Episode #160: How to Make Connections In Your Problem Based Lesson – A Math Mentoring Moment
We chat with Nicole Whitty about the importance of big ideas and intentionality when leading your lessons. In this Math Mentoring Moment Episode we dig into how you can learn “who heard what” in your math lesson; why focusing on the intentionality of your problem based lesson will help make more connections during the consolidation of your lesson; and, what you can do when some kids are ‘getting it’ and others aren’t quite there yet.
- How you can learn “who heard what” in your math lesson;
- Why focusing on the intentionality of your problem based lesson will help make more connections during the consolidation of your lesson;
- How to set up your problem based lesson to maximize sense making;
- What you can do when some kids are ‘getting it’ and others aren’t quite there yet;
Squares To Triangles Unit: https://learn.makemathmoments.com/task/squares-triangles/
Visible Learning: An Interview with John Hattie https://makemathmoments.com/episode35/
Dane Ehlert’s Blog https://whenmathhappens.com/
Make Math Moments Problem Based Units https://learn.makemathmoments.com
Nichole Whitty: They were able to do it, or at least get a lot of the steps. Some of them weren't sure on the square root or how to officially work it out. But some of my classes completely got there. But when we sit back down, and you give them a problem and they actually see just a right triangle on the page, they're like, "Well, what do you mean look for X?" What is this?
Jon Orr: Hey, Math Moment Makers. On this episode, we are chatting with Nichole Whitty about the importance of big ideas and intentionality when leading your math lessons.
Kyle Pearce: Yes. In this math mentoring moment episode, we're going to dig into how you can learn, "Who heard what," as Lucy West would say, in your lesson. Why focusing on the intentionality of your problem-based math lesson will help make more connections during the consolidation. And what you can do when some kids are supposedly getting it, and others don't quite seem like they're ready yet.
Let's do this.
Welcome to the Making Math Moments That Matter podcast. I'm Kyle Pearce.
Jon Orr: And I'm Jon Orr. We are who math teachers from makemathmoments.com, who together-
Kyle Pearce: With you, the community of Math Moment Makers worldwide, who want to build and deliver problem-based math lessons that spark curiosity-
Jon Orr: Fuel sense making-
Kyle Pearce: And ignite your teacher moves. Welcome my friends to another Math Mentoring Moment episode. Today, we're going to be hanging out with a fellow educator. And we are in episode 160. Jon, if I do the math on that, that means we've passed like three full years of weekly episodes. That is pretty fantastic.
Jon Orr: It was December. If you're listening to this the week it goes live, it's December. And it was a December, Kyle, if you remember, when we were like, "Hey, you know what? We should start this thing." And well, we kicked out three episodes right at the beginning, and we never looked back, three years later.
Kyle Pearce: Holy smokes, who would've thought that we would've made it this far. But my friend, we have learned so much along this journey. We have had such a blast, and actually, as you're going to hear today with Nichole, she has been listening since the very first episode, which is so awesome. So just, Nichole, if you haven't yet do us a huge favor and actually do all the other Math Moment Makers from around the world of favor, hit that pause button, and go and leave us a rating and review on whatever podcast platform you're on, Apple podcast, Google podcast, Spotify, wherever you're at. It really helps to ensure that we can continue building the Math Moment Maker community.
Jon Orr: Yes. So we're not going to waste anymore time. Let's get right into it. Let's chat with Nichole.
Kyle Pearce: Hey, Hey there, Nichole. Thanks for coming on to the podcast with us. The Make Math Moments That Matter podcast. And our wonderful audience, I think, are going to be really, really excited to dive into another Math Mentoring Moment episode. So how are you doing? Where are you coming from? And can you give us a little bit of a back story? Who is this Nichole that we're hanging out with tonight?
Nichole Whitty: Yes. Hi. So how I'm doing, I'm all right. I actually recently was sick with COVID for two weeks, so no making it back into the classroom, but it's been awesome to be back. It was weird to be gone for so long. And going back has just made me remember like, oh, I am passionate about this. I love this job. And I'm teaching, actually, in Houston, Texas. I teach in Cypress in the Cy-Fair school district, but live closer to downtown Houston. And a backstory about me is I teach geometry. This is my fourth year of teaching. So started at the same school. I've been at this school for four years now, through all the crazy COVID stuff that we've experienced and whatnot. And I started off teaching algebra one, and that was my first two years. And now I've been doing geometry, and shifted into some more pre-AP advanced classes as well.
