Wednesday, 6 February 2019

The Thinking Classroom - Note-Taking (Part 2)

So in my last post I wrote about note-taking, as a partial response to questions about #VNPS and notes.

Specifically, that our practices need to be coherent, and that we can "only work toward coherence in [our] teaching practice by thinking deeply about what [we] do, how [we] do, when [we] do, while constantly considering what [we] learn from [our] students moment-to-moment, day-to-day."

I also hoped to spark some reflection on the 'permanence' of notes.  I tried to emphasize that it isn't whether students need something permanent.  Rather, "It is about whether they have created personal meanings through the act of note-making, in a way that may consolidate, structure, and sequence their thinking, and perhaps also prompt further wonderings."

I also briefly wrote about studenting, before really trying to reiterate the idea that, as teachers, one of our tasks is to try to build meaning into what students do.

That was a quick re-cap of Part 1.

In this post, I'd like to share some ideas that might help build meaning into note-taking (or note-making).  I have to admit that I tried structuring this post into similar categories but didn't really have enough time to do it justice.  Instead, I'll just write about them in no particular order (although you might see that they are all related -- hence the 'coherence' point I attempted to stress in the previous post).

1. Using Pictures
In the class we often take pictures of our work.  Sometimes we're tricked into mistaking the storage of the images for a wealth of knowledge.  Certainly students might.  But these just get lost in a sea of selfies or fun memes -- collaged and compressed over time, drained of meaning.

One way that I help students add meaning to these, is by setting up explicit activities that ask them questions about the images.  It can be their group's work, or it can be another group's work.  The key is that students have had the experience during class of solving these problems, and now we ask them to make sense of those experiences, and to reflect on possibilities.

1a. Printed images with additional prompts.

I might give prompts that relate to general 'mathematical processes' (general overarching skills), like in these example from a few years ago:

I try to take specific pieces of work from their experience, and then build prompts that are structured under broader skills like representations, connections, and so on.

I might also include something like this:



Where I ask students to think about this very interesting mistake.  There are several intentions here.  First and foremost, I am attempting to place value in these mistakes, and framing them as important opportunities to learn from.  Second, I am being specific about the ways through which we might value these mistakes.  Not only as learning opportunities, but recognizing that they all stem from useful and interesting logic.

(of course I recognize that there are different ways of framing the word 'mistake' that can also be powerful, but I won't go there for now... I'll go with elaborating on this old document of mine)

These are done collaboratively, in visibly random groups, on #vnps.  When I go around to manage 'flow', it's a bit different than a problem that students solve, because the discussions are more meta.  They're about broad ideas, and may involve a large variety of examples.  Some kids will have lots of words written down, and others will have lots of discussions, and others will play with their thumbs.  This is often something that I work toward - in building student capacities for doing this.  At the same time, number 5 also allows me the opportunity to extend and change problems (or they can do it on their own) so then they can create infinitely many exercises (e.g. go around and add x's or constants, or different constrains and restrictions to number 5).

1b. Using Desmos Activity Builder to encourage reflection

Another way I might do this, is to throw it on Desmos.

This strategy was inspired by Thach-Thao Phan @MathPhan

She made a desmos activity specifically for homework in a thinking classroom.  She only tweeted about it once here



I liked the idea, and so I subsequently worked on my own alterations (we have to make them our own, right?) here:


And here's an example of what one question might look like from the kids.




.You might recognize the problem from Peter Liljedahl's website as the Pirate and the Diamond problem (which I usually change the story and use a different context for)

But the idea is that the template can be used for any board work (as long as there's enough redundancy around the room), as long as you are specific about what you put in.

In fact, I prepared the document and edited the desmos activity during class *while* managing flow in the room.  So I promise it can be super quick.

2. Parallel Problems

When we are managing flow in the thinking classroom, it's common strategy to think about the kinds of prompts we might give.  Whether problems we provide students (when they are done) are extensions, parallel, or gear-shift problems.  I will write more about my thoughts about these two ideas later, because I do believe there's quite a lot of nuance in that.  For now, I will  briefly describe extensions as pushing deeper into the concepts or broader around the concepts, parallel as similar problems that provide an additional opportunity for students, and gear-shift problems are ones where we switch the focus slightly to a different detail.  These are done on the fly (but rely on experience, knowledge, and imagination on the part of the teacher), and are focused on responding to our students in the fleeting moments of the classroom.

But beside during the problem, I've also used parallel problems to help me set up for 'notes.'

Sometimes during the day after an activity (which may take a day or several days), I begin the class with a parallel problem.  This might be a more succinct version of the problems that students have experienced on the previous day.  Then as they work on the problem, this time I am managing the class in a different way.  I am now focusing on aspects like precision, mathematical vocabulary, and really pushing for detailed understanding.  I am also asking students to verbalize, and, yes, write down these details.  So in other words, they're using this short problem to create notes with.  

Once students have all solved the problem, which should be quicker because it's not the first time, I gather the kids to remind them about our learnings from the problem, and then I send them off to annotate the problem/strategy/solutions with definitions, other examples, and other related concepts.  Putting their own names to the concepts and ideas.

3. Summary

Sometimes I also explicitly ask kids to work together on creating mindful notes. Just kidding, I don't use the word 'mindful' with them - I know that Peter's framework has 'mindful notes', but with kids, I actually tend to go with 'meaningful' notes or 'purposeful' notes.  I find that it's an adjective that I can play with, and one that they can grab onto a lot easier.

These can come in a lot of different forms.  Kids can work on these on their own, like in Alex Overwijk's @AlexOverwijk example here:


Here are some of my kids examples as well:






These are without explicit prompts of what they should be writing down.  And the last two pictures are electronic files (with one of them being a google doc that contained a picture of her work as well).

There are others that have done this, too, like this recent tweet by Lam Nguyen @NguyenMath




4. Structured Sheets

You may also prepare something in advance for students to collaborate on, think about, and then write in for themselves.  Laura Wheeler @wheeler_laura has these course packs, for example, that she provides her students.  I think of them as shelves that you create that students to put stuff in.


As for me, I tend to like to shape the shelves with a bit more questions.  See a sample file in this PDF, and the images below:


Usually I also have students work on these collaborately on the boards, as well.  That way I can listen to their conversations about these concepts.

5. Quizzes, Tests, and Reviews

Do your kids throw out quizzes and tests into the trash after you give them back?  I'm not saying it doesn't happen anymore, but it's certainly a lot less than before.  I believe that it's also important to build meaning into those experiences as well (as I tried to write about here).

Along with activities, these can also be amazing opportunities for collaboration and note-making/sense-making.

It helps a lot that I spiral through my courses.  Which means that we revisit the main concepts of the course several times throughout the year.  (To me, it actually means a lot more than just hitting the same topics multiple times...  it also has to do with responding to students and recognizing paths.  but I think that's another post for another time).

This can either be built INTO the quiz (e.g. questions in the quiz containing things like encouraging an elaboration on 'mistakes', the 'why' questions...etc), or it can be structured alongside the quiz, or after they have been returned (as an activity).

Group tests can help this along as well. (oh man, another topic I should write about at some point, too).

~~

How do we help students make meaning out of notes? What structures do we build in order for thinking to flourish?  Meanings are personal.  So ultimately, that's something each one of us would have to answer for ourselves, within our own circumstances, leveraging our own experiences, and acting on our own goals.  My examples are things I've tried and that has, at different points in time, worked for me with some kids, and bombed with others.  And so, how might you help students make meaning out of notes?

I'd love to hear about it


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