Andrew Knauft (@aknauft) <a href="https://twitter.com/aknauft/status/1152247009698439175?ref_src=twsrc%5Etfw">July 19, 2019</a></blockquote>
<br />
There's that sink at the beginning before the colon or the equals, and the source at the end after the dot. And the component name in the middle.<br />
<br />
Starting (slowly, slowly) to see a structure.<br />
<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-8058475192043539382019-07-21T07:09:00.001-07:002019-08-01T08:05:59.428-07:00Learning CL: Day 3Yesterday ended with a whimper. I became thoroughly confused and discouraged. Again. I think I've come to the end of the big picture explanations on the Desmos CL doc. The rest is a huge list of scripts that fascinate and terrify.<br />
<br />
To keep track of open questions, I'm going to bold them.<br />
<br />
Today I'm going to look at Jocelyn Dagenais's (@jocedage)<a href="https://teacher.desmos.com/collection/5cacb59a0847cb0c70183e13" target="_blank"> Intro to CL collection</a> that he very graciously shared with me on the train back from OAME this May. By the way, OAME (Ontario Association of Math Teachers) puts on one heckuva great conference. Next year it'll be in Oshawa, and the lineup is just stellar.<br />
<br />
<span style="font-size: large;">Example 1:</span><br />
<br />
Shows me one major advantage with CL, over using just the regular activity builder, is that on a single screen, you can have a graph AND an input, and the graph is not static - what the student types in the input immediately shows up on the graph. In the regular activity builder, that could only happen if the graph was the only thing on the screen, and students could get things to appear on the graph as usual with the Desmos graphing calculator. (The problem with that is that sometimes they accidentally got things to disappear too tho!) In activity builder, as soon as you'd add any other component besides the graph to a screen, the graph became static to the students. With CL, they can type their equation in the input box, and see the graph on the same screen, and there's no chance that they can inadvertently delete anything from the graph, which happened a lot.<br />
<br />
In screen 1, there is a note (with instructions), an input (with the latex option selected), and a graph. They're all labelled - note1, input1, and graph1. The script is behind the graph:<br />
<blockquote class="tr_bq">
<span style="color: #6aa84f;">function("f"):simpleFunction(input1.latex)</span></blockquote>
<b>I guess that since the script is in the graph's gearbox, that means that whatever source is specified in the script will automatically be linked to this graph? In other words, there's no need to specify that the input is the source? Is there ever?</b><br />
<br />
Anyway, I get that the : indicates that the graph is something that will receive (bc it's a sink) data from somewhere else, and where it will receive data from is indicated by the "input1" part. The dot latex specifies the type of data. For the simpleFunction part, I looked back at the Desmos CL doc and found this under Functions:<br />
<br />
<div class="documentation-table-name" style="background-color: white; box-sizing: border-box; font-family: HelveticaNeue-Light, "Helvetica Neue Light", "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;">
<h4 style="box-sizing: border-box; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; margin: 0px;">
<a href="https://teacher.desmos.com/computation-layer/documentation#functions:simpleFunction" id="functions:simpleFunction" style="box-sizing: border-box; outline: none; text-decoration-line: none;"><span style="color: blue;">simpleFunction</span></a></h4>
</div>
<span style="color: blue;"><span style="background-color: white; font-family: , "helvetica neue light" , "helvetica neue" , "helvetica" , "arial" , "lucida grande" , sans-serif; font-size: 14.4px;">Takes a latex string and returns a function which can, for example, be passed into the function sink of a calculator.The first argument is the latex string, and additional arguments are The names of the variables to treat as input variables (defaults to)one-variable function in terms of x if not specified</span> </span><br />
<br />
<span style="font-family: inherit;">So that explains why "simpleFunction" is there, it's giving instructions for what to do with the argument. (argument here must means what's in the brackets). "The first argument" would be "input1" and that's what students are typing into the input box, which is being interpreted as latex bc Jocelyn selected that when he made the screen. This script says to put whatever the student typed in note1 into the graph, and graph it.</span><br />
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit;">Did the graph and the note need to be labelled here? They're not referenced in the script. <i>No they didn't - I just deleted those labels and all still worked.</i></span><br />
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit; font-size: large;">Example 2:</span><br />
Also has a graph and a note, but instead of an input, a table, labelled graph1, note1, and table1. The table allows for 3 different functions to be typed in, and so 3 functions to be graphed at the same time. The script is again behind the graph:<br />
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<blockquote class="tr_bq">
<span style="color: #6aa84f;">function("f"): simpleFunction(table1.cellContent(1,2),"x")</span></blockquote>
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<span style="color: #6aa84f;">function("g"): simpleFunction(table1.cellContent(2,2),"x")</span></blockquote>
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<span style="color: #6aa84f;">function("h"): simpleFunction(table1.cellContent(3,2),"x")</span></blockquote>
</blockquote>
The "cellContent(1,2)" must be a data type and also point to that particular cell in table1. It's the source for which the graph is the sink. <b>So I don't need to specify anywhere that this is a source, it's understood by the simpleFunction syntax I guess?</b><br />
<br />
The x would be the "additional arguments" mentioned under "simpleFunction" above. Not sure why it's in quotation marks. This looks different not only because it's a table instead of an input but also because this time the latex wasn't selected by Jocelyn, although it doesn't appear to be an option anyway with tables? So the data type isn't latex. I don't understand why then, when I, as a student, type x^2 into the cell, it displays not as x^2 but in the proper superscript notation? <i>Played around with a sandbox activity - each column of the table has a pull-down menu, where you can toggle between "format as text" and "format as math". The initial default is math.</i><br />
<i><br /></i>
I also noticed if I click on "edit graph" to see the actual graph (I'm in teacher mode), that the first 3 rows of the expression list have got f(x), g(x), and h(x) typed in them, but the orange alert triangle is showing. If I remove those 3 rows, the graphs no longer show up when I type in a function as a student. Same is true of example 1, didn't notice that before. So in order to use the graph as a sink I need to label the row(s), kind of like the table cells were labelled.<br />
<i><br /></i>
<i>Example 2.1:</i><br />
<i><br /></i>
Similar to previous example but allows for implicit equations, like conics, to be entered into the table cells. The script looks very different though:<br />
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<blockquote class="tr_bq">
<span style="color: #6aa84f;">eq1 = parseEquation(table3.cellContent(1,2))</span></blockquote>
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<span style="color: #6aa84f;">eq2 = parseEquation(table3.cellContent(2,2))</span></blockquote>
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<span style="color: #6aa84f;">function("f"): eq1.differenceFunction("x","y")</span></blockquote>
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<span style="color: #6aa84f;">function("g"): eq2.differenceFunction("x","y")</span></blockquote>
</blockquote>
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The first 2 lines define variables eq1 and eq2 and they are whatever is typed into the table cells. Looked up parseEquation: </blockquote>
<div class="documentation-table-name dcg-hovered" style="background-color: white; box-sizing: border-box; font-family: HelveticaNeue-Light, "Helvetica Neue Light", "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;">
<blockquote class="tr_bq" style="background-color: white; box-sizing: border-box; font-family: HelveticaNeue-Light, "Helvetica Neue Light", "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif; font-size: 14.4px; line-height: 1.3em; padding: 5px 0px; width: 280px;">
<span style="color: blue;"><a class="dcg-hovered" href="https://teacher.desmos.com/computation-layer/documentation#functions:parseEquation" id="functions:parseEquation" style="box-sizing: border-box; outline: none;">parseEquation</a><span class="" style="box-sizing: border-box;">Takes a latex string, e.g. "2x+y=1" - and returns an equation object</span></span></blockquote>
</div>
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While looking through the CL doc for "differenceFunction: I saw this:<br />
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<div class="documentation-table-name dcg-hovered" style="background-color: white; box-sizing: border-box; font-family: HelveticaNeue-Light, "Helvetica Neue Light", "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;">
<h4 class="dcg-hovered" style="box-sizing: border-box; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; margin: 0px;">
<a class="dcg-hovered" href="https://teacher.desmos.com/computation-layer/documentation#components:sketch:sinks:allowEraser" id="components:sketch:sinks:allowEraser" style="box-sizing: border-box; outline: none;"><span class="dcg-hovered" style="box-sizing: border-box;"><span style="color: blue;">allowEraser</span></span></a></h4>
</div>
<div class="cl-description" style="background-color: white; box-sizing: border-box; font-family: HelveticaNeue-Light, "Helvetica Neue Light", "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif; font-size: 14.4px; line-height: 1.3em; padding: 5px 0px; width: 280px;">
<span class="" style="box-sizing: border-box;"><span style="color: blue;">Sometimes you only want students to be able to clear, not erase. Set this to false if that's the mood you're in.</span></span></div>
</blockquote>
</blockquote>
They crack me up those Desmos folks. Ok so I differenceFunction says<br />
<div class="documentation-table-name" style="background-color: white; box-sizing: border-box; font-family: HelveticaNeue-Light, "Helvetica Neue Light", "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;">
<h4 style="box-sizing: border-box; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; margin: 0px;">
</h4>
<h4 style="box-sizing: border-box; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; margin: 0px;">
<a href="https://teacher.desmos.com/computation-layer/documentation#types:equation:differenceFunction" id="types:equation:differenceFunction" style="box-sizing: border-box; outline: none; text-decoration-line: none;"><span style="color: blue;">differenceFunction</span></a></h4>
</div>
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<span style="color: blue;"><span style="background-color: white; font-family: , "helvetica neue light" , "helvetica neue" , "helvetica" , "arial" , "lucida grande" , sans-serif; font-size: 14.4px;">simpleFunction representing for (lhs) - (rhs) of an equation. Useful for setting equal to zero to test or plot</span> </span></blockquote>
Sooooo hmmmm. This may be where I stop today. This must be what my students feel like when they say - I can follow when you do it Mrs, but I know I couldn't do it on my own. But it definitely helps to have these examples, and the CL doc list. Today was better.<br />
<br />
I'm off to Austria for a week or so, and it's highly unlikely that while I'm there I'll be computation layering, especially as I'll be at a GeoGebra conference, and learning all kinds of GeoGebra stuff there.<br />
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<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-88248056485292950652019-07-20T12:29:00.001-07:002019-07-29T06:50:51.064-07:00Learning Computation Layer in Desmos: Day 2Re-read my own notes from day 1, and I feel pretty ok with it. Still reading the <a href="https://teacher.desmos.com/computation-layer/documentation" target="_blank">Desmos CL documentation.</a><br />
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<span style="font-size: large;">Sources:</span><br />
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So there's naming a component, which is different from script. You can name a component and not have any script associated with it, but not the other way.<br />
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"We can read things off all of its sources." I don't know what that means. <i>(see day 4 for answer)</i><br />
