December 28, 2021
Pam Harris
Episode 80

Math is Figure-Out-Able with Pam Harris

Ep 80: Resolutions Anyone?

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Math is Figure-Out-Able with Pam Harris

Ep 80: Resolutions Anyone?

Dec 28, 2021
Episode 80

Pam Harris

We've come to the end of another year, and we'd thought we'd leave you with some suggestions on goals you can set for your teaching. In this episode Pam and Kim highlight some transformative goals that you probably haven't considered before. How could your math class look next year or next semester?

Talking Points:

- Learners setting goals around mathematical behaviors or practice standards.
- Teacher goals centered around the NCTM mathematics teaching practices.
- Teacher goal to elicit and use evidence of student thinking.
- SMART goals.
- Hey Australia! We appreciate you!

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We've come to the end of another year, and we'd thought we'd leave you with some suggestions on goals you can set for your teaching. In this episode Pam and Kim highlight some transformative goals that you probably haven't considered before. How could your math class look next year or next semester?

Talking Points:

- Learners setting goals around mathematical behaviors or practice standards.
- Teacher goals centered around the NCTM mathematics teaching practices.
- Teacher goal to elicit and use evidence of student thinking.
- SMART goals.
- Hey Australia! We appreciate you!

Pam Harris:

Hey fellow mathematicians. Welcome to the podcast where Math is Figure-Out-Able. I'm Pam.

Kim Montague:And I'm Kim.

Pam Harris:And we make the case that mathematizing is not about mimicking steps, or rote memorizing facts. But it's about thinking and reasoning, about creating and using mental relationships. We take the strong stance that not only are algorithms not particularly helpful in teaching, but that mimicking algorithms actually keep students from being the mathematicians they can be. We answer the question, if not algorithms and step by step procedures, then what?

Kim Montague:Okay, so if you are a resolution maker, then it might be the time of the year where you're making some considerations around that, right? It's December, end of December. And often we take stock of our lives and make some new goals for the new year.

Pam Harris:New Year's coming. It's resolution time. What are you thinking about? How are you going to improve? What are the new goals that you have for this year? Kim, you might find it interesting, I actually usually make most of my resolutions, in kind of August or September.

Kim Montague:Really?

Pam Harris:Because I mean, I've always been a teacher.

Kim Montague:Yeah.

Pam Harris:So for me, it's always like the school year. However, I do make some resolutions. I do set some goals in January, maybe I just do more.

Kim Montague:Yeah.

Pam Harris:You know there's something about that new semester.

Kim Montague:That's reasonable.

Pam Harris:But so many people do it at this time of the year, that we thought we would bring a few things forward that we think about when we set resolutions and we have a really cool story to start out with.

Kim Montague:Yeah, absolutely. So and this is actually perfect timing, because we're, a lot of people are entering into their second semester. So I think it's appropriate as well. So we have this incredible friend who is a teacher and a leader in Michigan. We love her so much. Her name is Kristen Fraying.

Pam Harris:Wahoo, Kristen.

Kim Montague:And I had the opportunity to watch some film of Kristen not too long ago when she was teaching virtually with some of her students. And I believe that they were maybe sixth graders, seventh graders maybe. And we asked Kristen to take some film of her virtual teaching. And she sent it to me, and I got to watch it. And I have to tell you Pam, I was just so interested in some of the things that she was doing, some of the teacher moves.

Pam Harris:She is thoughtful.

Kim Montague:She's so thoughtful. Yes, she is. So thoughtful.

Pam Harris:We have learned a lot from Kristen. It's a really good collegial relationship.

