Fun activity for linear systems

I got this idea literally on my way into my classroom today, so I'll make it better next time, but based on how well it went today, I'll definitely try it again:

This is what I told them to do, and how I demo'd it for them on the board:

Me: Next work out how much x + y is for your ordered pair, and write the equation to express the result like this, but of course put your own result:

Me: Next work out how much x - y is for your ordered pair, and write the equation that expresses that result:

Me: Ready? Okay, Susie, tell us how much your x + y and your x - y were:

Me: How can we figure out what Susie's ordered pair was?
Class: Guessing? Asking Susie? We can't?

They didn't see this as a system of linear equations, which is weird because that's what we were doing yesterday.....it seems that since they each had a secret ordered pair and equations of their own making, it all looked different than it had yesterday.

So I gave them a hint:

Me: What happens if we add the two equations together?

Class: Oh! We get 2x = 18..... so x = 9?

Me: I don't know......Susie is that right? Was your x = 9?

Class: Whoah!!!!!!!!!! For real?

I swear it was as if I had just levitated. Like I had David Blain-ed right there and then.

Now that the cat was out of the bag, it was a simple matter for them to find Susie's y coordinate. Next I asked Joe to give us his equations, and for everyone to direct their solutions to him. Now Joe got to have that feeling of satisfaction that we (sometimes) get - to say to someone yes, you're right, you got it!

All I said next was okay who wants to go next and my board lit up like a geogebra Christmas tree. Everyone wanted someone to figure out their secret ordered pair.

Then I told them that this is how teachers make up questions for them - starting with the ordered pair, then working out equations using it, but of course the equations aren't usually as simple as x + y = ... or x - y = ....

Take-aways for me:

• Getting them to SEE something clearly is so much harder, but so much better, than getting them to DO something correctly
• The initial steps were simple enough to bring everyone in, unsuspecting of the learning that awaited them
• The system was just easy enough to solve quickly, so good to start with that, but next time I'll have them make up more complex linear equations afterward
• Each person made up their own unique numbers, so they kind of owned them, which made it more important that someone else get the right answer than if I had made it up
• I have to hand it to me, I shut up really well, and let the owner of the solution give the nod each time
• Nice lead-in to the next thing we're doing, which is solving word problems using systems. I'm hoping it'll help them make the connection between the variable and the quantity it represents.

Weird how the best inspirations seem to hit me at the least convenient time, like on my way into class, but it happens often enough that it can't be a coincidence. Desperate need truly is the mother of invention!

A horrible moment

Sometimes I think someone could write a sitcom using my life, and it would be really funny. But it doesn't feel funny at the moment.....

To get how horrible today was, you have to understand that I teach online, in a live classroom, in which I cannot see my students, and they cannot see me.  But I can share my screen with them, and give them control of my cursor. Who would do that?

I would. And I was doing just that this afternoon with my students. I shared a geogebra file, and I gave cursor control to one student. He then inadvertently minimized my geogebra file, which revealed my twitter @mentions page, which was still there because I had checked it just before class. A couple of kids said haha miss you're on twitter, bad teacher! I didn't think anything of it, I just minimized that and got geogebra back, and we continued.Then class was over. I logged out of class, went back to twitter to see what they had seen for those few seconds.

You know how sometimes you get people following you and you immediately block them because they are clearly, um, not using twitter for the same reason you are? Well one of those people had, just moments before class started, sent me a message that was, in this person's words, "naughty and nice." I had immediately blocked that person, but that doesn't erase it from the display.....and that is what my students saw when geogebra got minimized.

Not exactly I Love Lucy, is it? This is what I looked like, I'm sure.

All I hope is that by the time Monday rolls around, I will be able to laugh at this. And be employed at the same time.

A wonderful moment!

Today one of the things I wanted my students to do was to go to a site that I love called www.betterexplained.com, read any post that they fancied, and leave a comment right there on the site. I wanted them to read Kalid Azad's brilliant blog, which is not only brilliant, but brilliantly written.

I also wanted them to experience firsthand some of the wonderful resources that are out there, and maybe even get an appreciation for blogging, since they'll be doing that soon for me.

Well, during class, one student posted a question very quickly, because he had already read an article earlier in the week (why? because it's a flipped class, and students can go at their own pace!). Fine. They are all working, I'm helping kids etc, when literally 6 minutes later, this young man private messages me:

"HE JUST ANSWERED ME!"

And he had! During class! Talk about your teachable moment! I stopped everything, we all checked it out, and they were pretty impressed that there was someone from "the outside world" communicating with one of ours!

I had reassured them that he would answer them, but this was completely unexpected! The fellow who left the question said he felt kind of famous! Couldn't have asked for a better way to show them that there is a whole world out there, in which they can safely and joyfully participate in lifelong learning.

Thanks, Kalid!

Gotta love geogebra tube!

Now that geogebra tube is here, it's super easy to give anybody a geogebra worksheet to play with, even if they don't have geogebra installed on their computer. I just give the kids this link, they do the activity, take a snapshot (amazing how many don't know how to do that, talk about just-in-time learning) and upload that to their dropbox for me to see.

Tried embedding it here but having problems getting it to appear exactly as it should, but the link works great.

Who I am NOT!

I have several friends, some of whom are teachers, who think I am some sort of technological genius. I tell them excitedly about something new that I have learned how to do with googledocs, or camtasia, or about a conversation I had on twitter, and they just say, "Oh Audrey, you are such a technological genius!"  Then they shake their heads, chuckle affectionately, and stop listening to me.

 
But I so want them to listen to me. Because of the fact that I am NOT a technological genius. There are many, many people out there who are WAY smarter than me, and who have figured out how to do all this really cool stuff, and what's more, they love to tell people about it, for free! And because of those people, look at what I, NOT a technological genius, can do!

 
This week's new thing I learned how to do:

Like for example, after last week's epic victory for one of my flipped classes that I felt was slipping away from me, I decided that one improvement to my whole modus operandi would be to give quick quizlets that would give me and the kids instant, online feedback. When neither explorelearning's gizmos nor khanacademy's practice questions covered exactly what I wanted, I realized it was time to make my own, using the assessment templates made available to the world at the blog of Andy Schwen. One of those really smart people I was talking about.


