Ep 70. Making Math Notes Meaningful

Johanna Kuiper 0:00
If you could eliminate one aspect of math class, what would you take away? For me, it would be taking notes. I hate taking notes so much, both as a student and professional development, but even more so as a teacher facilitating notes. And you might think I’m crazy. Or you might be on my side and intrigued at the possibility of relieving yourself from that duty as well. Whether you fall into that first category, the last one, or somewhere in between, let’s get started.

Johanna Kuiper 0:33
Welcome to solving for the undefined podcast. I’m your host, Johanna, founder of Miss Kuiper’s Classroom, the place that equips teachers and creating a healthy math classroom where students can thrive, no matter their academic abilities. But it’s not always about the numbers. And that’s why I’m here, bringing you the formulas to solve your problems, math and otherwise, plus strategies on cultivating that necessary math mindset. And that’s what you can count on.

Johanna Kuiper 1:02
Hello, hello. Welcome to a brand new episode. I know in that intro, I threw a pretty bold statement out you have I don’t facilitate notes in my classroom. And I don’t, I no longer write things under my document camera for my students to copy down in their notebooks. And honestly, I think it’s a waste of time.

Johanna Kuiper 1:25
Because how often does one of these following scenarios occur? One, a student follows behind and is copying notes after the fact, to students don’t take any notes because they don’t bring their notebook. Or they just don’t take notes to begin with. Or for students who do copy the notes, they either don’t understand them, or they never look back at them in the moment when they’re doing math. And it just becomes a dead weight in their backpack. And of course, there are that small percentage of students who go back use them and understand them. But how small is that percentage? Why am I wasting my time and my students time to help the two students in my class who will fall into that last category.

Johanna Kuiper 2:13
And I know as teachers, if we can do something that helps even just one student, it’s worth doing. But I want to maximize my effect within the classroom to help mold these students into mathematicians, students are always going to make bad choices no matter what I present them with. But that doesn’t absolve us of the responsibility to continue to try to do better for all of our students. So that’s why I made a pivot, and I will never go back to facilitating notes in my classroom.

Johanna Kuiper 2:48
So let’s start from the top. The whole point of notes is to consolidate learning, and for students to have something to refer back to when they are in the midst of problem solving. But most of the time, when you’re doing notes in a classroom, it’s taking place before any learning has actually happened in regards to that topic, making it almost meaningless for the students who are writing anything down. And maybe for the students who do understand it. We’re taking away that discovery and investigation, which therefore takes away their ownership of the learning. And as math teachers, we’ve always said that in order to learn math, you have to do math. And that applies here. If we’re just going through the process and writing things down in our notebooks before we actually understand and learn and discover what’s going on. Students are not going to be able to learn math, not in a way that’s meaningful and long term and something that’s going to help them move on in progress in their understanding. In order to learn math, they have to do math. And that means diving in and discovering and investigating the math itself, we cannot do the work for them.

Johanna Kuiper 4:02
Going back the whole point of notes is to consolidate learning, and that still needs to take place. So I’m going to share with you today in this episode what I do instead of having the traditional interactive notebook or taking the more traditional style of notes with direct instruction, and that is students take their own notes at the end of a class after a series of investigation, and or practice. So whenever I introduce a brand new concept or idea to my students, I like to do a discovery or investigation lesson. And then after students have completed that, and together we’ve made the necessary connections. That’s when I have students do notes. But if we’ve already done a discovery activity, like maybe the day before, and now I just need students to kind of practice to formalize or solidify their thinking. I’ll give them sort of

Johanna Kuiper 4:59
a hands on activity or a thin sliced set of problems. And there was actually a really great training recently from Jamie at Jamie Miller math about thin slice problems. So if you took that you might already understand what thin slice problems are, or if thin slice problems is a brand new idea to you, I do share a little bit more info about thin sliced problems back in episode 45. But I’m not going to take time here today to explain that because I want to talk more about notes. So whether I do the investigation activity or a hands on or practice like thin slice problems, after we complete that, that’s when students do notes. And this style of notes is a lot more active and require students involvement, then something that you would do under a document camera where students are just copying what you write.