Jon Orr: Nichole, we ask everybody the same few questions. As you know, you said, you've listened to, before we hit record here, you said you've listened to a few episodes before. So the question we're going to throw at you right now is, we ask everybody what their math moment is. If you think back to your... usually it's your childhood, it's like as soon as we say math class, usually when we say that to people, it jogs a memory from a long time ago that says, this is what they remember about math class. I'm wondering what that is for you.
Nichole Whitty: So that one for me, I've thought about this a lot, because I've been listening to the podcast since the first episode. So I always think about it. And there's one from when I was younger that pops to mind, but there's none that really feel like they shaped me. But the things that stand out are like when we were doing hands on projects, or more realistic ones. And I think the one that I decided on that really stood out to me the most was when we did a project, I think it was seventh grade with my math teacher, Mr. Torres. We did this project where you had something like a thousand dollars, and they started off by teaching us how to write a check. And then you had a thousand dollars, and you had a catalog with things that were certain prices. And your goal was to spend as close to a thousand dollars as you could. So sometimes you had to revise it. Maybe you spent this money initially and you're like, wait, I need to rearrange it. So I can have just $20 left instead of $30. And that just stood out to me because it was something that dealt with money that was realistic. And although you were buying like arbitrary couches or something, it just was fun to get that experience.
Kyle Pearce: We're kind of wondering, a thousand dollars. I was trying to think, what would I have bought at the time when I was in school? We're wondering-
Jon Orr: A Walkman and a Diskman. A Diskman for sure.
Kyle Pearce: There it is.
Jon Orr: And a bunch of CDs.
Kyle Pearce: And probably, like a Columbia house unlimited subscription or something.
Jon Orr: I always wanted one of those.
Kyle Pearce: I was a sucker for that, eh.
Nichole Whitty: I've never heard of that.
Jon Orr: I never did that. That must be a Canadian thing.
Kyle Pearce: Yeah, totally. Totally.
Jon Orr: You would've had something similar. It was like, we got these things in the mail and it promised you for $1, you could get like 25 CDs. But you had to sign up to subscription, right? And it was like-
Nichole Whitty: Yes.
Jon Orr: As a kid, you thought, this is the best deal ever. But then my dad's like, "No, it's not. And here's why."
Nichole Whitty: Now you look back, you're like a thousand... Yeah. I don't even know what would've been in the catalog. I was thinking it was furniture. I don't remember the specifics, but yeah. Now I think, what would I get with a thousand dollars? How much could you actually buy?
Kyle Pearce: Super cool. And you know, normally you had already mentioned that you don't know if it necessarily had a huge impact or influence on, let's say, your journey. But I'm wondering, has that moment influenced how you're teaching today? Because you had mentioned, and you were very specific about it, that it was these sort of memories of actual projects, or things that were a little bit more hands on, or maybe active learning type experiences. How does that fit into how you're teaching in your classroom right now?
Nichole Whitty: I feel like I'm in this hard spot right now, because I have a lot of big goals. But I'm still early on in my career, so it's hard to do this growth. So I'm not incorporating a lot of projects, but it's a desire that I have, especially in geometry. Some of my other favorite memories are from geometry. We built a kite, and had to do properties of quadrilaterals. And we actually got to fly them, and mini golf. I think that along with that checks' hands on project really makes me want to get my students involved, especially for those that aren't necessarily just learners in a traditional sense, like ones that are more hands on, kinesthetic. And so I just want to get them engaged in that, and get them thinking, and applying it to things that you actually see around.
Jon Orr: Yeah, totally. And some courses lend themselves better to that. And sometimes, how do I bring these project based learning, or these big projects that you can apply all these concepts to. I've always been drawn to that as well. And thinking about how can I bring this in? Especially for of our classes where our streaming is students going to the workplace, or students going into apprenticeship programs. I've always wanted to build a program just like that. That would be for the future Jon is going to think about that for a moment. But Nichole, I'm wondering what you are currently working on. What's a challenge or a pain point that you're struggling with now, and you want to brainstorm with Kyle and I here on this episode? We'll brainstorm and talk about what some next steps are. But Hey, let's hear what the challenge is.