And here it is, my first attempt! If you're not sure what this is about, the quickest way to find out is to try the quizlet yourself. If you are willing to input your actual email address, then you'll get to see what the students see when they do this. Don't worry about getting anything wrong, it doesn't count! For "first name, last name" just put any name you want, and don't worry about "hour" either. Just make sure you click submit after you've selected your answers, then check your email. For the most interesting email, make sure you get at least one wrong, trust me.



If you did this, you should have received an email, from me, that looks something like this, which is the one I got when I did it, pretending to be one of my own students:

You should see the score, the questions that you got wrong, and an explanation.
(Once I really get going with this, the name and the hour will matter, because that's how you can give the same quiz to different classes, in whatever school year you want.)

Now for the real payoff....inspiration!

I know my questions and my explanations are rudimentary and not terribly deep. But I already have ideas of how to improve on it: instead of text explanations, a link to a better explanation on the web, and instead of text questions and answers, ones with pictures in them..... and I can't wait to try it out - how many people do you know who feel that way about their job?

Which is the real reason I want my friends to listen to me. They are missing out on so much, all because of the misperception that you have to be a technological genius to do this. They think I actually know how it all works! I'm pretty sure Andy Schwen would be able to set them straight on that....as poor Andy knows all too well, I needed a lot of hand-holding, but with his help, I did it, which means anyone can! His instructions are amazing and easy to follow. And there are a lot of people out there who offer the same thing to the world - their own expertise and help, for FREE!
To my friends who don't listen to me: You owe it to yourself to try this, or SOMETHING! But don't listen to me because you think I am a technological genius, listen to me because I am NOT!

Don't MAKE me right-click you!

From my perspective, the class that had the most negative feedback about flipping last week went much better this week. In fact, I think it's that feedback that may well have saved that particular class from entering a death spiral. What's with the right-click? In the live, virtual classroom, it's all I need to remove a student. Significant to today's topic....

My week (why didn't I do this one day at a time?!?):

Monday: Face the music.
I let them all know that I had read their comments about flipping very carefully and taken them very seriously. I told them the main themes I had inferred, paraphrased of course:

• too many voicethreads to watch in a week
• too much work to do in a week
• not enough time during class for questions and individual help
• not enough teacher to go around for all the people who need help
• foolish banter going on in the chat during class is very distracting
• nobody wants to ask questions on the voicethread because nobody wants to look stupid
• it's better to learn something live with a group so you can hear their questions

Then I gave them my pledge to do the following:

• I will control my urge to talk
• no more than 3 voicethreads per week
• which will result in less work
• I will give more time for questions during class
• I will be more systematic about helping people
• Which will result in more teacher to go around
• I will remove from class anyone who continues to distract with foolish banter (everyone is one right-click away from that in the online class!)
• I will mix things up so that sometimes we are doing a lesson and sometimes we are doing work.

What I ask of them:

• control your urge to banter foolishly
• ask for help only after you have made the effort - ie watched the lesson, or tried some examples, or something
• take the responsibility to prove to me that you have made the effort - ie leave a comment on the voicethread, hand things in, keep your checklist up to date, use it to ask for help
• if you are too self-conscious to post a question on the voicethread, make it a private question, which I will answer publicly, but without identifying who asked it

That little speech took a while, of course, so right away, on Monday, they did not have enough time to get the gizmo and the worksheet on distance formula done....oh well, I told them today is an exception. They worked well, things were quiet. Voicethread on slope for homework.

Tuesday: Taking it out for a test drive.

Started out with foolish banter! Incredible! Did Audrey do what she said she would? No. Wimp that I am, I scolded with "Seriously? After what I said yesterday?"  "Sorry miss". The rest of the period was work, questions, help, etc, great. I got to everyone that needed me, but not too many needed me. No voicethread for homework.

Wednesday: Right-click day

Foolish banter. Wow. Right-clicked one kid out of there. Did not even have to tell anyone why. Foolish banter stopped immediately. Did an activity on slope with everyone in the class. Because I need to talk to them as a class a little bit and because they need to work together and know what they are all thinking. And I thought it would give a visual on what we're doing next. But it took too long. Sigh. They had only 25 minutes to do work/ask questions. So I eliminated one item from the checklist. I figured I'm the one who should pay, not them. One girl immediately thanked me! Nice! Tonight: voicethread on midpoint.

Thursday: Turning point? Maybe?
No banter. I got an inspiration: I wrote the current tasks on the eboard and systematically went through them like "Who has questions about this?", starting with the least recent item. I then helped that group in a bor. Came back to main room, repeated for the next task. Answered everyone's questions, got in some practice with those who needed it. I had 8 minutes left at the end of the period for miscellaneous stuff, like questions about tomorrow's topic, from someone going ahead! Wow. That felt good. I also had a talk with the one who got right-clicked. All good. I noticed that one person had already filled in the feedback paragraph for this week, and she is very happy with the new structure. She even said that she likes having a place to give feedback! Can't ask for more than that.

Friday: Bring it on.
We'll see what happens. I hope I don't have to right-click, but I got my finger on the trigger. I enjoyed yesterday too much to slide back now, and I think everyone else did too. Last night they had to watch the third and final voicethread for the week, on division points of a line segment. So far, I see 5 comments (out of 11 students). I'll group them as yesterday, but this time I'll start with the most recent task, which is the division point practice questions. That way, the kids who are the most up to date don't have to wait for everyone else, and hey, maybe they'll even be able to help the others. 
  
Now that things are more organized, I can think straight. My deep thoughts are flowing.