Johanna Kuiper 5:51
And I like to call it active notes. And basically, it’s just a graphic organizer like a foldable, so if I took a piece of paper and folded it, hamburger style, I believe it is. And three sides of it have a graphic organizer for students to fill in information. And I’m gonna go over each component of this foldable. So on the very front of the foldable, I have a two by two graph. Now the top two boxes are for the big ideas. And the bottom two is for a pre made example problem. But the way that it’s different is those big ideas, I put three main ideas about the topic, but one of them is incorrect. And so that right side of the top row is where students have to go through and figure out which part is incorrect. And then same thing for the example problem. I have a worked out example problem that students can go through, but one piece of it is wrong, there’s a mistake within the problem. And so on the bottom right hand side is where students have to find the error, explain what’s wrong, and then rework the example problem. I’m going to share with you the actual example that I use for the big ideas and the error for the Pythagorean Theorem, but not the example problem only because it’s very much like an error analysis problem. And I feel like you will understand that because you use them in your classroom. So the three main ideas that I have for the Pythagorean theorem for solving for the hypotenuse is one, the Pythagorean Theorem only works for right triangles to the longest side of a triangle is called the high partners and the two small sides are the legs, and three, to find the hypotenuse, you add the two leg lengths together, then square root.

Johanna Kuiper 7:45
So think about which one you think was the incorrect one. And then think about how you would explain what’s wrong and fix it. If you didn’t catch it, it was number three. The big idea said to find the hypothesis, you add the two leg lengths together, then square root it, but it’s missing one step, you want to square the side, the leg lengths of the right triangle, add them together, then square root that answer. And so those three big ideas, the mistake was something small, but it wasn’t necessarily obvious, where sometimes when you’re doing an error analysis problem, the error is like big and obvious. And I didn’t want that I want students to have to think critically about it, because it’s almost right. But it’s not precise. And in math, we attend to precision. And so I wanted to bring that to example for them in the form of their notes. So that is the front page where they’re taking it and fixing an error of it. And that makes it more active because they’re engaging with it to figure out what’s wrong and fix it. Now if you opened up the foldable to the inside of our hamburger folded paper. On the left side, you’d have what I call a problem skeleton. So it has the bare bones of what the problem could be. But students are making their own example problem. So for the Pythagorean theorem one, I have a right triangle with a blank line underneath the two legs, and a question mark on the hype hot news. And the direction say, choose two numbers to be the leg, the length of the legs, then solve the problem for the length of the hypotenuse. And I give students free range to choose whatever they want. But I also give them three options to choose from that I just write on the whiteboard, because I don’t want the actual process of making up their own problem be the stopping point from them doing this. So I do give them options to choose from. But I also allow them to use their own creativity to create their own problem. And what’s really cool about

Johanna Kuiper 10:00
This is their personality will kind of come through. And the very first time I used this style of notes, one of my students was like, we can write any number, and then proceeded to use, you know, like 69, and 420. And so they just, they showed their personality and create creativity at quote, unquote, through making their own problem. Another really important thing about the problem skeleton is they’re not just creating their own example problem. But then they’re also going through and annotating what they did. So I have a space that says, Write down what you did in order to solve the problem. And what’s really powerful about this section is, they’re writing it in their own vernacular, and I just, I love the word vernacular. But basically, it just means they’re writing it in their own words. And so it’s something that they’re going to be able to understand more so than if I told them what to write. So I hope that goes without saying, Do not tell them what to write, it has to come from their own mind. Otherwise, you’re taking away the whole benefit of doing this style of notes in the first place, you’re taking away that ownership. So relinquish the ownership back to our students, and allow them to write down what they see that they are working through. And of course, if there’s an error, sit down and talk, talk it through with them, don’t just tell them what to write. So that’s the inside left of our foldable, solve the annotate the problem. Now on the right side, I give them three problems. Now, if you listen back to Episode 68, about the mild, medium and spicy problems, how I level practice, this is kind of where I implement one of that piece, or one time that I implement the mild, medium and spicy. So on the right hand side, I have three problems based on what they just learned about or what they investigated, or what they practiced. And so the mild problem, a medium problem and a spicy problem. Now, this next part might be a little controversial. I think that’s how you say controversial. I practice the word so many times, it doesn’t sound right anymore. But this might not be the normal thing to say about the mild, medium and spicy problems or practice problems in general, I make this optional. This is not something I make my students to do. This is purely for them to check their own understanding. It’s not something I grade, it’s not something I require them to do. This is literally for them to see if they actually understood how to use the Pythagorean Theorem problem in terms of finding the length of the hypotenuse. And I even include the bare bones answers on the back of the foldable for them to check their work, because I truly want it to be about them seeing and reflecting, do I know how to solve based on what I’ve discovered in practice so far? That’s it. And that’s actually the same idea that I employ for my homework, my quote unquote, homework as well, is it’s just an opportunity for students to check their understanding and to practice their knowledge. It’s not something I have them turn in, or I even look at it at all. It’s literally just for students. And if you want more information on that I share more back in episode 40. It’s called homework yay or nay. And I kind of just go into all the things about homework, and then how to make it more equitable, equitable for your students. Alright, going back to notes, everything that I’ve shared with you so far about notes is something that I implemented this past year in my classroom. So one thing that’s interesting is I took a training on Friday. And one of the things we talked about was notes. And there is new research from Peter Liljedahl, building thinking classrooms about taking notes in your class. And I’m going to share that with you. And this is not something I’ve done yet. But since we’re on the topic of notes, this is something I wanted to share with you just to continue to spread the information that I am receiving. So the way that he has seen notes progress is very similar to what I shared with you earlier. But the one key difference is it being more freeform so there’s no pre made piece of paper that or graphic organizer that students are filling in, and you do it more on the fly. And that doesn’t mean you can’t prepare it, but you are creating it. Like it’s a quadrant that you create, and your students work with their teams to fill it