Nichole Whitty: Yeah. So something that I've been working on a lot is, first off, trying to find more geometry tasks. But the main thing is with my tasks, I'm really struggling with how to tie it all together. So it's not super easy for me to articulate this, but I feel as if students will do this task, and a lot of times it's me coaching them with it. But they get to the end and they do all this math and they're like, "oh." Just some that come to mind are like the sinkhole task from Robert Kaplinsky with volume. And they'll get to the end, and they're like, "Oh, that's what volume is. Yeah, I need to do volume, not just area of a circle, because I'm filling a space. That makes so much sense." And then they're like, "Oh, I could find the area of the circle and multiply it by the height."
And then they do all this rich work. But when it comes time to do our practices and or tests or something like that... So I'm in a school where everything's kind of planned for me. So when I have to veer back towards that, I have a lot of trouble with stripping the students of almost that math identity, and all of that problem solving and work that they just did. So I give my explanation to help them, and it almost feels as if all the work that they just did is taken away. And they're just lost again.
Kyle Pearce: I feel your pain, because we've been there. And I think you'll always have to grapple with that no matter what. There's going to be these times where, I feel like you'll be teaching and you sort of have these little mini revelations. Sometimes you think, "Hey, I've got this under control." And then you say something, and you sort of see the look on students' faces and you sort of go, "Oh, maybe that wasn't what we needed to do next." And sometimes it's almost like Cathy Fasano calls it, we tend to rob the thinking of students often and we don't mean to, we're just trying our best to help. And we're trying our best to make sure that they're sort of making sense of the math.
So I'm wondering, when you're in this process and students are solving the problems, what does that look like and sound like as they're working? And then, you were mentioning about the connections piece. Just trying to paint myself a bit of a pick of what that might look like and sound like. And like you said, it's sort of hard to articulate, I'm sure. But if someone's at home and they're thinking, what would it be like? And you could even use an example of, maybe it's that sinkhole lesson from Robert Kaplinsky, or maybe it's something else that you've done recently. What would that look like and sound like, just to kind of give us a bit of backdrop?
Nichole Whitty: So as they're doing a task, I have white books, so I always have them up there. Sometimes they're sitting down, but I usually like to get them up. So it's just more low stakes. Emphasize like, "Hey, you have this dry eraser, you can erase it." So as they're working, a lot of times... I think something else that I've struggled with is how to set up the lesson appropriately. Maybe I just jump into the task without necessarily all their prior knowledge. So then as they're working sometimes, I have to coach them, but I'll have little prompts that I tell them, or I'll just ask them questions. I do a lot of questions throughout, walking around. And then I love how you guys say like, "Hey, look over at other people." So I'll encourage that. But majority... So I recently did a task that it was from Dane Ehlert, I'm not sure if that's how you say his last name.
Kyle Pearce: Yeah.
Nichole Whitty: Yeah. Down in Waco, so near me. And it was, he had taken this clip, I think from ESPN, about a golf tournament. And this guy hits it. And the news guys would say, "Oh, they did a little, A squared, B squared equals C squared." So I did that with my students. We talked about correcting the formula, and then they got up and were starting to actually try and figure out the distance, and coaching them through that. So they were able to do it, or at least get a lot of the steps. Some of them weren't sure on the square root or how to officially work it out. But some of my classes completely got there. But when we sit back down, and you give them a problem and they actually see just a right triangle on the page, they're like, "Well, what do you mean look for X? What is this? That it just says X there. I don't even know what that means." So it goes from this meaning, to all of a sudden, when it's just on the paper, they're like, "Well, I don't know." Even if I just solved something like that. So it's tricky to make that tie in.
Jon Orr: So I'm picturing, they're working at the boards. Some of them are coming up with solutions. Some of them maybe need some next steps. I'm wondering, what does it feel like when some of the students have a solution, and then some of them don't? What are you doing that at that moment? Is it like, "Hey everyone, come back to their seats?" Or is it, you go back to your seat when you're done? Can you zero in on that one moment where it's like, I gave them a task, they're working. You did your circulating, you did your prompting questions. Because I think a lot of us, who are teaching in this way, do of these things. We give those little prompts to keep kids going, and keep them in the flow. And then, we may have started it lots of different ways, but the board's working now. But there's a moment there that's like, some kids have it. What are you, particularly, doing around that moment?