• Every week from now on, every class will be invited to give feedback. For now, I'll suggest a topic, but it will always be open-ended. It's absolutely invaluable. Thanks to just this one week, I feel so much better about this class. I knew it was getting off track, but I just couldn't get my hands back on the steering wheel. Thank goodness for these kids and their intelligent, honest, constructive words.
• Immediately after each voicethread, their first task will be a super-quick quiz, like 4 or 5 questions, with immediate feedback for them AND for me, something that shows up at my end right away so I can see who is doing it and how they are doing. Like the gizmo assessment questions at explorelearning, or the khan academy practice questions, or, if I can get my act together, my own questions using Andy Schwen's assessment template. The key is- I don't have to spend any time checking their checklists, or asking them, to find out if it's done or if they're getting it. I just have to look at my computer screen. Then it is ON, and I know where to start to fix any basic problems before they dive into the fun stuff. It could even be a way for some of them to skip over a voicethread! I just thought of that - if they already know something, they shouldn't have to "learn" it from me!

• Once a week, I'll have a period in which we all do the same thing, either all together or in groups, whatever, an activity in which we learn/discuss/react to/process something together. That day there will be no work to hand in or correct. So it will have to be on something that they are ready to go deeper into, or maybe an intro to what's next. There might be a voicethread for homework, but that's it. That will be their work for the day. Ideas for that:

• Individual or small group presentations.
• A Malcolm Swann activity in small groups.
• Watch a video and react to it.
• Read a blog and react to it.
• A webquest.

Now I don't want to give the impression that I enjoyed kicking someone out of my class. My own reluctance to follow through with it is proof of that. I much prefer getting my message across by modelling the behaviours I value, like maturity, accountability, open-mindedness etc, but you know how it is. Sometimes people just need more than that, myself included, After all, I needed to hear the brutal truth from my students in order to grow as a teacher. It was kind of like being right-clicked. I didn't like it but it ultimately helped, which I hope is the same outcome for these kids.

Fingers crossed. And poised on the mouse.

Mind = blown

I decided to use this week's checklist to ask my students for some feedback on the flipped class, and the result is "Mind = blown". Here are some really positive ones (I didn't edit for spelling):

Frankly I LOVE evrything about it! I really like the fact that the VTs can be watched from home even if my internet is slow and hates me :) BTW cool checklist

Wow! I just love Flipped classes.It’s great to be able to have group-work, or even class-work, without having to be afraid to ask questions about any of the work. And it’s great homework-wise because it gives us more time for other class’ homework and assignments.Flipped classes FTW!

I like it, I like how i can look at the checklist and do a bunch of notes whenever i want and not have to wait to do them in class everyday. It makes things less stressful, because i don't feel like I have a bunch of homework when I know what is planned for the week and get it done as soon as possible. I'm happy with the flipped class, i can't think of anyway to improve it.  

 Coming to school and doing the work here, getting the help I need, and actually discussing the work with the other people in my class is awesome!:) :) I also like the fact that on nights that I don't work, I can go ahead and do the homework for night/days to come! :) Lovin' It!

Honestly, I've been sitting here for a minute trying to think about what I don't like and I can't think of anything.

And here are some that are mixed (my bold): 

I like that we are able to ask you questions during class about work we are having problems with during class time, although i dont like that when we are sent home with homework we only have a voice thread to learn from and cant ask questions about the lesson. Nothing to be imporved.

I think it is a lot easier not having homework in the evening, but it is a bit harder to take notes and do examples from voicethreads than it is during class.

 I like it but in class we dont have that much time to work cause we always have to go over something first so it only leaves us with like 30 minutes to do work. sometimes not even that.

I like the voicethreads better than the khan videos! The voicethreads are not that bad its only when we have voicethreads every night plus the worksheets you give us plus all our other homework it really gets too much but one or 2 per week is fine. I also think the flip classroom works part time because seriously you have time to answer like 2 or 3 people a class and a lot more so i think this part dosnt work at all but doing the work during class i dont mind. I wouldnt mind either if it was the other way because i think it wouldnt really be different than what is happeneing now.

So important for me to hear all of this. It makes me realize a few mistakes I've been making:

• I have been talking too much. Partly that is because I can't see them, and I feel insecure about what they are doing or not doing. Why? I don't know. But they could have used more class time to work.
• I also have been piling on the lessons in too short a time in one particular class. That class has a lot of kids who are very weak and need almost constant help, so I need to slow things down a bit. Letting that government June exam get the best of me I guess...
• I have tried to answer all questions posted on the voicethreads asap but then I forget to tell them that. They could always check back themselves, but it would be nice if they could get a notification when I do that. SO remind them to ask questions but when they do check back.

It also makes me realize a few things I didn't know:

• That they actually ARE doing group work even when I haven't specifically asked them to.  It IS happening organically, at least in some classes, just as I had hoped!
• How well flipping works, and the way it works in general, can be so different from one class to another. My Science Math kids seem to be almost 100% in love with it, but my Tech Sci kids, not all are lovin' it. All the mixed comments came from that group. Makes sense, because they need more time to get their work done, and they need more help, and they are not getting either. I can't honestly say I didn't know it, but I definitely didn't know THEY knew it!

What I shall now do:

• I shall renew my efforts to shut up.
• I shall be more systematic helping individual students. 5 mins per, and if that's not enough, they work with someone else, or rewatch the lesson, or go to khanacademy for a video or a practice.
• I shall ALWAYS include, in each week's checklist, a open-ended question, that gives them a chance to speak their mind. Maybe this will be a natural progression for them into blogging.
• I shall tell them that was my evil plan all along. Then they'll have Minds = blown.

(I sure hope that expression is ok, not some reference to something, well inappropriate!) 

You are not your mark.

After a few weeks of flipping, and having time to actually talk to my students and listen to them, I now realize how much I've been missing all these years. I used to give tests, mark them, give them back, and that was it. No discussion, no probing to find better strategies for success, no insight gained into the child, only a number recorded. This week I asked for a self-assessment on their last test. I have read some pretty heart-wrenching entries, this one in particular:

My results are poor. First, I don't really understand why i failed. I went to tutoring and really studied hard because of my other test result which wasn't that good either. I don't really know what happened. Maybe I need more practice I guess. 