Kim Montague:She's wonderful. And so one, I wanted to tell you about one of the things that I saw her do that I immediately loved and know that I'm going to put in practice. And it was that to begin her lesson, which was going to be a problem string, and then carry into this rich task that she was going to do. She asked the kids to review some mathematical behaviors that she had already talked about and put in place. And it were, there were some things like asking questions, and solidify their thinking, and change their mind, and justify with evidence. And there were a whole host of things that they could do. And what she asked the kids to do was to, I think she was on a jam board, to create a post-it note with whatever behavior that they were going to demonstrate or hold themselves accountable to, for that particular day, for that particular lesson. And so they each had chosen something that they were going to hold themselves accountable to, jotted it down. And then that was set aside, she delivered this brilliant problem string. And then when the problem string was over, she asked the kids to evaluate themselves on what they had decided that they were going to be very aware of. And I just, as I watched this happening, I was so impressed that she would give her kids the ownership of that. First of all, that they knew mathematical behaviors that they should be displaying, or that she wanted them to be displaying. And then a lot of kids were able to say because they had it had been in the forefront. They had been aware of what they had said that they were going to work towards. They evaluated themselves. And not everybody said, you know, I did a great job. I was you know, did that but they did then come back and have a conversation about who had held themselves accountable and who had risen to that challenge. And I just, you know, I watched it, I was so excited to see that for her kids. And anyway, it got you and I thinking about some things.

Pam Harris:And maybe before, Yeah, maybe before you go into that I want to slow down just a couple things.

Kim Montague:Okay.

Pam Harris:So just to be clear, this was during COVID. And so it was a virtual lesson, which is why she was using a jam board. So you could totally do this on a post it note or you know other ways when you're in person. But they were virtual. I know you said it, but I'm just going to reiterate that these were things that had already been exemplified.

Kim Montague:Yes.

Pam Harris:So they had talked about when we're in the middle of a problem string, a goal could be that I'm going to try to represent my thinking. Or a goal could be, I'm going to make sure I understand the strategy that wasn't mine that's being shared. Another, like sort of student expectation or a mathematical behavior could be I'm going to ask a clarifying question if I don't understand somebody else's strategy. Or I'm going to be the one who offers share my strategy today.

Kim Montague:Shares.

Pam Harris:Is that what you just said?

Kim Montague:Yep, shares.

Pam Harris:Yeah. So maybe I don't typically share. And that's the thing I don't like to do. But I recognize that that's the behaviors that I bring my work to my colleagues for comment and review and to my, to my fellow students, for them to review and comment on it. And so today, I'm going to choose that. And the kids get to choose, right?

Kim Montague:Right.

Pam Harris:You get to choose that sort of thing. I'm sure that's something that Kristen had talked to them about, individually, some about some of their strengths, some of the things that they could work on, and maybe even suggesting some of the ways that, some of the goals that might be more profitable for them. Like knowing Kristen, I'm sure that at some point, she had conversations with, "Hey, you're always choosing that goal, you're actually pretty good at that goal. How about, you know, let's think about another goal that you can choose." You know, like, sort of keeping it real. It's not a cop out kind of thing. So I thought that was noteworthy. And then, brilliantly, here's what I was not expecting you to say, that then at the end of the string, she had them evaluate how well they did.

Kim Montague:Yeah.

Pam Harris:Ah, like I'm doing that brain blow kind of like where my hands are, above my head, like, wow, like, maybe because I'm so bad at that. Like, that should be my resolution. My resolution should be how I will bring to closure things. In fact, I'll shout out another good friend of ours, Nicole Bridge, is probably the best live tweeter I've ever met. Salute to Nicole for being the best. She can, and she's not only like tweets a lot while you're, like I was speaking and she was live tweeting a lot of things I was saying. But the thing that's impressive about Nicole, is she tweets the good stuff. Like it's not like some, and she quotes it correctly. Like I have a hard time with that. As soon as I quote something correctly, I've lost the next, you know, three minutes, because I'm trying to get it out on a tweet or whatever. Anyway, she's amazing. But one of the things that she told me after we were in a workshop together. I was doing the workshop and she was there. She said, "You end badly." Well, Nicole, tell me how you really think. And she was very polite about it everything. But we had some really fruitful conversations about sort of bringing things to closure and helping the people that I'm working with make sense of what just happened. And helping them set goals from there and evaluate kind of. And brilliantly here, Kristen is helping those students evaluate the goals they had set, how it had worked for them in that case, then they can move on and set new goals. So we're talking about goals. Okay, So Kim, I interrupted you. So you and I've been talking about resolutions and goals.