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On screen 5, in the input, I entered 4^2, and this is what happened:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCeEubwdu-Clo9mKAjobInOM5FowcJnPobN4wlCexCA1KgtYaLOoPNQ7RmVT5ZJocO9faABpIKfmGyJn2dYaPw_ZSJgvlhUD1rjunY2bqTytIQZqUf7xRYhfJFwXJHt9i5FSrLCPmApu4/s1600/screen+5.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="123" data-original-width="494" height="98" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCeEubwdu-Clo9mKAjobInOM5FowcJnPobN4wlCexCA1KgtYaLOoPNQ7RmVT5ZJocO9faABpIKfmGyJn2dYaPw_ZSJgvlhUD1rjunY2bqTytIQZqUf7xRYhfJFwXJHt9i5FSrLCPmApu4/s400/screen+5.JPG" width="400" /></a></div>
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So 4^2 is being both converted into proper math notation AND evaluated. In GeoGebra, this happens in object boxes. To display 4^2 properly you use latex, and to display the value of 4^2 you type exactly that into an object box. Anyway.</div>
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The script was in the gearbox for the note. I just realized that I'm not sure where to put the script. <b>Would it have made sense for the script to go anywhere else than under the note? </b>Anyway this part of it defines the content sink with the : and the quotation marks enclose the string to be displayed. Not sure what the ${} is about. The script looks like:</div>
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content: "<br />
You entered: ${l}<br />
which evaluates to: ${v}"</blockquote>
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Earlier in the script the variables v and l are defined:</div>
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v = exp5.numericValue<br />
l = exp5.latex</blockquote>
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and both those variables belong to exp5, which is the name of the input. So does this mean the exp5 is the source here? I typed 4^2 into the input and it got injected into the note AND the input. <b>Soooooo the input is the source and the sink here?</b></div>
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Moving on, but not feeling steady.</div>
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<span style="font-size: large;">Functions:</span></div>
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So the = is used to define a source (or a variable) whereas the : is used to define a sink? This script</div>
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latex = exp6.latex</blockquote>
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uses exp6 as a source. I don't know why the word latex is at the beginning, but I think the one that's after the dot is there to define the type of data it is. Also, I don't know why we're seeing false and true suddenly.</div>
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Am I getting confused because I'm assuming I should already understand this but it will in fact be explained later?</div>
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Day 2 not going so well. I think it's time I looked at <a href="http://www.mrchowmath.com/blog/a-fools-guide-to-learning-cl" target="_blank">Jay Chow's site.</a></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-20840255029358895142019-07-19T07:40:00.002-07:002019-08-01T07:22:38.089-07:00Learning Computation Layer in Desmos: Day 1I've decided to document my learning, questions, notes, neuron-firings...and my poor ol' neglected blog seems to be as good a place as any to do that. I'll use italics when I think I've answered my own question. I want to make clear that all this is in no way meant as a critique of the Desmos team's writing or teaching abilities - both are epic. I'm expressing the thoughts/reactions/difficulties I'm having as I work through it all, in case I am not alone, and in case there's someone out there who can untangle this for me.<br />
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<span style="font-size: large;">Day 1:</span></div>
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I've read <a href="https://teacher.desmos.com/computation-layer/documentation" target="_blank">this</a> before, not sure why I think this time will be different and suddenly all will be clear, but here goes.<br />
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First words that I get snagged on "<span style="font-family: inherit;"><i class="" style="background-color: white; box-sizing: border-box;">Sinks</i><span style="background-color: white;"> are the data that you set for a component. The text label on an action button. A variable in a graph. The text a student sees in a note</span></span><span style="background-color: white; font-family: , "helvetica neue light" , "helvetica neue" , "helvetica" , "arial" , "lucida grande" , sans-serif;">." </span>"set for a component" means inject into a component so that component now contains that value? <i>The example with the slope and the graph confirms that to be the case.</i></div>
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Next snag: "graph and math input" this terminology seems important but it is sort of appearing out of nowhere. I'm inferring from the example that a math input is a number? <i>Ohh input refers to the type of component, nothing to do with CL, it's just one of the options you can put on a screen when you make any Desmos activity? I straight up did not get that any of the other times I read this. Holy crap.</i></div>
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"Next we'll need..........exp1" good, clear, I expected that the source needs to have a sink. But then "<span style="background-color: white;"><span style="font-family: inherit;">To add a CL script</span></span><span style="background-color: white; font-family: , "helvetica neue light" , "helvetica neue" , "helvetica" , "arial" , "lucida grande" , sans-serif;">" </span>where did "script" come from? <i>(answered later) </i><b>And "preset options"? </b><i>I believe preset options are the set of possible data types for a given type of component. Eg in an input component, if the f(x)math option is selected, the data type must be number or latex, and if text is selected, the data type has to be content.</i></div>
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The "Try It" is great, and it also shows the actual activity screens where we can look into the gearbox. I'd like to have Try Its for my kids somehow somewhere about something. <i>Now I see that the input, which is the source, only needed to be given a name, but the graph, which is the sink, needed more - it needed what I'm guessing is the script, or instructions, which look like this: number("m"): exp1.numericValue . (There's that syntax that confounds me but I know this is just an intro example)</i></div>
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"Data types" "strings" more new vocab. Starting with 3 simple data types number, string, and boolean, and my question about strings is answered.</div>
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<span style="font-size: large;">"General syntax" - deep breaths.</span></div>
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Sinks are always followed by a ":" "<span style="background-color: white; font-family: , "helvetica neue light" , "helvetica neue" , "helvetica" , "arial" , "lucida grande" , sans-serif;">For example, the "content" sink of a note lets you define what the note says"</span> and I am snagged. Don't know what content sink is. But at least I now know that note is the same as the note component in a Desmos activity.</div>
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content: "Hello! I'm the computation layer!" s<b>o the colon after the word content means that this component is being defined as a sink? </b><i>Yes! </i><b>In other words, something whose content is coming from somewhere else? </b><i>Not really, it's coming from what's between the quotation marks. </i><b>Also I notice the "overriding whatever's already there" - that's important to note but then why would anyone even type anything in the original note if it's not going to show up because of the CL? </b><i>Because only the teacher would see what typed in the original note, and that might be a note to self type of thing. </i><b>Also not sure why this is a sink.</b> I got why the graph in the previous example was a sink, something in it was coming from another component, which was the source. <b>But what other component is the source for this sink? </b><i>There isn't in this case, because what's being injected into the note is what's between the quotation marks. It's functionally equivalent to just typing "Hello...layer!" into the note</i> <b>And I don't know why the word "content" is even there. </b><i>Because that's the data type for this sink.</i></div>
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<b>"Some sinks take a single parameter as an argument" new vocab again. I mean I know what argument and parameter mean in math but not here. </b><i>They mean pretty much the same thing here.</i></div>
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number("m"): 1.5</div>
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number("b"): 2</div>
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I see the colons which mean that these components are sinks. But suddenly there are brackets and quotation marks, which I'm sure will be explained later, but I'm starting to feel like I'm getting lost again. <b>And there isn't a source component for which this is the sink? The source is just the numbers 1.5 and 2? </b><i>Yup. In this case, m will always only be 1.5 and b will be 2. Functionally equivalent to typing y = 1.5x + 2 in the graph.</i></div>
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Variables: I do not understand this at all. <i>Oh. In the Try It script I replaced "hello world" with "wut up" and that's what was displayed in the preview! So the script content: greeting means that whatever the content of the variable "greeting" is will be displayed in the note.</i></div>
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"You can reference variables defined....using the script keyword" I did the same experiment, changed hello world to wut up on screen 3 then the preview for this screen, screen 4 showed wut up. </div>
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content: note3.script.greeting the : means this component is a sink, script means I guess use the script that accompanies the variable greeting. What is the "note3" for tho? I don't see anything <i>- wait it's on screen 3, that's the name of the note on screen 3. </i><b>But why is it here in this script and doesn't this make note3 a source?</b><i> It does. Not sure what my confusion was about here.</i></div>
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Sources: : "Each component has a different set of sources" - <b>has or could have? Does this have anything to do with data types?</b><i> Yes. </i><br />
"expression input" new vocab. "We can read things off all its sources" now it sounds like they really meant "has" and not "could have".</div>
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Been at this for about 1.5 hours. Back to vacation hours.</div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-45214714956104062042019-07-19T06:11:00.000-07:002019-07-19T06:11:08.323-07:00Learning the Desmos Computation LayerI have tried to get my head around this. It's not that I don't understand the whole source/sink thing, and it's not that I don't get the big idea - that when you add CL to your Desmos activity, what happens during the activity depends on what the student does - I get that. I love that. It gives Desmos that conditional property that I use so much in GeoGebra. I WANT THAT.<br />
<br />
I think it's the syntax that escapes me. I wish someone could just make a diagram about that - this goes here, this needs brackets...anyway if I ever figure this out I shall try to make something like that myself so other people in the age range in which I find myself have a chance.<br />
<br />
So for now I'm trying again, starting with the <a href="https://teacher.desmos.com/computation-layer/documentation" target="_blank">Desmos CL documentation</a>. I'll also use <a href="http://www.mrchowmath.com/blog/a-fools-guide-to-learning-cl" target="_blank">Jay Chow's (@mrchowmath) resources</a>, and <a href="https://teacher.desmos.com/collection/5cacb59a0847cb0c70183e13" target="_blank">this treasure trove of a collection</a> that Jocelyn Dagenais (@jocedage) shared with me.<br />
<br />
Wish me luck, I'm going in.Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-1043597826599085122.post-45213351281702043692019-06-13T05:12:00.001-07:002019-06-13T06:38:31.289-07:00What If I Show All the Answers?A slight tweak that seems to be making a difference these days is showing my students everything - all the answers, all the solutions, to an assignment just before it's due. About a day before it's due actually.<br />
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<b><span style="font-size: large;">The Problem with the old follow up:</span></b><br />
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I used to show the solutions (beautiful colourful step-by-step solutions mind you - I am an artist you know) <b><i>after </i></b>handing back the assignments, making sure to point out common errors, subtle details that may have been missed, how their work should look etc and it seemed for the most part to go over like a lead balloon. And I was pretty sure that almost no one was going back to correct their work, or to figure out where they went wrong, or at the very least to inform themselves of what the right procedure/answer was. The only person doing any follow-up was me.<br />