Another one that's hard to read, because he is being a bit hard on himself, but on the other hand, he is doing some self-analysis as a result:

Extremely disapointed in myself...It was leagues below my self standards. That did not go well at all, some of my errors were just lack of paid attention but I'm a bit troubled by others that I was originally quite confident about. I suppose tonight I may need to ask you about them should the oppotunity arrise and you have time. I apologize for that

Then there is the child who feels she must "redeem" herself, as if she has committed a crime:

I was very disappointed with myself in this test because many of the mistakes should have been easily avoided. When I look at the test, I understand all my mistakes. I found it very easy while doing it but I am a very fast paced person so little details always escape me. If there is a way I could redeem my mark I would gladly take home an extra assignment or something.

And I got to have a chuckle at this one:

BOO YAH, little errors but still VERY HAPPY

How many kids have I missed out on during my 20-odd years of teaching?

Today I would like to say to my students, past, present, and future, that in my class:

1. You are not your mark. Just like my salary does not represent me. I know that right now, to the colleges or universities you're applying to, it seems like you are your mark. But you know better. And I do too.

2. The goal is not perfection, it's growth. And the growth doesn't even have to be in math, it can be that you learn something about how you learn best, or a better way to get organized, or you discover that you love factoring! Yes, factoring!

3. When you learn something, and you share it, everyone wins. When you don't share it, it stops with you. Almost no point to that. What you shared with me in this self-assessment is WAY more important than your mark.

4. When you answer your own questions, you get inspiration. You cannot attach a number to that. When you answer the test questions, all you get is a mark. I'm a math teacher, a number geek, and even I prefer the inspiration over the number.

5. Math and science are not the most important things in the world. The arts are just as important. Just try living without movies, music, photography, books, poetry, dance. Or blogs!

I guess this is what they mean (and I forget who said this) by don't teach the content, teach the student!

And the evolution continues....

I have written a lot about how I use googledocs to track my students in my flipped classroom. If this is your first time reading my deep thoughts, then here are a few of my earlier posts that lead up to this one:
the googledocs checklist, how it looks to the teacher, handling all the gorgeous data, parent reactions.

Well, now I'm using my beloved checklists as a two-way communications device.  I'm finding that just showing the kids the results of their updates is having a huge impact. At the very least, the ones who update everyday love to see how pretty it looks as a spreadsheet, AND, believe it or not, that seems to motivate the others to update more often, and hence be more organized, because they like to see all the pretty colours! And no one wants to see any red.

More importantly, though, showing them their own week-at-a-glance gives me a way to communicate with them in case I don't get to them in class. It also enriches our time in class in ways I hadn't even anticipated!

Here's the routine I've fallen into so that I can quickly assess their progress on the fly, give feedback, and more importantly, get feedback:

Every day:
     To handle the INCOMING info (from students to me): I:

• check for their updates
• colour updates with day of the week, using an abridged and pastelled version of roygbiv:  (Mon = orange, Tue = yellow, Wed = green, Thur = blue, Fri = pink, Sat/Sun = lilac, any day after that = deep purple)
• check for items I can verify, ie if they say "I left a comment on voicethread" I go to voicethread and verify, or if they say "uploaded to dropbox" I check their dropbox

     OUTGOING info (from me to student): I:

• insert comments aimed at the students (not just at me like before) as necessary "ie received" or "not rec'd" or "good comment" or "way to go" (to insert comment, right click on cell in spreadsheet)
• flag, with bright orange, anything that doesn't check out - ie they say they handed something in but I don't see it, or the comment didn't appear at voicethread
• check for any entries with "need help", then flag that with bright orange also
• after all comments are in, and all flags shaded, rearrange in order by student (using data > sort)

      IT'S GO TIME: Now I'm ready for the dialogue! Next class I:

• give them whatever feedback I have put in the comments
• talk to them about anything that's flagged bright orange - ie if they say they did something but I can't see it, or if they said "need help", we talk about that (note that if I don't get to someone, I know that they will still see my comment, at least at the end of the week)
• document that by inserting another comment, like "helped with #3" or "did the worksheet but forgot to upload"

At the end of the weekend:

      Summarize the week's communications, INCOMING, OUTGOING, whatever, as soon as the Sunday
      night deadline is up. I:

• check each student's data  for missing items, and flag those items with red.
• check for students that haven't checked anything all week and make a manual entry for them, which I then shade completely red.
• go to "view list", "show colours", then display one child at a time
• take a snapshot, and send it to them
• if necessary, send their parents the snapshot
• next day in class, process, discuss, suggest, encourage self-assessment

Interpreting their snapshots:

• If it looks like this:
  
  
  I can safely assume they are at least checking in on a regular basis. Note at the bottom are my comments, in footnote form.
• If it looks like this:
  
  
  
  they might be cramming everything in too short a time.
• And how unappealing is this:
  
  
  
  This is someone who is either forgetting to update (in which case, they're missing out on a lot of connection potential with me, and I'm missing out on a lot of data about how they work), or they're not doing anything, in which case, intervention of some kind is needed, and easily set into motion with one look at all the red.

Other enrichment that's happening:

• The things I discover during some talks: one student has been asking me for help before watching the videos! He was frank about it, and knew it couldn't go on. Another admitted she was simply copying her answers then handing it in like that. All I had to ask her was where is your work, and she caved like a tower of jello. I'm not saying I am the first teacher to discover this kind of thing, and I'm not really shocked, it's just that it seems to be their own consciences at work here, because we are talking one one on one.
• Some kids will never ask for help in class, but they will via the checklist.
• Whenever they have the chance to type an answer, rather than check off one from a list, it makes for interesting reading. I asked for their feelings about their test results, and here are some of the things they wrote:

Should have taken my time but I think my score was pretty good, but I should have done better

I hate the fact I made a silly mistake on a MULTIPLE CHOICE question.... But I'll survive. Loved the test, not too hard! :D

I had 100% already so i compared my solutions with my classmates to discover the different ways of solving the problems

I think i did very well considering how difficult it was for me to understand all the work. I studied hard and it paid off

Next:  

• Some kids won't ever ask for help, no matter what , so I want to more regularly question kids individually.
• I still need to get them collaborating more. I had hoped it would happen organically, like they would group themselves according to what they were currently working on. Today, 4 kids actually asked to work together, which is a first, but for the most part, they don't.
• I need to give them work that lends itself to collaboration. Malcolm Swan comes to mind.
• Time to use those google accounts for self-correcting quizzes, a la Andy Schwen! I wrote my own set of instructions for this back in July, and now I'd better re-read those and hope my own post makes sense to me....