Nichole Whitty: Yeah. So I've actually been thinking about that a lot lately. And I'm been thinking about how I really like the episode where y'all talk about start small, because I think about how some students will give up so quickly. So having to keep them in the flow, and then like you said, some will finish it within like a minute or two because we just have students on wildly different levels. So it depends on the task. Often, I try to go around and prompt them more. And if they've finished, I'll often go over and say, are you confident in your answer? Talk about it with your group mates and come up with an explanation for this to prove it in order to justify it. So sometimes it looks like that. But then there have been times, I think with that most recent one I've done with Pythagorean theorem, I was like, "Oh, okay, once you get it, you can look around the room and then find your seat." And so it's been hard to know what to push them with, and how to extend their thinking if they do finish early.
Jon Orr: So let's say they land at their seat. Is it now just like, "Hey, you did the problem that we were doing together." Now, is the flow of your day of your lesson there, here's the next stage. We got to practice this skill, and here's some practice questions. And then, you just keep going? Or what does that look like?
Nichole Whitty: So it's kind of different on every day. And especially since I have... So at my school, my schedule's made for me every day. My copies are made for me every day. And then, what I'm going to teach on that day is made for me. Which is a blessing and a curse because I have some wiggle room, but then I need to feel like I need to stick to that because we have seven other geometry teachers, and students are constantly switching. But often it looks like... So I haven't fully gained my confidence, I think, in asking the students to justify. Because as y'all know, so many students have such a fear of math, and just feel nervous about that or feel nervous about talking in front of the class. So sometimes I'll have them present, but usually that's later in the year. If a group is willing, then usually at the end, I will at least have one group discuss their solutions.
And if they're not, then what I'll do is I'll have them tell it to me, and I'll go through it. And so we'll kind of look at one or two of the solutions, but then usually, it's we will jump into maybe filling in some notes that's over that. Like, "Hey, let's talk about what this is, and then let's do a practice problem or so together." I usually just try to have them start on their own though, rather than me work the problems for them. But we usually do write a little bit about it.
Kyle Pearce: Awesome. Awesome. So there's a lot going on there, and it seems like you're in there, you're trying to push students for more. I liked how you're trying to sort of tease out some more thinking. I'm wondering, so when the problem is sort of, we'll say, the room is feeling like, okay, we've come to some consensus. How are students... are they given an opportunity to... You had mentioned that one student, before they went to their seat, have a look around. Is there any purposeful connection making, or anything like that? Are you doing a formal, let's say, consolidation where students come and check out a particular solution, and certain ideas are drawn out. What does that piece look like?
Nichole Whitty: So kind of same. It can be all over the place, but often I try to draw them in to look at one of the whiteboards, or one of the white books, and see this solution. And then sometimes, I'll ask other students, "Okay, do you see where this number came from?" One of my favorite tasks that I actually just did today, but with a group of teachers, is the In and Out 100 by 100 Burger. And so I did that one, and I always have them... whenever I do it with students too, I say, "Okay, let's look at this one. Do you see any numbers on here that you did not have in your problem?" So I like to ask questions such as that. Like, can you figure out where this number came from? How is this similar to yours? But some tasks, I think, lend themselves to that more than others. Whereas when I'm doing that Pythagorean theorem one, there's not really a lot of wiggle room. That one has pretty much just the one way that you can set it up. There are different ways to solve it, but students can get kind of lost. So sometimes, I will have the opportunity to show some off, but sometimes the work is just kind of not fully there, so I'll show a little bit. But then I extend the thinking to get there.
Kyle Pearce: Now, I'm wondering, specifically to this Pythagorean theorem problem, and like you've already mentioned, I think every problem, every concept, is going to be a little bit different. So it might not be the same every time. But I'm wondering, with the Pythagorean theorem problem, have they already been introduced to that concept, or is this something that they're kind of bumping into through the questioning or through the information, the limited information that they're given with that problem? Because you had mentioned with Pythagorean theorem, immediately what popped in my mind was that there isn't a whole lot of variety. But is that because they already know the Pythagorean theorem? So they sort of jump to, maybe, the algorithm? Or what might that look like and sound like? And like I said, I'm sure it's different depending on the concept, but I'm curious in particular about that one.