<br />
What was it about follow-up that was so not worth it from their point of view? Well, for one thing, I could tell that as soon as they got their assignments back with their mark on it, it was ancient history. It's got a mark, it's over, not much I can do about it now. Also, it takes a lot of discipline to redo something. It's a lot easier to assume - well I know better now, I'm sure I'll do better next time. I could have, of course, asked them to re-submit, or to do some kind of reflective writing, but then it would be ANOTHER thing that I'd have to chase kids for. Nevertheless, I needed to do something, because I kept seeing the same mistakes on subsequent tests that I'd seen on the formative assignments.<br />
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And I was really miffed that my beautiful work wasn't getting any attention. For its beauty or for its math.<br />
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SO on a whim last week, the day before an assignment was due, I made the full step-by-step solutions available, and asked them to do their own corrections BEFORE handing in their assignment. I still planned to do the corrections myself ( I wasn't trying to offload my job to them!) but I wanted to make sure they were actually looking at the solutions. And they did. Because now, before handing it in and ending their participation, everyone had a stake in looking at the solutions now - those that were feeling pretty sure of their work as well as those who weren't.</div>
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I added a 4th marking criterion - there had to be evidence that they had corrected their work, like check marks, or x's, and the correct procedure and answer as needed. I told them the important thing was that by the time they handed it in to me, they knew what they knew, and what they didn't know.</div>
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Here are a few samples of what I received:</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2wDuZcOF50xJgU5y5Xd_2h0WSpOE7vkNFjq0tfrJ4bG9jJSQpVfwZQbP3d2wIThNOQz6E3F36PR9Jp6x4Wfp1bp7FNe_u3kkqBY0q5UN29TWMuoGvY9vexvkMIGAyAVbQCH3kVXlXfWM/s1600/solutions+abbey.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="338" data-original-width="515" height="262" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2wDuZcOF50xJgU5y5Xd_2h0WSpOE7vkNFjq0tfrJ4bG9jJSQpVfwZQbP3d2wIThNOQz6E3F36PR9Jp6x4Wfp1bp7FNe_u3kkqBY0q5UN29TWMuoGvY9vexvkMIGAyAVbQCH3kVXlXfWM/s400/solutions+abbey.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: large;">All checks</span></td></tr>
</tbody></table>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSLSWftzCkwHhv4Zyyu4anoMzwUXuBr-y7vXZhkoQdKAV_cHeKPhHGJk-P1h-llKh6iyHGrejtKrq_kh30bNCwYQLVaqBW9bjbfZY2QwQNUokD9eihqvb6PRlwOfhsy_caH172ctJArfg/s1600/solutions+brianna.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="518" data-original-width="1008" height="205" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSLSWftzCkwHhv4Zyyu4anoMzwUXuBr-y7vXZhkoQdKAV_cHeKPhHGJk-P1h-llKh6iyHGrejtKrq_kh30bNCwYQLVaqBW9bjbfZY2QwQNUokD9eihqvb6PRlwOfhsy_caH172ctJArfg/s400/solutions+brianna.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: large;">Mistakes detected and corrected</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxE2pDGv5LhFzBBXdsWrsEUmgDKIP8_ErF0s9XUsV6cVqAOb732KHtAHqdgTSH5gV9VicB_Pvn_MtaYYFsJ84b0xlcyz4qvIhNU3VzLml3pLtd2ZQvx_nyYNDvsYSdXUea2gOTAUpWGrk/s1600/solutions+chris.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="422" data-original-width="465" height="362" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxE2pDGv5LhFzBBXdsWrsEUmgDKIP8_ErF0s9XUsV6cVqAOb732KHtAHqdgTSH5gV9VicB_Pvn_MtaYYFsJ84b0xlcyz4qvIhNU3VzLml3pLtd2ZQvx_nyYNDvsYSdXUea2gOTAUpWGrk/s400/solutions+chris.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: large;">A note-to-self</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0dn2dERfiCFo8fO6CU35Lw5_3bUOWcmKwVBGPng7l-nh4wlUH7XDusWxm3cq4KOGV23PUC_tEE7rbDuuinQ7Pcaz9eVtipvRnZyWYaKkUEldFpG3BMZPBks7uRZPmQXAEpPLaudBlZso/s1600/solutions+janie.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="551" data-original-width="446" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0dn2dERfiCFo8fO6CU35Lw5_3bUOWcmKwVBGPng7l-nh4wlUH7XDusWxm3cq4KOGV23PUC_tEE7rbDuuinQ7Pcaz9eVtipvRnZyWYaKkUEldFpG3BMZPBks7uRZPmQXAEpPLaudBlZso/s400/solutions+janie.JPG" width="323" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: large;">Visible learning, imho</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm0N59cglLbi5xDMAmJvRjdg1FtPiSGx_YvwRSidQmOfi4Y756ssmxzmip0iBC3d50PpS2xym7vfIclE_C4pmnsoiJrgsM4lo_lEJnEGxd2iReJOBrW3g-3spKgimutxoQ9GofUm3RBx0/s1600/solutions+jayda.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="62" data-original-width="189" height="131" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm0N59cglLbi5xDMAmJvRjdg1FtPiSGx_YvwRSidQmOfi4Y756ssmxzmip0iBC3d50PpS2xym7vfIclE_C4pmnsoiJrgsM4lo_lEJnEGxd2iReJOBrW3g-3spKgimutxoQ9GofUm3RBx0/s400/solutions+jayda.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: large;">Self assessment!</span></td></tr>
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<span style="font-size: large;"><b>A few things I noticed:</b></span></div>
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<ul>
<li>A lot fewer no-shows. Almost everyone got this in on time.</li>
<li>Some students switched to a different coloured writing implement when they switched to correction mode. I like that - I'm going to insist on that next time. It makes it easier for me to distinguish, and I like the idea of a concrete gesture to signify a new stage of working, a new way of thinking.</li>
<li>This time, when there weren't any questions, I wasn't worried about what that meant - I knew where they were, and I knew that THEY knew where they were.</li>
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<b><span style="font-size: large;">Next assignment:</span></b></div>
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SO I did something similar for the next assignment, which, because it was much longer and more complex. I didn't think it was fair to ask them to correct. Nevertheless I did make the solutions available before the due date, in a more gradual fashion, that is, at first only within the classroom, as they were working, and only as needed. I helped kids individually, and of course first asked them to show me what they had already done. I then made the solutions fully available at our LMS the day before the due date. Naturally I wanted to diminish the temptation of taking the easy way out and copying.<br />
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During the in-class session, and even in between, when I was getting lots of questions via email and twitter, it seemed as though for everyone, being able to confirm, re-interpret, or correct made it all more doable. I heard them answering their own questions - oh I see where I went wrong, or oh find the solution set means solve for x - all things that I know I said, or would have said while doing my old follow-up, but which would have fallen on deaf ears. And I got to witness them not only reading the solutions but digesting them in the context of their own path thus far. I got way more questions, and way better questions than I'd ever gotten on the day before an assignment was due. I suspect that for some kids, this was the time when they'd hide from view, not wanting to admit how much they were not able to do on their own. Maybe having the solutions was a license for them to at least try, and then magically, to realize that they actually could do this.</div>
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On the due date, I went over the solutions in class one more time. And the response was very different than if this had been the first time they'd seen them - kids noticing all those little things that I'd struggled before to highlight, figuratively and literally with all my beautiful-coloured tools. Or noticing that their way was slightly different than mine, but legitimate anyway. It was a wrap-up that held a lot more meaning, because it felt like the end of a journey we had been on together.</div>
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<b><span style="font-size: large;">Next year:</span></b></div>
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I'm so doing this again next year. I already find my worksheets are getting a lot better as a result of being more confident that more kids will do more of them. I think I'll add a reflective component to it. Identify where you went wrong, or what you got right after struggling with it. When did you look at the solutions. Tell me about this journey!</div>
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Unknownnoreply@blogger.com6tag:blogger.com,1999:blog-1043597826599085122.post-20759711392562720042018-09-18T09:22:00.002-07:002018-09-18T09:22:40.385-07:00Dot Producting That Makes Mathematical SenseNote to self for next year when you do dot product: You know how you've tried so many times to get the dot product to make sense to your students, and failed?<br />
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Well, Future Audrey, this went well.<br />
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<span style="font-size: large;">While waiting for kids to arrive:</span><br />
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I wrote <3, -4> on the board and asked all students, as they entered class, to write another vector that was orthogonal to it, but it had to be different to everyone else's. After the easy ones were done, ie <4, 3> and <-4, -3>, others had to go with ones that were collinear to one of those. This was to remind all that when 2 vectors are orthogonal, 3 things have to have happened between their components: a switch, exactly one sign change, and a multiplication by some scale factor (which can of course be 1). Also a good opener, bc kids who are early or on time got the chance to put the easy ones up, and those who arrived late were quickly able to catch on and jump in right away.<br />
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<span style="font-size: large;">Now that everyone was there and warmed up:</span><br />
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All voted as to the truth of these statements:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBDEZWgZXD5tU6ridincW-i7WOcldyYkToiGEH5gji5ixzUQ_o1ASLNNOKZrAo3wgOpIge7Jy5CONz5kcsplYOb8cFVUQRw9P-DLpPJf9hH3htaaJUyOGrAOL1vhrAmd1SqSIba-i99uA/s1600/dp1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="648" data-original-width="873" height="237" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBDEZWgZXD5tU6ridincW-i7WOcldyYkToiGEH5gji5ixzUQ_o1ASLNNOKZrAo3wgOpIge7Jy5CONz5kcsplYOb8cFVUQRw9P-DLpPJf9hH3htaaJUyOGrAOL1vhrAmd1SqSIba-i99uA/s320/dp1.PNG" width="320" /></a></div>
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For 3/4 = 6/8 I asked: How do you know it's true?<br />
-I punched 3/4 then 6/8 into my calculator<br />
-Iimmediately recognized that num and denom had both been doubled<br />
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But only one student talked about cross product. This was an eye-opener to the rest. They are used to "cross-multiplying" to solve proportions but they didn't know where it came from...we tried that out on a few known true proportions.<br />
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Next eg on the slide: For 3/4 = -24/32 I asked what's the fastest way to tell this is false?<br />
-Opposite sign<br />
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Ok then I inserted negatives in various positions and did T or F each time? We agreed that only if there are an even number of negatives in total is it true.<br />
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Last eg we knew must be true because both are = 3/4, but we used cross product to check. Agreed that it was at least as fast as dividing twice<br />
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<span style="font-size: large;">Back to orthogonality:</span></div>
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Went through these:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihtn3IyZGUt9TXjd8hM8WduATRTilQY235mItYaMF4kRDsc5hRtmR_FUYRSNuG0LhGR9IyAsiYNX3KxiyH087XGsWcsRqN-bIYQDCQwuQIR2a8Um5HYv05Wxx9Xs3mPhmIObngJK0neqY/s1600/dp2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="651" data-original-width="877" height="237" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihtn3IyZGUt9TXjd8hM8WduATRTilQY235mItYaMF4kRDsc5hRtmR_FUYRSNuG0LhGR9IyAsiYNX3KxiyH087XGsWcsRqN-bIYQDCQwuQIR2a8Um5HYv05Wxx9Xs3mPhmIObngJK0neqY/s320/dp2.PNG" width="320" /></a></div>
And I first asked in each case, are the signs a deal-breaker? Agreed that here we want to see a total nbr of negs that is odd, since that means exactly ONE sign change has happened.. First two egs easy to decide.<br />
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3rd eg: I asked: Write how you're checking for proportionality. Established that to accommodate the switch, we compare 4.2 to 3, and 2.8 to 2. Got 4.2/3 = 1.4, and 2.8/2 also = 1.4 so they're good. 4th eg immediately eliminated by signs. 5th eg we worked out on board fully, showing who was divided by whom, and that each quotient came to same nbr.</div>