Now I just have to figure out a way to do all this and NOT spend every waking moment on the computer, so that my family won't disown me.....another post entirely. Maybe even another blog entirely.

The tip of the geogebra-berg

I have a few lessons that, over the years, I have worked hard on to improve, and that, as a result, I felt not-embarrassed to share. (Is that the best teachers ever feel - not embarrassed? Aren't we ever pleased with our work? But I digress.) This year, I am using geogebra right out of the gate, and I am amazed to see how much of a difference it has made, even on those not-embarrassing lessons.

Here's an activity I did last week, along with one I plan to do this week that builds on it. I wanted them to work together to develop a procedure for finding the rule of an absolute value function, so I made up some geogebra worksheets. In each example, they are given some points, and they have to input the rule that fits all the points. And of course, change the function's colour to match the points, since I am a geek for colour-coding. I started out easy, by giving them a few examples where they know the vertex and one other point:


This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com


Note that geogebra doesn't give them the rule, it just graphs the rule that they type into the input bar at the bottom, so they have to put the vertex into the rule properly, and they have to figure out the value of parameter a. The hardest part for them seemed to be getting used to using geogebra, but in no time, I had all kinds of ggb files uploaded to their dropboxes:

Note that for the black one, all I gave them was the vertex. "But that's not enough information!" some objected. "Well," I said, "it might not be enough for you all to get the exact same answer, but it is enough to get AN answer..." just to warm them up to the idea of minimum conditions.

The next worksheet was a bit more challenging:


This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com


Again, I shut myself up, and just said, you know everything you need to do this, work together, check out each others' ideas...In the red function, some tried making A the vertex, which geogebra soon showed them couldn't be. The tool did the intervention, not me.

Most figured out the red and turquoise functions pretty quickly. I saw some nice discussions happening in the breakout rooms. Some found h, the x-coordinate of the vertex, by using midpoint, others found slope of one side of the function.

But the purple example was REALLY cool to watch. It took a while for them to absorb the significance of not having that vertex. You don't realize what you have until it's gone! I did have to give a few hints, like which one of those points is the vertex ("oh! none!"), would you expect the vertex to be above those three points or below ("oh! below! ok I got it!") A couple of kids jumped right into the algebra - found the rules of the two linear halves of the function, then solved the system to find their meeting point. But others just used the line drawing feature in ggb to DRAW the answer. They drew two lines with equal and opposite slopes, located their meeting point on the graph, then boom, they had the graph of the function, which then revealed the rule, instead of vice-versa:

Now I figured my job was to show that these two methods of finding the answer were related. That each drawing step corresponds to an algebra step. AND, something I previously only dreamed of getting through to my students, that if it's possible to draw one and only one function to fit the points, that must mean there is enough info to find the rule algebraically. So I spent some time next class comparing and aligning the steps:

I think, I hope, that this validated the kids who drew the answer, and opened the minds of those who algebra-ed the answer, to see that even the most abstract of ideas has a foundation in the concrete world. Geogebra is 100% responsible for however much of that idea made its way through their neurons.

Next job for geogebra:

This coming week, we're doing the square root function. When we get to finding the rule, I will re-use the first worksheet, by merely replacing the words "absolute value" with "square root", and see what happens. I am hoping like crazy that someone will say, "Hey isn't that the exact same worksheet?" "Same points," I will say, "but now they belong to another function." And I will have shown them that these points didn't BELONG to any one particular function to begin with, we are the ones deciding that - bending the points to our will, if you will. And who knows, maybe someone will learn something that I hadn't anticipated, or even known myself!

And my next not-embarrassing lesson to be geogebra-ed:

I call it "The Big Picture", which is coming up in a few weeks. It brings together a few different functions. Enough said. The problem is, for every idea I have about how I will do that, 5 more seem to bubble up. It feels like I'm standing on an iceberg. It's a bit scary but, as my yoga instructor says, "Bring it on."

By the way, I would love to share my ggb files here, but I'm not sure how to do that. They are embedded, but does that mean they can be downloaded? Don't know.  I know I can upload to the geogebra wiki, which I will, but as soon as I can figure out how to do that here, I will. Any advice would be GREATLY appreciated.

My first video lesson

OMG it works!

Parent reactions to googledocs checklists

Since I am a parent, and I would love for any of my own kids' teachers to do the kind of tracking I talked about in my last post, I decided to contact a few parents. I started with the kids who needed a little, um, friendly boost to get them working. For example, I sent this snapshot of one student's summary to one parent, and cc'd the principal:

Remember, red is not good. The principal wrote me an email the next day to say that this snapshot had resulted in the parent coming to the school and meeting with a counselor, all for the purpose of getting her child on track. Apparently, this has been somewhat of a theme for this child. In short, this colorful snapshot had the impact that no other previous conversation had had in this particular household. The next snapshot looked much better:

Just another note about this particular student....notice the timestamp on the left in the last line.....this kid was doing math at midnight on a Friday night! I don't know what this says about me as a person, but that makes me feel....I don't know....like I have been given superpowers. Googlepowers! I am Thor! But I will not use these powers for evil.....

I want to empower my students, not just to tattle on them to their parents. If this doesn't result in anything positive for them, I'll just become a nag and it'll be more work that I make for myself and them. It HAS to result in growth.

But that's not to say that telling parents is a negative. Two other parents were very impressed and grateful for the information I sent them. In both cases, the outcome was positive and helpful for the kids involved. As it turned out, one was reluctant to ask for help with the math, and the other didn't even know where to find the checklists, but was too embarrassed to ask. He knows now, and so does his mom, and she was thrilled to have access to it!