Kim Montague:Yeah. And so we started thinking about what, you know, what could we suggest maybe, or recommend that people as teachers, leaders consider if they're a resolution maker. What could they do to make some resolutions for their teaching, for their profession, for their classroom? And so we just want to share a little bit about that today.

Pam Harris:So let's do that in two ways. One way is you might consider, could you do something similar with your students that Kristen did with her students? Could you say to them, "Hey, there are some mathematical behaviors that I want to encourage in class. So let's put them up there. And let's talk about and let's exemplify them. And let's set some goals that we're going to actively work towards these mathematical behaviors." And a place to get some of those can be the math practice standards. So you could say, "It is a mathematical thing to make sense of problems and persevere in solving them." And then, as you circulate, I notice a student making sense of problems, you could say, "I noticed you're making sense of that problem. I noticed you're working really hard to persevere in making sense of that. And solving that. That is a mathematical behavior, well done." Like that could be something that you verbally acknowledge. It could be something that you acknowledge, as you give them feedback on on work and written work. But you can actually notice those, not just, "Oh, you get the right answer." Or "Oh, I see your strategy." But also some mathematical behaviors, like, "Oh, I noticed that you were reasoning abstractly there. You were really like thinking in big global terms. You weren't just solving that problem. You were kind of abstractly, quantitatively using what you did quantitatively and noticing a pattern and abstracting that out into some sort of like this general rule. Nice. That's a mathematical behavior to reason abstractly and quantitatively." You might notice as students are discussing and comparing two different strategies, you might say, "Oh, that's a really, the argument that you just made nice, nice viable argument. That is a mathematical.,.", and you could point to the standards on your wall, if you have them, or you've talked about him as a class, "You were just constructing viable arguments nice. I could see her... Oh, and you when you were, like, sort of poking at this generalization that we were starting to make, and you found this hole, you found that like, you found an exception. Nice critiquing the reasoning of others. Like that's a mathematical behavior, that you just critiqued our reasoning that we were coming up with." I'm going to note that. I'm going to sort of point that out, kind of set it up as an example. That, in other words, what we're suggesting is, that not only are we going to point out the content, things that students are doing,

Kim Montague:Yes.

Pam Harris:Nice strategy, good use of a model, correct answer, which we kind of want to de- emphasize the correct answer part. We're gonna like, we want the correct answer to be a given. And now we're going to talk about how we got there. So we do, it's not that we don't want you to point out the mathematical things that are happening in content. But we also want you to point out the mathematical behaviors that are happening, as they persevere, as they critique reasoning of others, as they model with mathematics, as they maybe use appropriate tools strategically. You might say, "Oh, I noticed that you reached for your calculator, and then you kind of paused. And I noticed that you kind of looked up and you decided you had power over that. Like you could do something without like, you even jotting something down, and kept track of your thinking. But you didn't in that moment, it wasn't a great use of a calculator, because you had power over those relationships. You could do something with that, nice." Pointing that out, making it a thing, then could allow you to do kind of what Kristen did. "Hey, in this next task that we're about to do choose, one of these mathematical behaviors that you're going to work on. And maybe you could set that as a goal." And then like Kristen,did, you could then follow up with, "How did you do on your goal? Let's all kind of take stock of how we just did there." Could that be something that you could consider as a resolution for you and your students? As you as you proceed from this New Year's time, this might make it a New Year's resolution.

Kim Montague:And I love that you're talking specifically about the practice standards, because those particular standards kind of encompass everything for that grade level, right? It's not just is as small as (unclear). Yeah, it's something that students can work on the entire next semester, or the next year. They can travel from one year to the next. Considering these behaviors and then the verb, right, that they're doing mathematically, they're reasoning they're constructing. They're attending they're looking for. Those are the mathematical behaviors that we want them to own.

Pam Harris:Yeah, nice. Nice, nice. So I didn't go through all of them. But hopefully, you got some sort of sense of how you could use those practice standards, just like Kim just said, Cool.

Kim Montague:Yeah.