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<span style="font-size: large;">Reframing: And this is the part I've messed up all these years (Sorry students of my past.):</span></div>
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After last eg I reframed that process this way:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1I20_HS_z-RAIEvouxHcgb-p2KgzdU9cG0y7ROT3WXlqFgXmRM_CCcMAINttz8D7dbMZtX3QqLx37yDjaIGYwAbtaYpN_i49CAqlBlmQiNSt0yBC1fncXN0Bd7vjj8MYx6gNQykqOUgg/s1600/dp3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="655" data-original-width="872" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1I20_HS_z-RAIEvouxHcgb-p2KgzdU9cG0y7ROT3WXlqFgXmRM_CCcMAINttz8D7dbMZtX3QqLx37yDjaIGYwAbtaYpN_i49CAqlBlmQiNSt0yBC1fncXN0Bd7vjj8MYx6gNQykqOUgg/s320/dp3.PNG" width="320" /></a></div>
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I asked do we really need to know how much 18.6/4.2 is, or is it enough to know what ELSE comes to the same thing? Then we used that "new" cross multiplication way of checking for proportionality to arrive at the last line.</div>
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Then asked them to compare the last line with the first, to detect where the 4.2 and the 34.1 came from. "They're the x components of the two vectors." And the 7.7 and the 18.6? "The y-components."</div>
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Emphasized that if the product of the x-components is equal to the product of the y components, we know that between the two vectors, a switch AND a scale factor multiplication have happened.</div>
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Moved to actual dot product definition now:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_rCAl_N6ICp3403Oaest0EmH0IZpxyoJ4j-CIod6S2GfR1Tnnh2eumOivZCz632o_Ykl5F8IgXRkGpIihJw-P9nJZBGuAP-DOZ6WZbyVsfBeIiKAib3z1oZJ4I7rdawqjrV8_X3c40NM/s1600/dp4.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="656" data-original-width="871" height="241" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_rCAl_N6ICp3403Oaest0EmH0IZpxyoJ4j-CIod6S2GfR1Tnnh2eumOivZCz632o_Ykl5F8IgXRkGpIihJw-P9nJZBGuAP-DOZ6WZbyVsfBeIiKAib3z1oZJ4I7rdawqjrV8_X3c40NM/s320/dp4.PNG" width="320" /></a></div>
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Took my time to highlight notation here - the dot, the subscripts, also that this involves multiplying the x components, and the y components, like we just did.</div>
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<span style="font-size: large;">Activate one last thing they already know:</span></div>
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I went to a blank screen and wrote: If a + b = 0, then what do you know for sure about those two numbers?</div>
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Various answers:</div>
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-they're both 0</div>
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-they cancel each other out</div>
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-they're the same number but one is + and one is -</div>
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We agreed that they must be opposites (allows for both = 0)</div>
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<span style="font-size: large;">Moved back to definition of dot product and wrote: </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs-PyBVwgFuYeI541Y8yDtBfbQZaQ784Qtu2AJdud7YFed95UqZStj23gkR9gku6wmBSHojDXW6-93YotlzMELtHBwv4vBa9hoaUlyCMs0iNH5-AFAEBjG6HORUQ9PtJslWqmNR22mpQI/s1600/dp5.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="649" data-original-width="869" height="238" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs-PyBVwgFuYeI541Y8yDtBfbQZaQ784Qtu2AJdud7YFed95UqZStj23gkR9gku6wmBSHojDXW6-93YotlzMELtHBwv4vBa9hoaUlyCMs0iNH5-AFAEBjG6HORUQ9PtJslWqmNR22mpQI/s320/dp5.PNG" width="320" /></a></div>
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and asked - what must be true about u<span style="font-size: xx-small;">x</span>v<span style="font-size: xx-small;">x</span> and u<span style="font-size: xx-small;">y</span>v<span style="font-size: xx-small;">y</span> if they too add up to zero?</div>
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-they must be opposites.</div>
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So now we know that there's been a sign change, a switch, and a scale factor multiplication.</div>
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Used dot product to detect orthogonality or lack of it on a few more egs.</div>
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We also moved on to what it means when dp comes to a positive, and a negative, but the why of that not so much - next year maybe you'll figure that out, Future Audrey.</div>
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Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-1043597826599085122.post-41527456817803881062018-06-12T08:55:00.000-07:002018-06-12T08:55:52.401-07:00Student-Created GeoGebras and Graspable MathI. Cannot. Wait. Till. Next. Year. When my students will use Graspable Math to work out their formula for the sticky zero in their GeoGebra OMG:<br />
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<script type="text/javascript">url = parent.document.URL; document.write('<iframe style="border: none" src=\'https://graspablemath.com/canvas/embed.html?load=_bd9ed6a05a393d33&options={"use_toolbar": true, "vertical_scroll": true}&parent_url='+url+'\' width=100% height=500px></iframe>');</script>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-49177315689450438082018-06-12T08:30:00.001-07:002020-07-16T12:25:00.767-07:00Reflections on Learn's Self Paced Blended Learning Year OneMy last post described the creation stages and final product of our first year in what we called the Self Paced Blended Learning project. This post is our collective reflections on the experience, so when I use "I" or "we", I'm speaking on behalf of the staff..<br />
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<b>The Creation Stage:</b><br />
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Simply put, this stage was a huge amount of work, and required some working through holidays, just to meet the deadlines. But the benefits far outweighed that.<br />
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I had thought it would be a simple matter to simply take all of the digital content we'd all created over the years for our own courses (yes we create our own and we have SO MUCH STUFF) and rearrange it all in one online space, in a visually appealing and easy-to-understand way. Hilarious. Adorable even.<br />
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When you have to add in context - those crucial bits of text that make it possible for a student aged 15-ish to keep motivated, to understand what to do, when to do it, and where to put their work, <i><b>and know that a real human being cares whether or not they are ok,</b></i> you quickly discover all kinds of holes. You also discover just how much just-in-time on-the-spot teaching and spontaneous learning happens during the live class! We all ended up creating many new resources to make the self-paced experience as close as possible to the real-time one.<br />
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At this point it's clear that even if no one had taken the SPBL course, this process would've ended up benefiting everyone - in the short term and the long term:<br />
<ul>
<li>Because of the SPBL deadlines, I was prepared and ready for my real-time classes an entire month ahead of time, which I had NEVER been in my entire career. That was a double edged sword, mind you, because it freed my mind to come up with lots more spontaneous ideas during class, which in turn meant more SPBL stuff to include in the weekly meetings...not a vicious cycle, but a self-perpetuating one!</li>
<li>As I mentioned before, a lot of holes got filled even for my Real-Time students. They benefited from much more thorough and frequent checks-for-understanding, as well as new and better voicethreads that otherwise wouldn't have been made, at least not all in one year.</li>
<li>Writing those <i>Introduction & Why Are We Learning This?</i> blurbs at the beginning of each unit gave me a deeper appreciation for the content. I've never been comfortable answering "When are we ever going to use this?" with "On the final exam", but neither have I ever given the question much deep thought. It made me appreciate how these things fit into the bigger picture. I should have been doing this all along. </li>
<li>The big picture - I had never had the opportunity to look at the whole course in one spot before, and as it took shape over the year, many opportunities to connect different topics were suddenly revealed to me. Orthogonal vectors & trigonometric points. Hyperbolas and rational functions. The linear thread through EVERYTHING - every single kind of equation we learn how to solve gets turned into some kind of linear equation! Who knew?</li>
<li>Also big picture, but for next year: The yearly overview makes it easy to schedule certain routines, like "Always Sometimes, or Never?" or "Which One Doesn't Belong?" on a regular basis, instead of whenever I happened to have the presence of mind to think of it.</li>
</ul>
<b>The Weekly Student Meetings:</b><br />
<br />
Ideally, every student should have the opportunity to get 100% of their teacher's attention and focus on a regular basis. What our SPBL students missed out on in the synchronous experience, such as social learning and the feeling of belonging to a group, they were compensated for in personalized learning.<br />
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Everything that happened in a meeting could also have happened in a real time class, but it's very different in a one-on-one. Put a student in a class of 20-30 people, in which the teacher says "What do you think of this?" Then put that same student in a one-on-one meeting with the same teacher saying the same thing, and those words will have a profoundly different impact. Words sound entirely different, indeed the message they convey IS entirely different, when you know they are directed at you and only you.<br />
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<b>The Overall Student Experience</b><br />
<br />
You might think that the amount of time the SPBL students spent on their own made the format rather impersonal and bereft of human interaction, but the exact opposite was true. First of all, in our weekly meetings, we're going over one person's work, focusing on exactly what they and only they need, as opposed to the usual showing of all the solutions to everyone, regardless of what kind of results they got.<br />
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<div class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;">
<span style="font-family: inherit;">Moreover, the one-on-one meetings made it impossible to hide, impossible to not make your personality known. By contrast, in an online synchronous class, where there is no body language to colour everything you say, it's the relatively rare student whose personality is accurately and fully transmitted to the other people online. Obviously, the teacher is an expert at that, but most students would rather remain as invisible as possible, choosing to text their comments rather than use their microphone. Of course this is not even remotely possible in the weekly meetings. It was nice to not be the only one using their voice for a change.</span></div>
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<span style="font-family: inherit;"><br /></span></div>
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<span style="font-family: inherit;">The agenda for each meeting was set by the teacher, and even though there were plenty of opportunities for the students to add his or her own items, it felt rather teacher-driven. Since SP students are required to be more active participants in these one-on-one sessions, we're hoping that next year they will be the ones driving the meetings.</span><br />
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit;">The meetings, along with the friendly tone of the blurbs and instructions scattered throughout Sakai, were hopefully enough to make the whole experience <i style="font-weight: bold;">human </i>for our inaugural students. It's hard to imagine anyone being able to complete a course that only involves automated interactions, in which no one is invested emotionally or even intellectually. Teenagers especially need to know someone cares about their success, even if they themselves get discouraged and lose motivation.</span></div>
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<span style="font-family: "times new roman" , serif;"><br /></span>
<span style="font-family: "times new roman" , serif;"><b>The Overall Teacher Experience</b></span><br />
<span style="font-family: "times new roman" , serif;"><b><br /></b></span></div>