Thoughts for the next phase of using these gdocs:

• How do I make this practice of updating checklists empowering for them?
• How truthful are they being? Some things I can check on directly, like things that are handed in, but not everything on the list is handed in. And shouldn't I find a way for them to value being honest other than just checking up on them?
• Should I give a mark for these checklists? They get marks for some of the items on the list, of course, but not all. A mark for keeping the list updated would be one sure way to get kids to do it. But I want their motivation to be deeper than that.
• Time to get some feedback from the kids - is this just another chore for you to get over with, or does it help? Have you learned anything about yourself as a result of doing this? Maybe I should send their own snapshots to them. I showed one girl hers, because it was a thing of beauty, as you can see:
  
  
  
  
  In fact, there's math here - when you check something everyday, you get a straight line, sort of....and she seemed to think it was pretty cool too. So before I ask for feedback, I should show them their own weekly snapshot maybe. Sigh. More work.

At any rate, a few cliches come to mind: A picture is worth a thousand words. To thine own self be true. But most of all, power corrupts! I am Thor!

Googledocs will you marry me?

First of all, a word about posting. I am not going to apologize for not posting in so long. The simple fact is that I haven't felt inspired to post until today. Yes, yes, I have been busy and tired etc but let's face it, that just doesn't cut it. The fact is that last year, I was always exhausted and busy but found the time to post anyway. I needed to. When you gotta write, you gotta write, am I right? And today, for the first time in a while, I feel that way again. I think it's because I have learned something, who knew? So here goes.

My ongoing affair with googledocs:

It is just unbelievable how much info I can keep track of with googledocs. And I did NOT have to get any training or spend huge amounts of time in order to get the payoff. I just follow the help instructions that come with a google account, that's it! My googledocs checklists make it possible for me to know, on any given day, who is behind, who needs help, who is ahead, who wants to redo a gizmo....and the quantitiy and quality of info they generate just keeps evolving. Here's the stage I'm at now:

The evolution of the quantity of info: It's in layers now!

1. Layer one: At the beginning of each week, I create a checklist for each class, using googledocs "create new form" feature. Just in case you're wondering how long that takes, not long. To demonstrate, I plan to do a video post about this soon - WITH MY FABULOUS NEW CAMTASIA STUDIO! (see later in this post!)
2. I share it with each class, and remind them to check things off as the week goes on.
3. I check the lists once a day for latest updates. Looks like this at first: (if you need to zoom in, click on the pic)

4. Layer two: Next I shade all entries for that day the same colour, so that I can quickly see the different days. Here's how it looks after three days: yellow day, green day, and orange day:

5. Layer three: Just by using the data > sort feature, I can now sort all the entries by name, so I can see each individual student's progress during the week:

6. Layer four: Scan entries for anything that needs my attention (like "need help" or "not happy with my results, please reset") or just the complete absence of an entry, and shade it red:

7. Layer five: Insert comments as needed, like "gizmo has been reset". This is also just a right-click feature on the googledoc. The comment pops up when your cursor hovers over it:

8. Next class, go through one kid at a time and discuss. Like "Wow you're burning through this stuff, let's check that you're really getting it." or "If you find this too easy, then check this out" or "You needed help with this, let's go over it".
9. Repeat from step 4 the next day. More colours get woven into the spreadsheet as the week goes on. It gets really pretty!
   
   
   I just want to emphasize that I AM NOT THE ONE FILLING THIS OUT! That's a HUGE time saver! That's been my major mistake all these years, keeping lists, checking things off, and I inevitably couldn't keep up. Now they do that part, which is good for them too, because it makes them take ownership of their own work ethic. But it's the combo of their entries, plus my layering of colours and comments, that provides the background I need to give them what they need. Truly, this is huge. And that's why I got so inspired to blog!

The evolution of the quality of info: It's about feelings now!

Another thing that has evolved is the choices I give them for each item. Last year, it usually looked like this:

Their only choices for response were kind of digital in nature - yes or no. Now it's more like this: (I made it extra big to make it easier to read white-on-black):

Now I want them to tell me not only what they did, but how they felt about it. The beginnings of self-evaluation, and I'm hoping self-awareness.

And now for my new love: Camtasia!

I don't know what is more exciting, that I have Camtasia now, or that it is SO FUN, or that it proves to me how flipping is really a more human way to teach and to learn. When I first tried to record, I found that I had to listen to the videos at techsmith first. Then I found I had to listen to a few of them more than once to really get it. I was thinking that if I were learning this in a class where everyone had to learn at the same pace, I would have gotten lost really fast. So it really is nice, in fact, perfect, to be able to control the speed of the lesson. Hmmm sounds familiar...... now where have I heard that before?

And now for the Camtasia. OMG IT IS SO AWESOME! I don't know how to do much yet, but I can just imagine the possibilities. Captions, sound effects, who knows what else.So excited to learn how to use this.

I made my first recording, but to embed it here, I apparently have to first upload it at either screencast or youtube, but then people there will see it, and it's just not good enough for that! I think I might become the Rebecca Black of teacher tube.....and I don't mean that as a put down of that poor girl, only of the reaction to her first video! Soon, though, I will have something to embed here, probably the googledocs demo.


 Man, learning is so good for you!

It takes a teacher

Summer vacation is just about over, and as usual, I did not achieve my yearly ridiculous goal of having my entire school year mapped out, with all my lessons, assignments, assessments, etc. ready to go, by the first day back. I guess it's time to let that dream go, because life just isn't like that, which means school shouldn't be either, right?

But I did do a heck of a lot of reading, thinking, experimenting, and learning, thanks to my colleagues and the lovely folks at twitter. And I noticed that a bazillion other teachers spent their summer the same way. So many new ideas, so little time! Project based learning, google+, skype in the classroom, student blogs, alternate assessments, collaborative problem-solving....but some of what I've read has been aimed against the flipping model. Since I remain resolved to use the model this year, and since I have never before been as proud to be a teacher as I am now, I felt compelled to respond to those objections.

Here's what I've read:

1. It really isn't that much different than the traditional model, since it is still the teacher delivering content rather than students discovering and collaborating.
2. It could be used as an excuse for giving busy work during class.
3. Getting students to watch videos, like those at Khan Academy, doesn't help them to solve real problems.
4. And besides, those Khan academy videos are boring.

Now here's what I THINK :

1. Sure, I am still delivering content.

I still feel compelled to, as I bet we all do, and maybe that will change one day, but for now I need to know that at least the minimum is out there for the kids to get.