Pam Harris:The second way that we might wonder if we could think about as we're setting new year's resolutions is in your teaching practice itself. Could you use maybe the mathematics teaching practices as the underlying sort of structure that you might consider, as you think, how might I refine the mathematics goals that I established to focus learning? How am I implement tasks that promote reasoning and problem solving, not just answer getting? How might I use and connect, Ooh, not just use mathematical representations, but use and connect mathematical representations. So I'm quoting the mathematics teaching practices that NCTM put out not too long ago, where they list the eight teaching practices that sort of correlate with the eight mathematical practice standards for students. And so how can I use those might I set some goals for myself to think about how can I better facilitate meaningful mathematical discourse? What are some things that I can do to get not just mathematical discourse happening, but meaningful, like discourse that moves the math forward? It's not all just about talk. We're not just trying to get kids talking. Talk isn't magical. We want to actually use talk to move the math forward. Not just the content, but also those mathematical behaviors that we just talked about from the practice standards. How can I better pose purposeful questions? How can I work on using conceptual understanding to really build fluency? I really want my kids to have like something as they hit a problem. I want them to have some relationships that ping for them, that they can use. That conceptual understanding is going to help them. Something's going to ping, "Ooh, I can use that understanding to help me fluently sort of move forward." How can I support productive struggle? I'm suggest one way that you can support productive struggle is to emphasize those practice standards like we just did. You know, if you make those a thing in your classrooms, and as part of what you do, the practice standards of looking forward and expressing regularity in repeated reasoning, that becomes a thing. As you're doing problem strings, you could say, "Ooh, remember, one of our things is that we're going to look for and express regularity in repeated reasoning." As the student might be, might be struggling you could you could support that struggle by saying, "What do you see in these example, in these problems that we've been doing in this string? Do you notice a pattern? How could you use that pattern in the next? Oh, I see how you've been solving that problems, those problems? Did you notice how so and so just solved it? Were you paying attention to that strategy? Could that strategy influence how you solve this next problem? Yeah, you could do it your your strategy? Again, have you considered that the other ways of thinking how that might affect this next problem?" Again, you're just sort of lobbing things out to see if they land in a student zone of proximal development, but you're recognizing, maybe, that you could support productive struggle and learning mathematics by helping students identify those practice standards and noticing them. Bringing them out making them a thing and your practice. And then the last one I'll just mentioned, could you set as a goal for yourself to elicit and use evidence of student thinking, what would it look like in your practice, to more elicit student thinking, grab that evidence and use it to to further the learning, y'all if you want to do more of that problem? Strings are a great way to do that. Problem strings are all about eliciting student thinking. And then using that student thinking, using that evidence of what they just did to further the mathematics as you go to the next problem in the string.

Kim Montague:Yeah, so as you're creating some sort of resolution for yourself or goal for yourself, you might just choose one or two that you're going to focus on for a determined amount of time, right? Like I'm a real big fan of SMART goals. They should be specific, measurable, achievable, relevant, and time bound. So you might say to yourself, "I'm going to choose posing purposeful questions, and that's going to be my focus for a month, and I'm going to do it in these ways." And then evaluate yourself just like Kristen did with her kids. She asked them to reflect. You might then take some time to reflect, did I do what I said I was gonna do.

Pam Harris:Brilliant. So as you make resolutions at this time of the year, consider making some towards teaching and helping your students set goals as learners. Hey, we'd like to do a quick shout out to Australia as one of the countries that is our top listeners to the podcast. How fun is that? So we were looking at some podcast data the other day, and it was like check out all the people in Australia that are listening to the podcast. We also have several folks in Australia taking online workshops and in Journey, our online continuing implementation support system. And we just are really loving all of the good folks from down under that are following or helping us with the math is fat Figure-Out-Able movement. So just a quick shout out to Australia. Thanks for joining us in our journey to make math more and more Figure-Out-Able. So if you want to learn more mathematics and refine your math teaching so that you and students are mathematizing more and more, then join the Math is Figure-Out-Able movement and help us spread the word that Math is Figure-Out-Able.

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