I was excited about this project when we first started talking about it, then when we were in the thick of it I got a bit discouraged, because it really seemed at one point like the content was too complex to be covered this way. I turned a corner about halfway through the year, when I began making actual slides for my meetings, and when the students started settling into the routine. It really helped when they did well in their midterms. That was when it stopped feeling like an experiment and started to feel like an exciting new direction for Learn. As is always the case with everything Learn does, it all comes down to the students.<br />
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If it works for them, we're in.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-13475544347029566932018-05-31T09:55:00.000-07:002018-05-31T09:56:23.190-07:00LEARN's Self-Paced Blended Learning: Year OneHave you ever put your life's work all in one place and tried to make it coherent and meaningful and beautiful? Me neither, until this year! This post is part one of two posts about an exciting new project at LEARN, where I am lucky enough to work.<br />
<br />
<span id="docs-internal-guid-923a09db-b1a4-2170-ccf1-a3d2ffadd2a5"><span style="vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">At LEARN, we offer fully synchronous online courses to Quebec's English high school students, and have been doing so for a long time...19 years to be exact. This year, we also offered some of the same courses in a different format, which we called "Self-Paced Blended Learning", or SPBL for short. We did this to accommodate the students who wanted to take our courses, but who couldn't fit them into a Monday-to-Friday schedule given their school’s cyclical schedules.</span></span></span><br />
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To achieve this, we had to find a way to make our courses available in a format that would allow for self-pacing, while at the same time address the fact that students at that age need guidance. To balance independence with support, we blended the asynchronous with the synchronous. We decided that in addition to the asynchronous delivery of digital resources, teachers would meet each student individually on a weekly basis. In addition, we'd create opportunities for students to interact with other students who were also following the course, both those in the SPBL format and those in the live (Real-Time) classes.<br />
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We're now coming to the end of Year 1, so it's time to record - and reflect on - what actually happened. Here goes!<br />
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<span style="font-size: large;"><b>The journey begins:</b></span><br />
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The first task for us was creating the online space for the course. This was started about 8 months before we launched the courses in September 2017, when we didn't even know who, if anyone, would be taking it. Each teacher filled in a template (provided by our project lead) for each unit in our course, which included everything the students would see - lessons, activities, quizzes - everything, as well as the context for each step. For example, a link to an assignment needed to be preceded by:<br />
<blockquote class="tr_bq">
<i>Please print this assignment, and complete it by Friday. Be sure to show all your work! You may hand it in via fax or your dropbox.</i></blockquote>
The writing of the context proved to be time-consuming, and also extremely important, because it was the human part. More about that later.<br />
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The contents of the template were then uploaded to our Learning Management System (which is Sakai), made to look cohesive and orderly, then vetted by fresh eyes. The plan was that all this would be done well before any student would see it - a good month at least, which we managed to meet, for the most part, despite simultaneously having a regular teaching load.<br />
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<span style="font-size: large;"><b>How it all ended up looking:</b></span><br />
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All of the materials were organized by unit, week, and lesson. Here's a snapshot of the landing page for one unit:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4En5RUFYoaNO4lJt4KPLcFZe_ahH7Dd6GwFH_qS_z9wouXxju_voqkQnP-4CCAwcAo1nmGeJ5JagRBrQHw_ggClhHFlE3DoiDsYalmkMP8rw6k8rC0pjMDIj-4Gk6jXLGOtD1zf9dTus/s1600/unit6.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="686" data-original-width="820" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4En5RUFYoaNO4lJt4KPLcFZe_ahH7Dd6GwFH_qS_z9wouXxju_voqkQnP-4CCAwcAo1nmGeJ5JagRBrQHw_ggClhHFlE3DoiDsYalmkMP8rw6k8rC0pjMDIj-4Gk6jXLGOtD1zf9dTus/s1600/unit6.PNG" /></a></div>
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Upon clicking on a week, students would see an overview of the week's lessons, plus a link to the checklist:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmf1_0B6ABD1JzjOR17-T-rZostkqb0np6GkffGuta5iCX43opT9c4v_O8TNZ0gS5PYa3UKi25XiqjKtMsyjHj626dbYYzBO20Nk7WUTTgI4_lnR05ahJh69ATJIuINUubyIlejcx1VVk/s1600/unit+6+week+32.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="433" data-original-width="679" height="408" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmf1_0B6ABD1JzjOR17-T-rZostkqb0np6GkffGuta5iCX43opT9c4v_O8TNZ0gS5PYa3UKi25XiqjKtMsyjHj626dbYYzBO20Nk7WUTTgI4_lnR05ahJh69ATJIuINUubyIlejcx1VVk/s640/unit+6+week+32.PNG" width="640" /></a></div>
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<span style="font-size: large;"><b>Lessons:</b></span><br />
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<b>A lesson</b> in this context was actually a single web page, which displayed a self-contained series of activities centered on a single topic. It generally included some kind of recorded delivery of content, (usually a Voicethread, which is an interactive format of content delivery), some practice work from the text, the answer key, and a check for understanding. It may also have included other types of interactive elements, such as a Desmos activity or an Explorelearning gizmo. Here's an example of a lesson page (rearranged slightly to fit here):<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbOitiWzv8oK7kB8LX3Q21zXViY-XzlzdkD0DGed4gd0Ngv32DGzdRdddbdAZ_EChsAs1GgZyvE-_0ZOUkr_ja2La3cmiCs90VB8bkcnM-w4Wa2uLxhT2OF4uMvcUIK5ml70d6knrSKew/s1600/unit6w32lesson6.2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="920" data-original-width="1452" height="404" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbOitiWzv8oK7kB8LX3Q21zXViY-XzlzdkD0DGed4gd0Ngv32DGzdRdddbdAZ_EChsAs1GgZyvE-_0ZOUkr_ja2La3cmiCs90VB8bkcnM-w4Wa2uLxhT2OF4uMvcUIK5ml70d6knrSKew/s640/unit6w32lesson6.2.png" width="640" /></a></div>
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<span style="font-size: large;"><b>Check for Understanding:</b></span><br />
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The check for understanding may have been a self-correcting multiple choice question as in this case, or a link to a googlequiz, GoFormative, Explorelearning gizmo, Seesaw reflection etc. Again, this served both the teacher and the student. Both had regular reassurance that progress was happening.<br />
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Each lesson page ended with a reminder to go update the checklist.<br />
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<span style="font-size: large;"><b>Checklists:</b></span><br />
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<b>The checklist</b> was a means for keeping student and teacher connected in between the weekly meetings. Not only did it help the teacher to track student pacing, but it was a way for a student to let the teacher know of any issues - specifically those related to the content, such as if they need help on one particular question or activity. They of course had other ways to contact us for more immediate issues, such as technical ones, but this was mainly for their reactions to the content.<br />
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Here's a partial screen capture of a checklist (created using google forms):<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOUhpzLGSfw_bnDzmdwddsQSf8DOVDEPvzGyDp7rEY5kH9JtGLvAk_nLO5j6SWzgGLeImFCdEBPTlpGVLkUCFRwNTY5z7nUk-blmAkzGhsjlRiLjjxKW4lsI8s5ZDlG3387jdbTtJfmjo/s1600/unit+6+week+32+checklist.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="786" data-original-width="562" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOUhpzLGSfw_bnDzmdwddsQSf8DOVDEPvzGyDp7rEY5kH9JtGLvAk_nLO5j6SWzgGLeImFCdEBPTlpGVLkUCFRwNTY5z7nUk-blmAkzGhsjlRiLjjxKW4lsI8s5ZDlG3387jdbTtJfmjo/s640/unit+6+week+32+checklist.PNG" width="456" /></a></div>
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The checklist included everything that was contained in a whole week. We used the checkbox format, and included "Other" in case students wanted to tell us anything over and above the checkbox options.<br />
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<span style="font-size: large;"><b>Assessment:</b></span><br />
<br />
Students wrote on good old-fashioned paper for some assignments and for all of their tests. Since all of our students attended a regular brick-and-mortar school, supervision was handled locally, and all paper & pencil work was transmitted to us via the school contact person. The SPBL students wrote the same assessments as our Real-Time students.<br />
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<span style="font-size: large;"><b>Weekly meetings with Students:</b></span><br />
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Each meeting included a close look at all of the student's own work, including and especially assessments. This was a golden opportunity to correct and redo any missed items right away, which is something that is essential for all students but which takes much longer in the real time class. Meetings were also used to look ahead at the next week. In addition, we might include any of those spontaneous things that may have happened during the live class, such as an interesting daily warmup or an announcement about one of our all-school Twitter chats (that's another blogpost!)<br />
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<span style="font-size: large;"><b>Weekly Meetings with Project Team:</b></span><br />
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Every week, we had a meeting involving the whole project team. These meetings were to our mental health what water is to a plant. We were extremely fortunate to have at the helm of these meetings a leader whose enthusiasm and insightful feedback kept us all moving ahead with our eyes on the prize. As a team, we evaluated our progress, compared notes, shared tips, reflected and generally forged our year-long path together.<br />
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This post describes the common experience from the teachers' point of view. Of course, there was some variation in the tools we each used, but the main components of the course structure, design, development and delivery...were the same. My next post will be our reflections about the actual boots-on-the-ground experience. Stay tuned!Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1043597826599085122.post-76285904296541569672018-03-23T08:43:00.001-07:002018-03-23T08:43:21.652-07:00Marrying Student-Created GeoGebras with the GeoGebra Group EnvironmentI've had my students<a href="http://audrey-mcsquared.blogspot.ca/2013/11/more-student-created-geogebras-and-some.html" target="_blank"> create function summaries using geogebra</a> before, and I've had them <a href="http://audrey-mcsquared.blogspot.ca/2017/11/geogebra-group-hug.html" target="_blank">doing activities in our class's GeoGebra Group</a> before, but this week is the first time I've done both at the same time. I'd been hesitant to marry these two things, even though I love them both, because I was unclear on when and how often a student can edit their own ggb when it lives online in a group. Well hello, the answer is whenever and as many times as they want. It doesn't matter if they turn it in or not, it doesn't matter if I tag it complete or not, none of that matters. Their own individual work is always open to them and anything they do is automatically saved, no matter when they do it. Just like the offline version, except WAY easier and cooler.<br />
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Why is it easier and cooler in the group environment? Usually, these summaries involve students using the offline GeoGebra, saving and numbering successive versions of their function summaries, sending each version to me, me downloading each version, me giving feedback on each version (using various tools completely separate from ggb, eg annotating a screen capture, or Camtasia video, or Smart Notebook etc) etc. But when it's all done in the group space there's no need for any of that - no saving, no numbering, no sending. And my feedback happens right there, in the same space as their work - right underneath it in fact, in a chat box, to which they can reply, also in the same space.<br />
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Here's what I did:<br />
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<span style="font-size: large;"><b>The Rollout:</b></span><br />