But that's just it! Now the content is just the minimum! 


It's just the starting point. From there I can go wherever I or my students want! We get to have time to work on those collaborative projects, or blogs, or student-led discussions, or WCYDWT problems, or whatever we didn't have time to do when the entire class was taken up with content delivery.

2. As for the busy work, well, two things:

First, I found that the process of flipping forced me, even freed me, to come up with much better activities than I ever had before. And I think they are about as far away from busy work as possible, but you can check that out in this post. It freed my mind, and the rest followed! (Thanks for the inspiration, ladies of En Vogue!)

Second, the whole busy work problem didn't start with flipping. Any teacher abusing class time that way was probably doing the same thing in the old system too. That's just not a good enough reason not to try something new. The vast majority of teachers are in the profession because they love to teach, not because of the light workload or the easy money, so please. And young Matt Damon agrees with me:



Sigh. Matt Damon. What was I talking about? Oh yeah!

3. True, but the videos aren't the whole story. And neither is flipping.

Within the systems in which the vast majority of us find ourselves, where we're handed a rigid curriculum in which students are measured by their end-of-year exam results, flipping is, at the very least, a BIG step in the right direction. It gives us (and by us I mean kids, teachers, and parents) two things: some sense of security that we're covering the content, plus, and more importantly, a taste of what things COULD be like.

I got to show a small group of keener beaners how to do a bunch of cool stuff on their TI calculators (see the post here) that I NEVER had time to do before, and that led to a discussion that was of their own interest. See? Flipping led to more student-centered, constructivist learning, so there!. I also got to help many students learn how to use tech tools, like Word and Geogebra, and in the process, cleared up some math issues they were having. Efficiency, technology, plus authenticity, so there!

4. This blog claims that the Khan Academy videos are boring.

Surely there is a nicer way to express that opinion? Talk about peripheral learning - is this good modelling for our students? I think it's great that that opinion has resulted in many teachers' creating their own high-quality videos, don't get me wrong. But we teachers are the harshest critics - of each other and ourselves. And besides, it's what the kids think that really counts, and I can say from last year's experience, in which all my students belonged to Khan Academy, that there are a lot of kids that love Sal Khan. They love his friendly, casual yet enthusiastic style. They also love having another teacher available to them if the one they've been tossed isn't cutting it. One student was honest enough to tell me that he understood way better from Sal than from me. I have no problem with that. Ahem.

And my main point, finally...

I see flipping as a natural response to a system that doesn't work. We needed to individiualize instruction, but couldn't with 30 kids in a class. We needed to encourage collaborative problem-solving but couldn't find the time in class. We needed to teach holisitically, because life isn't just one thing at a time, but we had to prepare them for single-subject exams. So someone came up with a work-around.

It's a step, a big, brilliant one, and it just figures that teachers came up with it. I can't wait to see what we'll come up with next!

How could we have been so foolish?

Parents used to smoke right next to their kids. Raw sewage used to be dumped straight into rivers and lakes. Gasoline used to be available with lead in it, as did paint. Doesn’t it make you gasp, and shake your head, and think, “How could they have been so foolish?”

When I hear things like this, I can’t help but wonder what we do, all of us, right now, about which one day, people will speak and shake their heads in disbelief. I’m pretty sure they’ll shudder at what cars did to the atmosphere, and how many trees were cut down to make room for more cows, destined to become burgers, and at how much water we wasted everyday.

What's this got to do with education?

Well, if we’re all lucky, they will also talk about the way we used to teach. With everyone doing the same thing at the same time, the teacher doing all the talking, learning only one subject at a time, and spending the year with a goal of writing down what you’ve learned during a three-hour exam. Yes, one day, I hope, they will shake their heads in profound disbelief at that. I hope they’re doing it now!

But the thing is, change is so tricky. Even those who want to change can be misguided about how to do it. Take me, for example. Being a technology enthusiast myself, I thought for a long time that the technology would change everything. Many times I would start by hearing about a certain tool and trying to force it into my class, just because it seemed cool or because someone else was all enthusiastic about it. Like voicethread – I first heard about it 3 years ago, and I had no idea how I could use it in my class, but I kept trying to make it fit. Googledocs, same thing, even though I had a better idea of how it would fit, like with online quizzes. I had a bit more success fitting the class blog in, but it still felt like I was forcing them to do it. And it was all very exciting, but it didn’t feel like a cohesive way of teaching or learning.

I was always starting with the tool or technology and trying to hammer it into the same old class model.

Then I tried the flipped class model, and that was the turning point.

My own breakthrough:

Once I adopted that model, the tools just lined up and marched into place to support it. I didn’t have to hammer anything in. Since the flipped class starts out based on ideas like: students need to move at their own pace, have some control over what they learn, and have access to a variety of people and resources, it just happens to work great with tools like voicethread, googledocs, and classblogs. It still seems an incredible coincidence how the flipped class opened everything up to make room for the exact tech I had been trying to fit in.

For example, I needed a way to record my lesson so that my students could listen and learn at their own speed. Aha – this is what I can use voicethread for! Then I needed a way to keep track of who did what when, and googledocs raised its hand and said “I can do that!”  It did it again when I needed self-assessments the kids can do to reassure themselves (and me) they’ve got the idea. And posting on the class blog became more of a natural consequence to the kids working at their own speed, rather than another forced assignment. They seemed to need to communicate with each other in the open forum that the blog provided, as you can see in this exchange:

I just listened to the Chasles Property voicethread. At first, I was a bit confused at where this was heading. But when I was at about half of the notes I got the hang of it! It’s pretty straightforward, like the rest of the unit.
Yesterday I also finished the EL activity C. I found it interesting that at the end, there was another connection to physics. These two subjects are decidedly very closely bonded!

Same here, I got confused at first, but then at the end it became clear. At first, I thought it had something to do with the magnitude. But then it wasn’t at all, just that the head(s) and tail(s) have to match! [=

Ya me too i was trying to figure out where this was going… i thought the law would be much more confusing then that! we already put it in practice without knowing it was a law!