Nichole Whitty: That is a good point. I didn't really think about that. They are supposed to know the Pythagorean theorem. But for this year especially, last year they knew it a little bit more. But this year, especially, I'm pretty sure that that was supposed to be taught when the shutdown happened here. And so we went virtual, but we weren't allowed to require students to be there or really teach. So I'm not sure how many of them actually learned it. They've heard of it. All of them when the video came on, it was like, "Oh yeah, that thing. A squared, B squared, C squared, something." So they've definitely heard of it. It wasn't brand new, like a discovery like you might actually do with the area of squares.
Kyle Pearce: That's interesting, because sometimes students have been introduced to an idea in prior years, and it's coming back again in a future grade. So I'm wondering, in terms of when you're starting a problem, I'm wondering in terms of how... I kind of go back to John Hattie. I think it was John Hattie who was talking about this funneling versus focus sort of questioning, or was that Peter?
Jon Orr: No.
Kyle Pearce: Jon, I don't know if you can help me with that.
Jon Orr: Well, no, that-
Kyle Pearce: Yeah. Okay, awesome. So, there're certain types of questions where we funnel them, and then there're other questions where they're more like focus. You're still asking a purposeful question, but we're not necessarily nudging them down a specific path. I'm wondering, what sort of information might be given to students?
And I guess, my immediate wonder is, when they go into a problem, typically, do they sort of already know that... do they already have the tools, quote-unquote, maybe the strategies or the formulas or whatever it might be? Or are the problems being presented in such a way where students can stumble upon the answer, but they might not necessarily make that connection? Because the reason why I'm asking that too, is because you had mentioned about trying to make those connections at the end. And I just wonder, how much room there students are doing to inquire or investigate in order to kind of bump into a few of these things. Or how much of it is sort of like we've already pre-taught some of these ideas, and now I want to give you this problem and see if you can manage.
Nichole Whitty: Yeah. So I like that question because the Pythagorean theorem one definitely falls more into the category of, I'm going to give you this problem and see if you can manage. I had not reviewed it with them. However, it was expected that it was prior knowledge, and they'd seen it at some point. And that's kind of hard with geometry, because most of our geometry curriculum they have seen before. Like, the vocabulary, they've learned it. The pictures, they've seen, and stuff like that. They know the different types of angles, even all the way almost to corresponding angles. They just might not remember it. So with the Pythagorean theorem, it was definitely more of, Hey, let's use this kind of as a review. And I think that's still partly where my comfort zone is as well, with having a curriculum that's made for me, and a schedule that's made for me, it's much easier for me to be like, "Oh, it's kind of, this is the review. Let's do a three act task here."
However, I have done some that are new to try and discover it, but it just feels kind of scary. And you've had some episodes where I've heard some other people talk about this. I'm like, "Oh, thank goodness. It's not just me. That feels like-
Kyle Pearce: You're not alone. Don't worry.
Nichole Whitty: So I've heard those and I'm like, "Oh, phew. Okay." But I've tried a few, like the cookie cutter task. So I did one like that, and they had had some prior knowledge, but I don't think they'd ever seen anything really like that. And that one definitely took a lot longer. And then back to the funneling and focusing, I think especially with that task, for a task where it is something new, it just depends on the group for me. So some groups will get it with just a couple focusing questions, really easy. But then some of my students don't even write anything down, because they just have no idea where to start. Because whatever their past was in math, they may not have the same level as the other students. So for them, sometimes I will funnel more, but it really depends group to group. And then also, based on the activity.
Jon Orr: Right, right. I want to head back to, or circle into, this disconnect between doing the task and then asking them to do another one, but it's slightly different, but they don't know how to make that connection. And I think we have some suggestions here for you, because I think Kyle and I were definitely in a place like that on our teaching journey. With us always wanting to do a three act math task or a problem based lesson, and we wanted them to be at the walls. And I wanted to see solutions and I wanted them to be engaged. And we really focused there. And we were really focused on the action happening. But I think what we got lost in is where the actual learning goal was. And so I'm wondering, when you're being handed these lessons that you're running, is there any discussion? What's the discussion about what is the main learn goal of that particular lesson? Is it written at the top, or is it something that you just intuitively know, or is it something that you have to think about?
What does that look like with this situation you're in?
Nichole Whitty: So learning goal for me, or for the students, or both?
Jon Orr: Yeah. For the students, when you start a lesson, what are you hoping the students will pull from this lesson, or learn during this lesson so that they walk out the door knowing X?