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The students login to our group at www.geogebra.org, where they see this post:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiegxjCqryk9xrAdin1Y8_Mf8iGtYhuy4iymErbZGHsXYtiU9xTFZ-8b7YKSMNeAyo9llab4Hq9Eve4uDEVKuCh6vaZnSjvY0HFgbHb-Jech6mgwH0E_ZLb0Q7jRaon7-rTRgAP7-wnOmE/s1600/grouptrigpost1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="609" data-original-width="675" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiegxjCqryk9xrAdin1Y8_Mf8iGtYhuy4iymErbZGHsXYtiU9xTFZ-8b7YKSMNeAyo9llab4Hq9Eve4uDEVKuCh6vaZnSjvY0HFgbHb-Jech6mgwH0E_ZLb0Q7jRaon7-rTRgAP7-wnOmE/s400/grouptrigpost1.PNG" width="400" /></a></div>
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...in which they find out they'll be doing a GeoGebra task, then coming back to this post to make a comment right underneath it, in the public comment space.<br />
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To get to the task, they just click on the "Trig Function Starter Kit" and see this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWmG_WhkNdD7zln-5Caz9PtAoiqmDzIlv2bStunRZTWgGC40kC1jtWo4MRlC4tjJkegNAPU55d5PWAQuOVuGBY5A-HepshZEl_FoWzQVC1bpQ7YZxKZPjcwI4YiYHvb_l0SbA1ZzXJnFQ/s1600/grouptrigpost4.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="891" data-original-width="1049" height="338" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWmG_WhkNdD7zln-5Caz9PtAoiqmDzIlv2bStunRZTWgGC40kC1jtWo4MRlC4tjJkegNAPU55d5PWAQuOVuGBY5A-HepshZEl_FoWzQVC1bpQ7YZxKZPjcwI4YiYHvb_l0SbA1ZzXJnFQ/s400/grouptrigpost4.PNG" width="400" /></a></div>
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The task on the first day: Input one of the two wave functions, with all 4 parameters, and add the a, b, h, and k sliders to the worksheet, so they can start experimenting. They played around with the sliders until they were ready to post a comment in the public comments section about which property(s) is(are) affected by which parameter. I wanted the discussion to be public so that they feel part of a community of learners, and they can learn socially. Here is a screen capture of some of the comments as they appeared in the public space:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizA-oZsxoavDw3RLSp1WJ72f3U_8aEVX1PanvzXNXmukpyAC-nV0ZVzaW2rLGDR9x_8nWZX8SGHFZ7DOqfZeCy42PKALuRGGRrUjv8VfSZ7unvQUWPVeTI7sXMJCGLIdTr1US0E-ujEVU/s1600/grouptrigpost2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="473" data-original-width="593" height="318" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizA-oZsxoavDw3RLSp1WJ72f3U_8aEVX1PanvzXNXmukpyAC-nV0ZVzaW2rLGDR9x_8nWZX8SGHFZ7DOqfZeCy42PKALuRGGRrUjv8VfSZ7unvQUWPVeTI7sXMJCGLIdTr1US0E-ujEVU/s400/grouptrigpost2.PNG" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1HMfaWMaNnXhgxdXd_53TrPTpO_fwcrHiTPurt-l2krrzCay575T7C689FE7gv2lHkXG8s14N-4dmaGBNSIVIk2LSbYeSr_BXccsXbxi7c8V8yv44tCvOPKqRx-Syzb21sXQnXnN9dx4/s1600/grouptrigpost3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="455" data-original-width="612" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1HMfaWMaNnXhgxdXd_53TrPTpO_fwcrHiTPurt-l2krrzCay575T7C689FE7gv2lHkXG8s14N-4dmaGBNSIVIk2LSbYeSr_BXccsXbxi7c8V8yv44tCvOPKqRx-Syzb21sXQnXnN9dx4/s400/grouptrigpost3.PNG" width="400" /></a></div>
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<b><span style="font-size: large;">The Gathering:</span></b><br />
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They of course can all see everyone else's comments, but I wanted to rearrange them to give a different perspective. By the next day, I had sorted all their comments by function, student, and parameter, as you see below. This way they could see who went with which function, and who had already decided to go for the bonus point ("K" at the bottom - I suspect that seeing this caused many to do the same the next day!). They could also see, in one slide, that everyone agreed that parameter a changed the amplitude:<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuC8XGdw0ez-wlggF0ehg99mmr1JGQvPa2udZb8r9sFhD6vigTqU3USeG9CWOXApJ5FeulCKPwBVJJ9_2Ow8U9ySkvcgcRSlZAdAo_HMsH8jc0ljIYCxz7i6Jt_mcH0OPfLApZ-CKppA0/s1600/grouptrigpost5.PNG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="555" data-original-width="822" height="270" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuC8XGdw0ez-wlggF0ehg99mmr1JGQvPa2udZb8r9sFhD6vigTqU3USeG9CWOXApJ5FeulCKPwBVJJ9_2Ow8U9ySkvcgcRSlZAdAo_HMsH8jc0ljIYCxz7i6Jt_mcH0OPfLApZ-CKppA0/s400/grouptrigpost5.PNG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="background-color: cyan; font-size: large;">Parameter a</span></td></tr>
</tbody></table>
<div style="text-align: center;">
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<tr><td style="text-align: center;"><div style="text-align: left;">
This sorting also revealed that everyone agreed on b affecting the frequency....</div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFV3W-z8mpqku-VnM9hYFOv3wVmZbx3d-1xBF_Id7b-j2EiyTe5J405_PujXomjdGucIfTduzYvUaZagxNL8vF3eljZhyphenhyphenMLRGvUGfjyyTy9U7HfhKWxElXW0CYvniInQTPM-QCWP-yQ1M/s1600/grouptrigpost6.PNG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="577" data-original-width="839" height="275" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFV3W-z8mpqku-VnM9hYFOv3wVmZbx3d-1xBF_Id7b-j2EiyTe5J405_PujXomjdGucIfTduzYvUaZagxNL8vF3eljZhyphenhyphenMLRGvUGfjyyTy9U7HfhKWxElXW0CYvniInQTPM-QCWP-yQ1M/s400/grouptrigpost6.PNG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="background-color: magenta; font-size: large;">Parameter b</span><br />
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<span style="font-size: large;"><span style="background-color: white; font-size: small;"><br /></span></span>
<span style="font-size: large;"><span style="background-color: white; font-size: small;">....but the one below showed that not everyone noticed that b also affects the period. I love how some students extended their comment to explain why: "...how wide the waves are", "...bigger b = smaller period" This is another reason I like the discussion to be public - so that everyone gets their brain stretched.</span></span></div>
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</tbody></table>
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<div style="text-align: center;">
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtams8JyijUKtb6LvdH1OO0xLNB2SeMKIcVU_CLTYv1gF9hrg_Wfsv0nby5IKMUG4q2VKvIbCi7E_HP6Pql-XUMyFhmev19xtSCUzzZzuidZdne4Qcw1pTOF-ps1iCZyiqSYsUvD0AqUI/s1600/grouptrigpost7.PNG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="574" data-original-width="833" height="275" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtams8JyijUKtb6LvdH1OO0xLNB2SeMKIcVU_CLTYv1gF9hrg_Wfsv0nby5IKMUG4q2VKvIbCi7E_HP6Pql-XUMyFhmev19xtSCUzzZzuidZdne4Qcw1pTOF-ps1iCZyiqSYsUvD0AqUI/s400/grouptrigpost7.PNG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="background-color: magenta; font-size: large;">Parameter b</span></td></tr>
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<b style="font-size: x-large;"><span style="font-size: large;">The Dynamic Phase:</span></b><br />
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Next it was time for them to add dynamic info to their ggb: the line of oscillation, textboxes showing the max and min, amplitude, frequency, and period. I emphasized that since we'd already decided that, for example, b affected the period, then the textbox about the period should include some kind of formula involving b...and amplitude should involve a etc, and in fact, they'd already seen those formulas in a <a href="https://voicethread.com/share/10137464/" target="_blank">voicethread</a>. So off they went to add to their ggbs. and I gave feedback in the private space. Lo and behold, there were mistakes aplenty, some of which I hinted at in my feedback. But I wanted them to be able to do their own detecting, to check their own formulas. So my next phase was...<br />
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<b><span style="font-size: large;">Check Your Own Formulas Geez!</span></b><br />
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Next day in class, we spent a few minutes filling in this table from the text:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF4IplUqbVPCxkMiM7XXI9po03bZMEODTWM1_PDuDCbAOL__8npqR6OJUXYPYB8hAhlGPEzMCnCdHCaeh4haqjXRiYvz-s2d8V-GuFsIoatieAFvB1uT9o8uQFLFJoN6L0djxE10suGQM/s1600/Picture1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="266" data-original-width="532" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF4IplUqbVPCxkMiM7XXI9po03bZMEODTWM1_PDuDCbAOL__8npqR6OJUXYPYB8hAhlGPEzMCnCdHCaeh4haqjXRiYvz-s2d8V-GuFsIoatieAFvB1uT9o8uQFLFJoN6L0djxE10suGQM/s400/Picture1.png" width="400" /></a></div>
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using what we <b><i>already knew</i></b> about how to find amplitude, period, maximum, and minimum. At this point they already, theoretically anyway, "knew" that amplitude = |a|, frequency = |b|, Max = k + |a|, etc. So this table was filled without geogebra, only math knowledge. Once we'd all agreed on the correct answers, and I'd done all the necessary intervention to make sure they were correct, I said ok - go to your geogebra and see if IT'S getting the right answers.....aaannnd....delightful <a href="http://audrey-mcsquared.blogspot.ca/2016/02/i-had-flashlight-moment-recently.html" target="_blank">flashlights</a> ensued!<br />
<div style="text-align: center;">
"oh no mine's giving -3 as the amplitude"</div>
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<div style="text-align: center;">
"mine says period is 2pi/3.5 how do I get it to actually calculate the period?"</div>
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<div style="text-align: center;">
"how do we set the b slider to pi/5?!"</div>
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<div style="text-align: left;">
Talk about differentiation, and just-in-time learning.</div>
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<b><span style="font-size: large;">A Turning Point</span></b><br />
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This step was really important, and it's one that I've been aware I needed to improve on - to <i>start with the math.</i> Instead of students relying on the tech, I want the tech to rely on them. It's one thing to get an answer right, it's another thing entirely to cause someone else - or in this case some<i>thing</i> else - to get it right. This step also addresses my fear of <a href="http://audrey-mcsquared.blogspot.ca/2013/12/digital-dust.html" target="_blank">digital dust</a> - that once these beautiful works of geogebra art are handed in, they are never looked at again. Starting this class with this table exercise went some way to motivating them to use their own work, but first they have to OWN their own work, to TRUST it. And in the process learn how to empower and trust themselves.<br />
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This time my feedback took even less time. A lot of things had already been fixed. But I did notice that things were getting verrrrrrrrry colourful!<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhze682l9tfVtDS9ylxH6Sfi3hBss93u5Q4rPAA1xOrO0LJGQcAtIzB-LRPNEHGORu-5MU8Cf-pcBgYNMvIjkfmnPRdT343ZwZ5DrdR4dNxt-4EbTjvTYV9D67EeC9Ham5OOBAQtD0dJJg/s1600/grouptrigpost8.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="788" data-original-width="1060" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhze682l9tfVtDS9ylxH6Sfi3hBss93u5Q4rPAA1xOrO0LJGQcAtIzB-LRPNEHGORu-5MU8Cf-pcBgYNMvIjkfmnPRdT343ZwZ5DrdR4dNxt-4EbTjvTYV9D67EeC9Ham5OOBAQtD0dJJg/s400/grouptrigpost8.PNG" width="400" /></a></div>
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<span style="font-size: large;"><b>Building on solid ground</b></span><br />
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The next task, version 2, involved adding features that depended on all the formulas already established and working properly in the first version. For example, I wanted them to add a dynamic textbox about the domain and range. Range, of course, depends on the max and min values, for which they've already written and verified their formulas: max = k + |a| and min = k - |a|. They could therefore just say "range = [k-|a|, k+|a|], and let geogebra do the calculations.<br />
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<span style="font-size: large;"><b>Cool, but the absolute best part...</b></span><br />
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This came about because my students instinctively did something in a way that I totally did NOT anticipate, and it actually made a lot more sense from a pedagogical point of view. So they kind of taught me how to teach them.<br />
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I had also asked for a few "sticky points", including what I call the boc (beginning of cycle) and eoc (end of cycle). (Sticky points btw are what I call points that always stay in the right location on the graph eg a y-intercept that is always on the y-axis no matter how the parameters are changed. <a href="http://audrey-mcsquared.blogspot.ca/2015/10/sticky-points.html" target="_blank">More on this here.</a>) The boc would therefore stick to wherever a basic cycle began, and the formulas I had in mind were boc = (h, f(h)), and eoc = (h + period, f(h + period)), but one student, who had elected to do the sine function, said to me, Mrs, isn't the boc just (h, k)?<br />
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And I replied "no, but you're close", thinking that she was confusing vertex with boc.<br />