Yeah, at first I thought they were going to give us an equation that we will need or a procedure leading to a law of physics, but instead it’s just a way to simply steps and expressions.

 It’s a law shown much more visually. I liked the four point theorem question, it showed me how Chasles Property is applied to find things that aren’t plainly shown.

Chasles Property is fun. It’s interesting when you have to think which way is the arrow and the tail should point. The four point theorem questions were also cool…

What's next:

The next thing I’m looking for is a tool for my online class that will facilitate the natural formation of workgroups during class, so that they can work together and be each others’ teachers. I don’t want to be the one always deciding who they will work with. It’s easy in the brick and mortar, not so easy online. I’m thinking maybe google+…we’ll see.

Just to be clear:

I’m not saying that anyone who wants to change has to use the flipped class model. I’m saying that you have to start with whatever model, or philosophy that suits you, and then let the technology support that. Chances are, there is something out there that does what you’re looking for. I think this is how real change will happen – start with ourselves, not the tools.

I’m also saying that “chalk and talk” will hopefully, one day, be spoken of with the same horror and incredulity as smoking around kids!

Thanks again, Mr. Schwen!

I have been using googledocs for a while now, and thanks to Andy Schwen, I have some major upgrades to add next year. I had been making online quizzes last year, but I didn't know how to fix it so that they could be automatically corrected. Now, thanks to Andy, my kids will know right away what they got right or wrong, kind of like the explorelearning assessments, except I will create the questions instead of the nice folks at explorelearning. Not only that, but I will get the most GORGEOUS data - about each kid, or about each class, or about only one question...the data and the display are just amazing! This is all thanks to Mr. Schwen, who has already put all these features into some googledocs files, which he is sharing with everyone. You just have to follow a few steps to get it working for you and your students.

Andy very kindly put together instructions for how to do this, both in video format and text, which you can find at his blog http://mrschwen.blogspot.com/. I, however, being of a certain age and tech ability, (guess which is high and which is low), had trouble filling in a few blanks in these steps, so I decided, with his permission, to put my own step-by-step together.

Overview in a nutshell:

• You will get 2 different files (from googledocs) that were created by Andy Schwen.
• You will input class/student info into one of these files.
• You will input quiz questions and answers into the other file.
• Thanks to Andy's expertise, these files will automatically be linked so that each will get information from the other, in order to make your life easy!

Here's what will happen as a result:

• Your students will access your quiz online, and answer the questions online. Here's a rough idea of how the quiz could look to them:

• Your students will know right away what they got right or wrong.
• You will also know right away what were the results for everyone who did the quiz. 
• You will also get gorgeous infographic results by student, class, or question. Here is a shot of a sample supplied by Andy:

• You will be able to make up new quizzes during the year, simply by inputting new questions and answers, and the whole procedure will repeat itself. Students do the new quiz, then they find out how they did, then you get to see all the results beautifully summarized. All the links will kick in and generate the data using the classes and names that are already there.
• You will be able to give the same quizzes (or whatever type of assessment you want) next year simply by inputting new class/student info. Of course, you will probably want to change the questions every year, as any teacher would....no one ever reuses tests, right? Me, never......ahem.

Okay, now here's how you get all that happening:


Step One: Google account, chrome, and browser windows:

• First of all, have two completely separate browser windows open, one which will always display these instructions, and the other which will retrieve the various docs or go to various sites. The window without the instructions should be a google chrome one, because I found things worked better that way. I am not enough of an expert to know why, but I found that not everything worked right when I used other browers. So you might have to download googlechrome, which is free, and lovely.
• The next steps are all to be done in the chrome window.
• Get yourself a google account. This is not the same as a gmail account. Gmail is an email account hosted by google, but the google account gives you access to googledocs, which is what you really need. You will be asked to supply an email address, and it doesn't have to be a gmail one. And it's also free.
• Login to your google account
• Click on "more" at the top of the screen, and you will see this:
  
• Click on "docs". You will see this, except there will not be any files listed, since you don't have any yet. I, however, have several, because I am a big shot.

Step two: Getting your classlist template

• Now you are ready to download the files created by Andy Schwen. At the top of the googledocs screen, there is a search box, next to which it says "Browse template gallery". Click that, then type, in the search field, "classlists". You will see:

• Click "Use this template"
• You will see:

• This may sound strange, but you must now close this file. I do not know why. After you close it, go back to your googledocs homepage, and you will see, at the top of your file list, Copy of Classlist Template, like so:

• Click on that, and you will once again see the excel sheet above. Now it's time to make a copy of it and rename it. Click file > Make a copy, and this window will invite you to give it a new name, my suggestion for which you can see here:

Click Ok. Give google a few seconds to save if needed.

• Now it's time to put your students' names into the appropriate columns. If you're like me, you don't know them yet, so for now, just make up some names, so you can see how it all comes together. I put 4 names into the period one column, and 4 into the period 2 when I first tried this out. Give google a few seconds, or click save if you're impatient.
• Once it's saved, select the part of the url address that is after the "key=" all the way to and including the "=en", like so:

Note that the highlighted text you see here won't be the same as yours, that's ok, you have different names than I do.
• Copy that for use in a few steps. This will be the link between these two files.

Step three: Getting your assessment template:

• The next file to download can be found using the exact same procedure as above. Googledocs homepage, search templates, but this time using "public assessment" in the search field, and you will see:

• Click "Use this template" as before. You will see:

• At the top right, click "See responses" and select spreadsheet view. You will see another spreadsheet, but this one's got lots of tabs at the bottom of the screen.
• Make a copy and rename as before, this time calling it "Practice assessment template".
• Click on the tab at the bottom right called "Setup and results" You will see:

• in cell D11, paste the stuff you copied before from your practice classlist like so:

Again, remember that your code will look different, but it should end in the =en. I have no idea what that means.
• Now if you click on the "all classes" tab, you should see your practice names, like magic! This file got them from the practice classlist file! Cool, no?

Step four: Making a quiz:

• I was able to follow Andy's instructions for this part very easily, so you should check them out here. You will be amazed!

Thanks again, Mr. Schwen!