Nichole Whitty: So it's really interesting. I've never thought about that before, but we don't talk about learning goals. And I remember that one of the episodes y'all went more into depth about, we need to focus on the goal. And just what you said with being really excited about the action and trying to get students engaged in losing sight of the goal. That episode really made me think. And then this question as well, because we don't discuss that very much. It's more like, in our meetings, it's a lot of housekeeping. But we don't have a lot of planning meetings where we're discussing what we expect the students to learn. So what it looks like for me, with what I'm expected for the students to know, it's like a note sheet with some fill in the blank usually. And it'll have the topic on there, or it'll have the three types of problems that they need to know how to solve.
And so then I'm expected to use that to teach them that. And often I don't use the note sheets. I go off on my own, and I do either to task or just more inquiry based or problem based stuff. But that's what it looks like for me to get that goal for students. Like, "Hey, these are the three types of problems." What comes to mind is we just did angle addition. So there's one that's just basic angle addition. Like this angle plus this angle gets you your total. You need to know how to do it when there's a bisector, an angle bisector with a total. And then you need to know how to do it when you're given an angle with just a bisector, but no total. So that's what it looks like when it's given to me, and what the students are expected to know.
Kyle Pearce: Yeah. As soon as you had mentioned that, it really struck a chord with me. Because I'm going back to all lot of many years of trying to make the switch to problem-based lessons. And I was using lots of three act maths type problems and a lot of the math moment style problems that we've been creating and lessons. And something that I think was missing as I was trying my darnedest to try to make this work in my classroom. And I think Jon would agree, is the intentionality of, what do I want students to walk away with? And I still struggle with that. It takes a lot of thinking and it takes a lot of pre-planning. And as soon as you can take that time ahead and really think about what matters. And really, that's what I think it comes down to, is what really matters here?
Because I go back to a lot of my old resources, I have these binders. And every now and again, I'll just open it up and look and see what I had in there. And it was sort of like, I heard you mention it, trying to put in all the different types of examples or special cases, or whatever it might be. We tend to throw these out there. But it's like, for what? And really, my for what was always trying to ensure that I prepared, quote-unquote, my students for any possibility, any curve ball that could come their way, they're going to be fine with it. But it was more about them memorizing steps and procedures. And I now look and I start to think about the big ideas. Like, what do I really want them to know about Pythagorean theorem? And for me, now I see that in such a different way.
I look at Pythagorean theorem as a relationship, not just like an equation, or not just this formula that we're going to fire numbers into and they're going to always get the right answer. It's making sure that they see the relationship and they make sense of the relationship. And oftentimes, a lot of this work is, well, we learned from The Five Practices. That book has really helped us with trying to anticipate what students might do. Cathy Fasano's work has really helped me with that as well. Is really trying to think of how might students come this problem. And then, again, what is it that I'm hoping that they'll walk away with? And when we think about this intentionality, the piece that I find is really helpful is, I start to see, and I start to make sense of the different solutions I'm seeing and the consolidation, like what we're going to try to connect, becomes a lot more clear ahead of time.
And then of course, some of that's happening in the moment as well. So it's not always perfect because some students will always come with something you didn't expect. But at least it's like, you've got the big ideas there. And it's almost like you're hoping a student will try this method and that method. And even if a student doesn't try this third method, maybe that's the method you want to share and almost share to them and say, "I was thinking about doing it this way." And then, giving them this opportunity to look and make those connections. I heard you mentioning that, trying to see, Hey, do you see these numbers in your work? Or do you see this idea in your work? Really trying to get them to think about that. And then, ultimately at the end of the day, what are you hoping that they know now or feel more confident with now than they did maybe before they entered into that lesson?
And the hard part is, of course, we would like them to take away all kinds of things. But if you only could make it manageable, what is it that we want them to walk away with? And I find as soon as I start to at least start thinking about that, that helps me to start thinking about what is my connection, my consolidation, going to look like and sound like? What is it that I want to make sure that I draw out here? So that students go like, "Okay, that makes sense."
Because another piece that we always seemed to leave on the table in our math class was assuming that everybody, quote-unquote, got it, or made sense of what happened. When in reality, some of the students there, they might have got a right answer, but they may not have actually understood what really happened. Maybe they lucked out. Or their neighbor gave them a hint, or whatever it was. And it's, to really make sure that they're getting the big idea. And then from that, possibly giving them a follow up prompt that might be something related to the context, but it could be completely different numbers. Just to give them that second at bat.