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And then one by one, my students, at least those who had also elected to do the sin function, thought about it, and said Mrs she's right. The sine function starts on the loo (note - that's what we call the line of oscillation), which is k. Then the cosine people started to ask well that's fine for you guys but what about the cos where does it start oh wait it starts at...the max oh ok. And one asked me privately "isn't that only if a is positive? If a is negative doesn't it start at its min? how do we do that in ggb?" And I, the teacher, who is supposed to know everything, didn't have an answer for her. Yet. It was awesome.<br />
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AND EVERYBODY LEARNED SOMETHING.<br />
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I had NOT anticipated anyone doing it this way - by using the key points (max, min, loo) that apply to the actual function they've chosen, and now I realize the HUGE benefit of doing it this way. It forces everyone to really look at the structure of the wave, that sin with a>0 is loo-max-loo-min-loo, cos with a>0 is max-loo-min-loo-max. And it's different when a<0. Next year....this will be in my improved game plan.<br />
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It's funny, I had originally let them do only one function, sine OR cos, because I didn't want to overload them, but it turned out to be a starting point for a deep discussion between two camps - the sine people and the cosine people. Once everyone's version 2's are all corrected and verified, I'll get to ask "Can anyone think of a formula for boc that would work for BOTH functions?" That'll be when boc = (h, f(h)) & eoc = (h+p, f(h+p) would have a bigger impact anyway. I'll also have them discuss which formulas are the same in both camps, and which are different. EEEEEEE I'm SO looking forward to that.<br />
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<b><span style="font-size: large;">The advantage of the function summary in GeoGebra:</span></b><br />
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I maintain that getting them to do this task, to make something else work properly by using their math knowledge, is the closest I can get my students to becoming teachers, which, it is generally agreed, is the best way to learn something - by teaching it. They're kind of teaching geogebra what to say, what to look like, and where to put the points so they stick. And it's lovely. Each discussion that springs out of these tasks is richer and more meaningful because of the ownership, or maybe it's called agency now, of the work. And each discussion leads to other even richer ones, for example after the boc one, we moved on to the eoc, which of course will have an x coordinate that is one period further afield than the boc. But the path to a student realizing that is fascinating to watch, and talk about an aha moment. And who already has a verified formula for the period? My kids do.<br />
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<b><span style="font-size: large;">The advantage of the marriage:</span></b><br />
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As I mentioned before, the flow is hugely improved. It's so many fewer steps, for all of us, to get the back-and-forth that's so valuable. I've always tried to set things up so that my students feel like I'm running the marathon alongside them, rather than just standing at the finish line with a red marker pen, but the way groups are set up, it's so much easier. This private convo:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdz4VcqK7zUkk4MBf520dTzXnaL4dyvDsvZrtJsCYqobO3L-Y7D8MHm5CZjtwD9htSGljp3271nLcC9VZ3M7Y1tSmTYoQxQfUHPJfqqq3BbqXioD7Ld_HN5AAB-oeclDkthxMVhWg5F6s/s1600/Capture.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="375" data-original-width="753" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdz4VcqK7zUkk4MBf520dTzXnaL4dyvDsvZrtJsCYqobO3L-Y7D8MHm5CZjtwD9htSGljp3271nLcC9VZ3M7Y1tSmTYoQxQfUHPJfqqq3BbqXioD7Ld_HN5AAB-oeclDkthxMVhWg5F6s/s400/Capture.PNG" width="400" /></a></div>
<br />
...which happened in the group space would otherwise have taken at least 3 save/upload/download/give feedback/upload/download cycles and it wouldn't all have been in one place. To say nothing of the impact of the public forum on that social aspect of learning. I feel I've only just seen the tip of that iceberg.Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-1043597826599085122.post-51036531031277884662018-01-17T13:03:00.000-08:002018-01-19T06:57:16.306-08:00First attempt at stations in the live online classI've been trying to find an alternative to the usual group work, and also, I've long been wanting to try out "stations" in my live, virtual classroom. The trick was how to simulate easy movement, make clear goals at each station so I don't get run ragged, keep things moving, and have time to process the math at the end. Today I finally did it.<br />
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In our environment, the closest thing to a station is what we call a breakout room, or bor for short. They are really just other websites, of course, that are somehow attached to the main classroom. Here is how they usually look from the dashboard:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDUo0YjxJufQg4qVKbIoivN8IlRIAWL4rjIH9v2GOeDam1LF9PZuRwlVzWAYZ9k-zbE_Bdu5d-X9HYDCWE1Ll870JcoGcpsQ2QzQbrqk8fuT18GgbzLKbQAhafUjaHMr-iKge3hFFgg4c/s1600/usualbors.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="98" data-original-width="95" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDUo0YjxJufQg4qVKbIoivN8IlRIAWL4rjIH9v2GOeDam1LF9PZuRwlVzWAYZ9k-zbE_Bdu5d-X9HYDCWE1Ll870JcoGcpsQ2QzQbrqk8fuT18GgbzLKbQAhafUjaHMr-iKge3hFFgg4c/s1600/usualbors.PNG" /></a></div>
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Usually, I put students into whichever room I want by dragging and dropping their name into it, much like moving a file into a folder, and in fact it ends up looking that way too (pretend I'm a student):<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjg33BKVxhxMqMuOAdYSi2e_qd64EK2fbngboZNaQOihMETigXvqmAkTGl9X9t8PLoCkyHLvzfv8BPC3T-8GCav9mJ0THXSl_YPoWcM9OCEmXn0b1F-4FWAYcgvGaC5Xi0xVGdWbKkGkT0/s1600/usualborswithname.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="114" data-original-width="175" height="130" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjg33BKVxhxMqMuOAdYSi2e_qd64EK2fbngboZNaQOihMETigXvqmAkTGl9X9t8PLoCkyHLvzfv8BPC3T-8GCav9mJ0THXSl_YPoWcM9OCEmXn0b1F-4FWAYcgvGaC5Xi0xVGdWbKkGkT0/s200/usualborswithname.PNG" width="200" /></a></div>
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But I can create as many bors as I want, and call them what I want, and make them any colour I want, so today, here is how my stations looked:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8PkWqbn5ShfrAkfegF_VLaKXWZ5Yn_lOcUwkTwHJnkBQGdpuuiUSklTrK6ctZiK5VPNTZMD9mpL0_BaqrK_VxPeomtLVrAb4m-_XPtU_3DrU-eLVN-28wWr8asd-IeYMh62yaurlcGeo/s1600/bors+-+Copy.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="137" data-original-width="183" height="149" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8PkWqbn5ShfrAkfegF_VLaKXWZ5Yn_lOcUwkTwHJnkBQGdpuuiUSklTrK6ctZiK5VPNTZMD9mpL0_BaqrK_VxPeomtLVrAb4m-_XPtU_3DrU-eLVN-28wWr8asd-IeYMh62yaurlcGeo/s200/bors+-+Copy.PNG" width="200" /></a></div>
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Why did I set them up this way? Because this was the activity:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEIrzWOWcXht97V15entIjt2igjg_my1RuZN1UvSPn3OyC95vgchAaVEDFG01xgo6ZfR43B3bzdcfx8m2DcrtoN8ZJLXdJvs6o6waemRDJCxg7B7ApMQXUcXfclh3FyDBEwwQox8dNvxA/s1600/task.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="641" data-original-width="858" height="297" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEIrzWOWcXht97V15entIjt2igjg_my1RuZN1UvSPn3OyC95vgchAaVEDFG01xgo6ZfR43B3bzdcfx8m2DcrtoN8ZJLXdJvs6o6waemRDJCxg7B7ApMQXUcXfclh3FyDBEwwQox8dNvxA/s400/task.PNG" width="400" /></a></div>
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The task was to shade equivalent boxes in matching colours, using the properties of exponents, and the exponential situations we've studied so far, including rational exponents, negative exponents, and the property (a^n)^m = a^(nm).<br />
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Here's how it went down, along with how it would look in a brick and mortar situation, in case it's hard to get your head around what the heck I'm talking about:<br />
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<span style="background-color: white;"><span style="font-size: large;">Step 1: Simulate easy movement:</span> </span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">First I gave them all moderator status so THEY could move themselves into and out of any bor they wanted. This way they all get to go to each room at their own pace, plus I found it was a nice break from me picking who is going to work with whom. Also it makes it feel more like they're moving around in a classroom station situation. We first practised that a bit, so they could get used to the controls.</span><br />
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<span style="background-color: white;"><b>Brick and mortar equivalence:</b> Kids can usually move around in a classroom.</span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;"><span style="font-size: large;">Step 2: Clear goals at stations</span></span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Upon entering a bor, they all saw the same slide, which was the one above. Then, if they were in the turquoise bor, they'd </span><span style="background-color: white;">colour in (using the virtual highlighter pen) all the things equivalent to </span><span style="background-color: cyan;">y = (1/2)^x</span><span style="background-color: white;">, if they were in the yellow bor, they'd colour all the things equivalent to </span><span style="background-color: yellow;">y = 3^x</span><span style="background-color: white;">, etc. </span><span style="background-color: white;">Students can see what bor they're in, so again, it's all as obvious as if they were in a brick and mortar classroom.</span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;"><b>Brick and Mortar equivalence to this:</b> Having 4 big tables, each with a giant place-mat like the above, preferably with a covering that makes it easy to erase, with each table equipped with highlighter pens in only one of the four colours, so there's a bunch of turquoise pens at one table, and a bunch of pink pens at another etc. It's important that the highlighter pens be erasable though, and I don't know if such a thing exists. So also you'd need erasers.</span><br />
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<span style="font-size: large;">Step 3: Keep things moving</span><br />
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After a few minutes, I said "Change rooms!" and watched their names jump around. I had already told them that if they agreed with the colouring that had already been done, leave it there, and see if there were any other things that should be coloured. If they disagreed with what was already coloured, they could change it. The idea was that this would filter out the easy egs from the harder ones, by a loosely formed consensus.<br />
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<b>Brick and mortar equivalence: </b>Saying change stations, whereupon students move to another table. They can change what's already coloured and add as needed. I'd probably have to make sure the right coloured pens would stay at the right table!<br />
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<span style="font-size: large;">Step 4: Keep things moving and varied</span><br />
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Repeat step 3 twice, so that everyone has had a chance to go to each station.<br />
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<span style="font-size: large;">Step 5: Process the math</span><br />
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I took snapshots of each of the final bor screens as everyone moved them selves back to the main classroom.<br />
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<b>Brick and mortar:</b> Telling everyone to go back to wherever they usually sit while I gather the place mats.<br />
