Routines for Synchronous Courses at LEARN

Two years ago I wrote about how we at LEARN 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.

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.

Real-Time Daily Routine:

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:

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.

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".

Other routines:

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.

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.

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.

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.

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. 

Resources organization: 

The rest of the routine is more easily explained by looking at the resources, and how they're organized on Sakai.

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.

A Unit:

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:

Week number and topic

A Week: 

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:

The view inside one week's folder

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 Week 13, Week 14, Week 15:

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.

A Class:

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.

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 (here's the link in case it's hard to read):

So the types of slides that happen everyday are: Title, Today, & Tonight. Everything else depends on the list for that day.

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:

What Happened in My Class After the Shutdown

Mar 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 necessarily 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.

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.

No tests and no final June exam meant I had more time during class to do three things:

• Cover the actual course material better and deeper than I was ever able to previously
• Cover topics that weren't on the course but were related/cool
• Do fun stuff just for fun

Today I'll start blogging about it all, starting with a few things I did under the heading...

Covering the course better:

1. Composites and Operations on Functions

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 Desmos activity on Operations on Trig Functions and this one on Composites of Trig Functions, 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):

Operations: Students were given 2 trig functions and they
decided which operation to do on them

Operations: Students chose which 2 functions AND which operation

Composites: Students chose which functions to composite, one trig and any other

Lo and behold, gardening and teaching intersected!

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):

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:

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?

2. Function Properties:

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 this year's version 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:

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 here, 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!)

Mystery sort #1

Mystery sort #2

Mystery sort #3

Mystery sort #4

Math and humanity intersected!

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!

3. Ellipses:

I gave them this GeoGebra, created by the brilliant Jennifer Silverman (@jensilvermath) so they could draw ellipses and experiment with the impact of changing string length and position of the pins:

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.

Next I edited Jennifer's to look like this: 

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.

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 this in-class activity:

The original Classkick slides

Sample student work (stickers are part of my feedback)

Sample student work

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.

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!

Finally, I returned to Jennifer's original GeoGebra, sort of, with this two-part activity, once they knew all the secrets of the ellipse, the geometric ones and the algebraic ones:

Screenshots: 

Part 1: Students draw the ellipse by typing in an algebraic rule

Part 2: Students draw the same ellipse by calculating string length and pin positions

All the things happened here. A deeper math dive, group cohesion, gardening, humanity.

Future posts about my pandemic classroom experience shall include:

• Topics that weren't part of the course but related/cool:
• Polar coordinates (thanks to Mrs McCarthy for this!)
• Binomial expansion
• Sum and difference of cubes
• Partial Fractions
• Sequences

• Fun stuff just for fun::
• All of Joel Bezaire's (@joelbezaire) Storytimes:
• Proof that the square root of 2 is irrational
• Pascal's Triangle
• Erathosthenes & the circumference of the earth
• The seven bridges of Konigsberg
• Desmos Challenge Creator:
•  Parabola Slalom
• Laser Challenge

Mentally 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.

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.

What I want to do BEFORE the exam is to actively, in a structured and gradually empowering way, help them:

• practice retrieving information
• organize all that math info in their minds to enable retrieval
• know what to expect on the day of the exam
• 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)
• try questions that they've never seen before but for which they nevertheless have all the tools they need
• come up with strategies to handle questions like the aforementioned
• practice pacing themselves
• develop independence and confidence

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.

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.

What I did this year: Outside of class

Review VoiceThreads: Review started outside of class. I didn't want to spend class time going over the basics, so for that I made review VoiceThreads. Here's a sample for the optimization unit.

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.

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:


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.

Review Packages: 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.

During class: Snappers, Zingers, and Deep Dives

A combination of quick-to-answer and not-so-quick questions that everybody gets to try:

Snappers: 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!

Zingers: 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...

Deeper dive: These I weave in between the snappers and the zingers.This is where we really get into it:

1. 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:
• express a vector as a linear combination of other vectors
• to find two missing parameters of a function
• to find the coordinates of the vertices of a polygon of constraints. It's everywhere.
2. 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.
3. Trying those questions they've never seen before, and for which they have all the tools
4. Going over strategies to deal with those questions they've never seen before, to identify the tools they need to mobilize

Overall: Variety Really Matters

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.

Today they wrote their exam, and tomorrow they write the second.

Fingers fervently crossed.

Exponent Mindfulness

In 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.

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.

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:

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.)

Anyway, so I showed them this:

We spent a few minutes working out each of these, just to re-convince everyone that these were in fact all equal to 16.

Back to 16, and I asked again, "That's it now, right? No other possibilities?"

My students know me well enough to know that answer to that. So we moved on to rational exponents:

I got a few really great answers added here, like 65536^(1/4) and 1048576^(1/5).

Me: So that's it right?

Students: Nope, that's never it is it?

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.

Marrying Zoom to VNPS

I'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.

The fantasy, or the ideal situation for a vnps class session (which I experienced and fell hard for at OAME 2019):

• The students are put into random groups of 3 and stationed at whiteboards around the room.
• The teacher gives each group of 3 one problem to work out on the whiteboard.
• Only one person in each group writes on the whiteboard, and does not speak, and the other 2 speak and do not write.
• 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.

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.


The reality of my online environment:

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.

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?

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!

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.

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.

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.

But this was a truly awesome start.

Day 11: More Diagramming

I 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 (which I already know there is) it's mine.

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.

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 "Sink Data Type", so that tells me it's something to do with a component into which something is being injected. (Maybe it's something that is to be displayed in an input to prompt students? No idea.) This at least helps me not get overwhelmed when I'm reading someone else's script.

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 this sample from Jocelyn's collection, 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.

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 sink data type is "number", your source data type can't be "content", but it could be "numericValue". 

Day 10: First Attempt at a How-To-Computation-Layer Diagram

I created and shared my first attempt at a CL diagram on twitter, and Jay Chow (thank heaven for Jay Chow y'all) replied:

Lines 1 and 2 👌🏽
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?

— Jay Chow (@mrchowmath) August 5, 2019

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:

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.

So for now I'm sticking with the ones that I know are good:

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 here is where I'm playing around.