It's like, okay, so you struggled through this problem. We've now made these connections together, and now I'm going to give you this slightly different. It's kind of like going back to my old notes. We'd give you this different scenario, and I want to see how you handle it now, based on what you know. And what I find is, when we do this, you learn so much about what students made sense of and what they're still not quite certain of. And that can really heavily help you with your planning the next day or even the next week. Rather than say, just rushing on to the next topic.
So I'm going to pause there and get your thoughts on that. Because I said a whole mouthful, but you really gave me a light bulb moment as you were chatting.
Nichole Whitty: Yeah. So I liked that a lot. And I think that y'all mentioned that in the episode from last week, maybe, about that follow up prompt, with a similar scenario or situation. And that's gotten me thinking a lot. That I kind of just jump into the basics, like what you expect to see on a math paper or on a math test, rather than really tie it in at all. It's kind of like, "Oh, okay. We talked about this, here's the method. Let's move on to this thing that I'm a little bit supposed to do."
So I really like the idea of coming up with the similar scenario to write that. And then, it also just made me think, it's so true, no matter what type of lesson you do, but especially with these. If you ask students to share their scenarios, there's still some students, even in that group maybe, there might have been one student leading it that didn't get it.
And it just made me think of the students who are hiding, and how that follow up prompt can pull them out. Because there's so many times the next day I come in and I'm like, "What did we do yesterday?" Even after that golf task, and one student said, "I think we watched a golf game." And the other students were like, "I couldn't tell you what we did." And so, I think it was two or three that said to me about the math. So I love that idea that you said, of that follow up prompt to just really drive that home almost, in a way that's still engaging and related and encourages thinking rather than just, "Hey, here's this problem with the right triangle. You know to use Pythagorean theorem, because I just told you, so go ahead and practice the steps I just showed you." So I like that idea a lot.
Jon Orr: Yeah. Now, like what Kyle said, it's a good way to not only practice, but also what he emphasized on, like seeing who isn't grasping it at that time, or seeing the big idea. But I think there's two big things you can be thinking about here as... Thinking about these huge ideas, the big ideas, can also be... They could be all about problem solving, seeing the big picture, like Kyle suggested. But I think you could also have your big idea, your learning goal, is to bridge that gap. Like we've seen the idea, we've seen this relationship that we're unfolding. But we also could tie it to the calculation side of things. So I think you're still like, Hey, we can progress into the note at the end of the lesson. I think that's still, after the next prompt, the follow up prompt. But then you can progress into the note. I think that's fine for you.
But I think the bigger idea is to make sure, what is that one big idea for you and for that lesson? And then make sure that what information are you going to get from your students that tells you they either got it or that they don't got it. Or they're on their way to understanding it, or they don't. And that's individually for each kid compared to like, Hey, the whole class got it. Because usually when I say that, I'm thinking about four kids who got it, but not everybody who got it. So some takeaways there.
But also wanted to bring up that, Kyle and I are making tasks on a regular basis and putting them up on our website. And the tasks that we're making there, almost, they zero in on the intentionality. It's like, we start there and then everything from that task and that unit unfolds those big ideas.
For example, when you go to look at one of those tasks, and you head to the guide tab, and you click on the intentionality, you'll see... We have a Pythagorean theorem one up there, and it's a four day unit that unpacks area, composite area, area of triangles, area of squares. How to find the root of a square, if you know it's area and vice versa. And then where's this relationship between the side lengths of a triangle come out. Does it always work? It's a four day, full day, unit. But if you look at the intentionality side of things, it starts with, here are the big ideas. It's translations, rotations, congruence. The Pythagorean theorem is in there, however, there's these other huge ideas that's really related to this one relationship that we look at with sides of triangles. So it's an important thing to definitely think about, because you want to make sure you bring that out in that lesson.
Nichole Whitty: Yeah. This has gotten me be thinking too. I mean, I like to blame it on the fact that I've taught different subjects at the years. And then it's so early on. But I need to take that ownership and look at our standards, because when you're given everything, you don't really think, "Oh, let me go, actually look." There has been a couple times, the beginning of this year, where I thought, I've never known if I truly have to teach this one little thing. Does it necessarily say that I have to teach segment addition when there's a midpoint and a total is given, and only one of the pieces is given. Or something like that. So I think that something important, moving forward that this has made me think about is, I need to know what those big goals are for me. So then I can translate that to the students as well.