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Step 5: I displayed each snapshot, we discussed, I showed the answers, and we discussed some more. <b>(Brick & Mortar I'd do the same.)</b> Here are a few of the actual ones, compared to the answer slides:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlScS4IMigBqW0u7vRcJMi761BmTe_3NUrnw-oN3V-2BKrEQ30J18tttuRc46YwthCNOVGXUszKFNMYlSN01AM1zs8OY8UKAmLcKIXyggIf3cShoDDuJU6Y6LNZ8cmdTTGcd8DjroEZjE/s1600/borblue.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="524" data-original-width="716" height="234" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlScS4IMigBqW0u7vRcJMi761BmTe_3NUrnw-oN3V-2BKrEQ30J18tttuRc46YwthCNOVGXUszKFNMYlSN01AM1zs8OY8UKAmLcKIXyggIf3cShoDDuJU6Y6LNZ8cmdTTGcd8DjroEZjE/s320/borblue.PNG" width="320" /></a></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDKqP16Ar6bVlx9vWmtcwPvPPWAg6XP4GZcgxfOrDCZvpTCFOwQ3qjJXM3UVKdCVFAZZw4aQCruBOPjeGU8meJN2XVbtwopDqh12Og9lgHac6tAWLT4hblar0fKrvJnor4z7QIf9CYf98/s1600/borturquoise.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="789" data-original-width="1045" height="241" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDKqP16Ar6bVlx9vWmtcwPvPPWAg6XP4GZcgxfOrDCZvpTCFOwQ3qjJXM3UVKdCVFAZZw4aQCruBOPjeGU8meJN2XVbtwopDqh12Og9lgHac6tAWLT4hblar0fKrvJnor4z7QIf9CYf98/s320/borturquoise.PNG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="color: cyan; font-size: small;">The turquoise were all correctly coloured</span></td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSD08VtkWOFF83EhdjKrKbKGgDHjFU_GkHuvVZBCkCGZlM1wE_6A-b-BJbOarQkrRXQx6WBR8CUH8-a04e5F2GJVXxgY_srmlZC6_v4kW10m163RpF-6zNF9gUOuWPWqu1GS20PuPBhvY/s1600/borgreen.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="519" data-original-width="696" height="238" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSD08VtkWOFF83EhdjKrKbKGgDHjFU_GkHuvVZBCkCGZlM1wE_6A-b-BJbOarQkrRXQx6WBR8CUH8-a04e5F2GJVXxgY_srmlZC6_v4kW10m163RpF-6zNF9gUOuWPWqu1GS20PuPBhvY/s320/borgreen.PNG" width="320" /></a></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBgpRr6VcFqN1I_nl9trDalEgoD393rWDYb1W6xrUMSJzmGWhBfDIqP3PFpAUznKKfZOjbB8wJtpIMofxp8RZdtTFywZAuA2KjUWSX5V5TEI4Lkm0huXCEImAycBjZuIooy7Qne-m4-_0/s1600/borgreen.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="772" data-original-width="1043" height="236" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBgpRr6VcFqN1I_nl9trDalEgoD393rWDYb1W6xrUMSJzmGWhBfDIqP3PFpAUznKKfZOjbB8wJtpIMofxp8RZdtTFywZAuA2KjUWSX5V5TEI4Lkm0huXCEImAycBjZuIooy7Qne-m4-_0/s320/borgreen.PNG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="color: lime; font-size: small;">The greens were mostly correct</span></td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGAxrWIe-FBX__FsmpDDyDjgftaU4Wgo9hRiz1L5N4LAsqAlU9uPpbqGJOjNZmAHIbTOJWN3r4O2GFD1327bpQDNaPbXcrdAbe2qtTSXZcz4sdSjdtjbzGnYZ3QH7ZfwP4Jz3NNJKGp9I/s1600/borpink.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="499" data-original-width="696" height="229" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGAxrWIe-FBX__FsmpDDyDjgftaU4Wgo9hRiz1L5N4LAsqAlU9uPpbqGJOjNZmAHIbTOJWN3r4O2GFD1327bpQDNaPbXcrdAbe2qtTSXZcz4sdSjdtjbzGnYZ3QH7ZfwP4Jz3NNJKGp9I/s320/borpink.PNG" width="320" /></a></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrJ8qUh2J2ihd9suzsbEvhfB8L4skdAQiZhxnNpUCMs36dumvZL-6FvS1MSKvuv3wBRm9MkW23B_XS4LDedLOCCmomOBcQgnlv3g7uAfm97qNtwgh1XUqUnW8EcSNQmMp6rVl65Y8TT7w/s1600/borpink.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="774" data-original-width="1028" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrJ8qUh2J2ihd9suzsbEvhfB8L4skdAQiZhxnNpUCMs36dumvZL-6FvS1MSKvuv3wBRm9MkW23B_XS4LDedLOCCmomOBcQgnlv3g7uAfm97qNtwgh1XUqUnW8EcSNQmMp6rVl65Y8TT7w/s320/borpink.PNG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="color: magenta; font-size: small;">Missing a few pinks and one incorrect</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1IBmZEKebKcVPq5XWLWreJmPj38Oq9H4cDK_1RvRkeq2nwsLsFU1nU2lZW7eiYy_Ko5x5WjB46iKTWssRqqlEuT9qruNmfqhoToofjNDnnVz-K6E6M9Kozxezh71rPTG12mhUY6fB1QQ/s1600/boryellow.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="517" data-original-width="695" height="238" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1IBmZEKebKcVPq5XWLWreJmPj38Oq9H4cDK_1RvRkeq2nwsLsFU1nU2lZW7eiYy_Ko5x5WjB46iKTWssRqqlEuT9qruNmfqhoToofjNDnnVz-K6E6M9Kozxezh71rPTG12mhUY6fB1QQ/s320/boryellow.PNG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Add caption</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeqczCZKsJxU-J97QmoRiPeagO9D2kMc3Sdg1I9wJOaTpau62OsHLNWol6yoareEiC7lYpN_pd-hIkoQmMaQZDWKLMtqpK8RJmLn2nvGyvqWykvBn8nUoBkj8kIurSlQ4v8RLD6YHD6HM/s1600/boryellow.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="780" data-original-width="1044" height="238" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeqczCZKsJxU-J97QmoRiPeagO9D2kMc3Sdg1I9wJOaTpau62OsHLNWol6yoareEiC7lYpN_pd-hIkoQmMaQZDWKLMtqpK8RJmLn2nvGyvqWykvBn8nUoBkj8kIurSlQ4v8RLD6YHD6HM/s320/boryellow.PNG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="background-color: yellow; font-size: small;">And missing a few yellows</span></td></tr>
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Here's where my evil plan started really playing out:<br />
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<ul>
<li>Each colour had some really obvious ones that were not in dispute, like 3^(-x) and (1/3)^x, so we didn't have to spend much time at all on those. </li>
<li>Each colour also had some that weren't so obvious, like why is 27^(-x/3) the same as (1/3)^x? Also the one about why losing 2/3 gave a base of 1/3. This was a chance to add a layer to their understanding of exponential properties. I asked for volunteers to explain these.</li>
<li>Each colour had something that I anticipated no one would colour, and bingo, I was right! These examples involved e, and for most this was the first time they'd seen it. So this was a nice way to introduce it.</li>
</ul>
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I usually try to think of what I'd do to improve, but all I can think of is additional examples to add. Since there was no dispute over the turquoise, that could use something in it to uncover a gap in understanding. Otherwise, this went well, and it didn't take a lot of set up, since there was only one slide for all the rooms. Also, I didn't have to chase after any actual pens!</div>
Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-1043597826599085122.post-62989857433879033812017-11-10T12:52:00.000-08:002017-11-10T12:52:36.813-08:00GeoGebra Group HugI've been getting my students to create their own GeoGebra applets for a while now. If you're interested in the big picture of what and why, you might want to <a href="https://audrey-mcsquared.blogspot.ca/2013/11/more-student-created-geogebras-and-some.html" target="_blank">read this first</a>. I'm doing the same overall thing this year, but this time, I'm incorporating GeoGebra groups. And this post is a big GeoGebra Group hug. Groups have been around for a good two years now, but it's only this year I really dove in.<br />
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Every year when it's time to get my students using GeoGebra, I start with the linear function, with which they are theoretically already familiar. This way we spend most of our time getting familiar with the platform as opposed to the math, first time around.<br />
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<span style="font-size: large;">How-to:</span><br />
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First, I created a group for us. Then, I had them create accounts at GeoGebra, and join our group. This is all pretty easy - <a href="https://www.geogebra.org/m/rQrbooeq" target="_blank">here are some instructions </a>if you need them. Here's my first post to the group, which was their first "task", visible as soon as they'd joined the group:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZWatG5WS04-FJgnPKIYbdGuN5nN-cZ4rYnv0QRD7iti7HUcFMWengQfkczutWY9-HsqTo-L_HPwxACEoSPDF7d3rt-6TFkjBNie940QJjmFhdrmzCn-QiU3ASMcGK3INluBeUqA9F7t4/s1600/task1post.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="423" data-original-width="1227" height="219" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZWatG5WS04-FJgnPKIYbdGuN5nN-cZ4rYnv0QRD7iti7HUcFMWengQfkczutWY9-HsqTo-L_HPwxACEoSPDF7d3rt-6TFkjBNie940QJjmFhdrmzCn-QiU3ASMcGK3INluBeUqA9F7t4/s640/task1post.PNG" width="640" /></a></div>
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As you can see, there is a place for them to comment right there under the post, which for this task, I didn't ask them to do (but some are just naturally friendly!). Comments posted here are visible to everyone in the group, and we can all reply to comments. Anyway, once they clicked where it says Linear1, they saw this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQ06ccny-LYq3YHNIFOzA9pvJTQj3B9-767AC7cTx-_IjBr9DIll-Fi_BQL_Mcat6rJYygubZp-OTriYh9tPdjRjzG-eD5P5aREEkz1aw0RMPtGPWOnrmF08Pfw0nsasFviBYhYSC8vO4/s1600/task1applet.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="714" data-original-width="891" height="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQ06ccny-LYq3YHNIFOzA9pvJTQj3B9-767AC7cTx-_IjBr9DIll-Fi_BQL_Mcat6rJYygubZp-OTriYh9tPdjRjzG-eD5P5aREEkz1aw0RMPtGPWOnrmF08Pfw0nsasFviBYhYSC8vO4/s640/task1applet.PNG" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaegTEJ03giEa5VEL9HnJvTxXv4lAx46czGpslVY1ogiy9QN_dtp-SZSBeiYPoZ565U96p8H8v_ASmeFcW4ZR_uNqlCzg692Up_BuuJYhYIcm6LV_5611tjEw2lAcKJiNCGKbcG0QHRLM/s1600/turnin.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="118" data-original-width="563" height="82" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaegTEJ03giEa5VEL9HnJvTxXv4lAx46czGpslVY1ogiy9QN_dtp-SZSBeiYPoZ565U96p8H8v_ASmeFcW4ZR_uNqlCzg692Up_BuuJYhYIcm6LV_5611tjEw2lAcKJiNCGKbcG0QHRLM/s400/turnin.PNG" width="400" /></a></div>
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How it looks to me, the owner of the group, is almost the same except instead of the turn in button, I have, for obvious reasons, this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7Bt4yCL595ZEtL6XT7dNlKpaq42egfyN0zsQLWnCqvuW4hZoZRMjBW6D_CEY74DD9qOJfgYCnlHmskwHIEdNmBJDxXIsmpDTnumYAihey4L_CW_Mhps6MqaYpUrrXafw8oLN0P18i0ig/s1600/complete.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="44" data-original-width="140" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7Bt4yCL595ZEtL6XT7dNlKpaq42egfyN0zsQLWnCqvuW4hZoZRMjBW6D_CEY74DD9qOJfgYCnlHmskwHIEdNmBJDxXIsmpDTnumYAihey4L_CW_Mhps6MqaYpUrrXafw8oLN0P18i0ig/s1600/complete.PNG" /></a></div>
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<span style="font-size: large;">Hugs right off the bat:</span><br />
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My first favourite thing is right there in the instructions - that they don't have to each make their own copy - it's all done. This alone saves them, and me, SO MANY CLICKS.<br />
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I gave them a simple task, which, once they were done, they just turned in by clicking the button. If they wanted to, here was another opportunity for them to make a comment, but the difference between doing it here and on the previous space is here only I will see it. Nice opportunity for intervention.<br />
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I also love love that I can reply here, and we can have a conversation if necessary. This is the first mathy edtech tool I know of that has this continuous two-way conversation capability.<br />
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Next lovely thing is as they were all working, I refreshed every so often so that I could see where they all were via a "feedback" table, which shows me, in one glance, who has started, who hasn't, who has left me a comment. Right now it doesn't look at all like it did live but it was pretty cool. An updated table appears later in this post.<br />
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Eventually, all were turned in, so the next phase was me looking at them all.<br />
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<span style="font-size: large;">After turn-in, more hugs:</span><br />
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Another enormous saving of clicks. All I had to do was open up one of their sheets, comment if I wanted (and I did), then click "complete" or "incomplete" and the next student's work is automatically opened. I think I screamed when that happened. I was like - you mean I don't have to save anything, then go somewhere else to open up the next one, wait for some program to start.......nope.<br />
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So this is now a cycle that repeated as needed. If anyone needed to fix something, they did, if they have a question, they put it in the comment, then turned it in etc etc.<br />
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<span style="font-size: large;">Bigger picture, bigger hugs:</span><br />
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After a few of these tasks, this is what my feedback table looks like:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRKhKe4W7qEnb8SjtEsxME7VEYl-5vMBQ3lZzSSyEMIVwwUcyB4HddIGVir8g6jURljeo0RhvloV47tzgIc788NtNR0f6QEOPRYW0e5Xr4We7tTyEbXnjoGb0xrz_MGtsdV0N4cT8WVGI/s1600/feedbacktable2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="785" data-original-width="794" height="632" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRKhKe4W7qEnb8SjtEsxME7VEYl-5vMBQ3lZzSSyEMIVwwUcyB4HddIGVir8g6jURljeo0RhvloV47tzgIc788NtNR0f6QEOPRYW0e5Xr4We7tTyEbXnjoGb0xrz_MGtsdV0N4cT8WVGI/s640/feedbacktable2.PNG" width="640" /></a></div>
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In a glance, I can see who has started, who hasn't, who has turned it in, whose is all good, whose needs fixing, who was late, who has left me a comment. I can open up anyone's work in a click. It's just lovely.<br />
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I love the flow. It's not quite live yet like a Desmos activity, but it's pretty close.<br />
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Next post will be about my next foray in which I used the public comments section.<br />
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<br />Unknownnoreply@blogger.com6