Johanna Kuiper 15:00
And so I’m going to explain the four quadrants. So you have your four quadrants. And I think in the training, he labels it A, B, C, and D, you don’t do that for your students, you just show them the notes. So in the top left, you have a skeleton problem. But this one is more that you already have the problem, but you’re making the spaces for students to fill in. So if I had a Pythagorean Theorem problem, I would have the triangle with the two sides and a question mark on the third side, and I would start the problem, but as a skeleton, so I’d say blink squared plus blank squared equals blank squared. And then students would then take the information that you know, and fill it in and complete the problem. So that’s quadrant, I guess, technically quadrant two if you’re thinking about it, but it’s the top left hand side, the top right hand side is a example problem that students are going to have to finish or like complete, and then they are going to annotate what they did. So basically, just your typical practice problem for whatever topic you’re using. And then the bottom right corner is, is where students are going to make their own example problem. So they can make up whatever they want, as an example problem. And then lastly, at the bottom left is where they’re going to write down things that they want to remember their notes to their future self. And a lot of those things that I just explained align with what I talked about in the beginning of the episode of what I do. For my students in terms of notes, it’s very much student based, they’re creating their own problems, they’re annotating, they’re writing down things that they want to remember. And the one thing that’s different is students are completing this with their team. So they’ve just completed an activity, whether it’s practice or discovery something on their vertical surfaces. And now they are doing their notes on their vertical surfaces together. And so they’re consolidating their learning and making meaningful notes together. And then after they’ve done this together, you can move into a phase of them, writing it down in their notebook. So making that four quadrants filling it in. And what’s cool is when you get to make your own example, or the things that they want to remember, they can look around to everyone’s board, and kind of add different things. So maybe our team forgot to write down a key piece of information about the Bottega and theorem, but I can look over at another team sport, and I see it. So now I’m going to write it down in my notes. And so you just want to make sure that you have that last piece of students kind of looking around and seeing what other people have written to make sure that they didn’t miss anything. And that’s how you can kind of make meaningful notes as a whole class. And again, this is not something I’ve tried in my own classroom, yet, I want to try it out this year and see how it goes, maybe, maybe I choose to make that shift from doing my, my version of active notes to doing this will kind of see what goes and I’ll make sure to report back and sit and share what I’ve noticed in how it benefits my students either way, the last thing I wanted to talk to you about was how I help students kind of reflect on their own notes. And the way that I do this is on assessments, I asked a set of questions at the very end of how did your notes help you? And what would you change for the next time? And that just gives students the opportunity to reflect? Were my notes helpful? Is there something I could have had, instead of what I do have? Or do I feel confident in the way that I have taken notes in my notebook to help me for an assessment? And I know this can be a controversial topic, again, of having students use their notes on an assessment. But if they didn’t understand it, then notes are not going to help them. And but it does help relieve anxiety for students who they just need that safety net of like, Oh, what if I’m not remembering correctly, because that’s me, I will get in my head and be like, Hmm, I don’t think it’s a squared plus b squared equals c squared. It’s something else. And so just having those notes with me is going to help reassure me that I am correct, and relieve that anxiety. And I feel like I’m going off on a tangent. So I’m just going to kind of wrap it up. Have I asked those questions on an assessment to help students reflect on their notes to help better them in the future? So all of these were pretty big ideas. So if you have questions, or when you have questions, feel free to reach out to me. I’m here to brains.

Johanna Kuiper 20:00
storm to be a feedback partner. And just let me know what you’re thinking and how you might use some of this to inspire you to do different things with notes in your classroom. So with that, Oh calc-u-later Thank you so much for tuning into today’s episode. To find all the links and resources to things talked about in this episode, head on over to Miss Kuiper’s classroom.com and click on podcast

Transcribed by https://otter.ai