Kyle Pearce: That's a huge, huge, big takeaway. And I know you're in year four. So congratulations to you for having these thoughts so early in your career. I was year four and still scrambling to put as many words down on my note as possible, and not really realizing that there was so much more to not only mathematics, but teaching mathematics. And clearly, you are well on your way there. It sounds like you've got a pretty active learning environment.
And the part I love so much is that you're taking these chances, and you're also being reflective about it as you go. And I think if you keep that sort of mindset, and that sort of approach to teaching, you're going to continually get better and better at this thing. And the beautiful part is, is that you can always get better. And I think that's what makes teaching so rewarding, is as long as you stay on that journey... You're starting early, which is great. So I'm a little jealous there, but we are super, super excited that you decided to come on here and have a chat with us. So before we go here, is there any last takeaways that you want to share? Or, I guess, if there's one thing that you do take away from this conversation, what's the big takeaway that you're going to chew on and hopefully start thinking on as you plan ahead for your next lessons?
Nichole Whitty: I mean, there's so much, right, as usual. Every time I listen to these podcasts, I'm like, oh my gosh, how do they come up with just one takeaway? There's so much richness in this. But I think the one that's really stood out to me the most is that follow up prompt. And that seems like such a, Oh, of course, why would I not do that in such a doable thing? And then I just love that it really shows you where students are truly at. So I think the biggest takeaway for me is that, when I do things like this, or even just miniature three act tasks, to do a follow up prompt, to truly gauge where my students are at and get that feedback. And they can't hide amongst the others. Just to see, did this get my learning goal through to them.
Jon Orr: Awesome. Awesome stuff to hear about that. Nichole, we want to thank you so much for joining us here on the Making Math Moments That Matter podcast. Like Kyle said, we wish you all the best. And I'm wondering, we usually check in with folks in a year or a little less than that. We're wondering if you'd be open to coming back on and chatting with us again and seeing how things have progressed, or changed, and also, get maybe another challenge in?
Nichole Whitty: Yeah, I would love to do that.
Jon Orr: Awesome.
Kyle Pearce: Love it. Love it. Well, thanks again. On behalf of the Math Moment Maker Community, your willingness and vulnerability to come on and share a common math task or math class struggle is huge. And I'm sure so helpful for so many others around the world. So thank you so much. And my friend, I hope we'll get to chat with you sometime soon.
Nichole Whitty: Yes. Thank you guys.
Kyle Pearce: Awesome. Have a great night.
Nichole Whitty: You too.
Kyle Pearce: As always, both Jon and I learned so much from these Math Mentoring Moment episodes. And I don't know about you, Jon, I can feel, after we have to do all this deep thinking, like we're listening to the scenario, trying to make sense, paint a picture in our minds. It really leaves us buzzing with energy and excited to dive into our next opportunity to do some math learning with students. But remember, you don't want all of this learning to wash away like footprints in the sand. So make sure that you're doing something to reflect on what you've learned here today.
Jon Orr: Yeah. And a great way to hold yourself accountable is to write it down, or even better, share it with someone, a partner, a colleague. Hey, get on over to the Math Maker Community, in private Facebook group, Math Maker's K to 12. Or, we're on social media @makemathmoments on Twitter, Instagram, all of those things. The other thing is, Hey, we talked with a member of the Math Maker Community and they filled out a form to be on the show and talk about a big challenge. You can also be on the show, chat with us. You can get that mentoring call with us where together we can brainstorm next steps on a challenge or a pebble in your shoes, as sometimes we say. You can apply over at makemathmoments.com/mentor. That's makemathmoments.com/mentor to be on the show.
Kyle Pearce: Awesome stuff. And remember, show notes, links to resources and complete transcripts to read from the web or download and take with you. Make sure you head on over to makemathmoments.com/episode160. That is makemathmoments.com/episode160.
Well, until next time, Math Moment Maker friends, I'm Kyle Pearce.
Jon Orr: And I'm Jon Orr.
Kyle Pearce: High fives for us.
Jon Orr: And high five for you.
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