Episode #63: Convincing Students To Value Struggle – A Math Mentoring Moment
Christina Marin is a dedicated and reflective middle school teacher from the Bay Area in California. We talk with Christina today about struggles around how students are resistant to learning through productive struggle. Especially students who have been successful in traditional math classes.
In our conversation we talk about how using purposeful questioning and planning can give you the confidence you need to convince students that the struggle is worth it.
- How to use purposeful questions to keep students in a state of flow.
- How planning your learning goals and your consolidation will give your students confidence.
- How to convince parents that teaching through struggle is worthwhile.
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Principles to Actions – 8 effective teaching practices – Executive Summary
3 part math lesson – John Van De Walle & Kyle’s 4 part math lesson
Episode 33 – 5 Practices with Peg Smith
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Christina Marin: The things that I think that I want to focus on, that are really at the forefront of my mind right now are getting students to buy in or try this type of teaching and questioning, and notice and wonder strategies that I’ve been trying out. And not just getting away from the direct instruction and showing students how to do the problem and then letting them try, because that’s what my students want. They’ve been very vocal about that. [crosstalk 00:00:27] about how you want to, or what their ideal math class is.
Kyle Pearce: That there is Christina Marin, a dedicated and reflective middle school teacher from the Bay Area in California. We talk with Christina today about struggles around how students are resistant to learning through productive struggle, especially students who have been successful in more traditional math class settings.
Jon Orr: What you’re about to hear is another Math Mentoring Moment episode where we speak with a Math Moment maker like you, who is struggling with an idea, and together we brainstorm a plan for improvement. In our conversation, we talk about how using purposeful questioning and planning can give you the confidence you need to convince students that the struggle is worth it.
Kyle Pearce: All right, my friends. Let’s hang on, and let’s do this. Welcome to the Making Math Moments that Matter podcast. I’m Kyle Pearce from tapintoteenminds.com.
Jon Orr: And I’m Jon Orr from mrorr-isageek.com. We’re two math teachers who, together…
Kyle Pearce: With you, the community of Math Moment Makers worldwide who want to build and develop math lessons that spark engagement.
Jon Orr: Fuel learning.
Kyle Pearce: And ignite teacher action. Welcome everyone to episode number 63, convincing students to value struggle. Another Math Monitoring Moment.
Jon Orr: Let’s get ready for another jam packed episode, but first we’d like to say thank you to all of you Math Moment Makers from around the globe who have taken the time to share feedback and leave us a review on Apple Podcast.
Kyle Pearce: This week, we want to highlight BethanyH713 who gave us a five star rating and review that said, “Math teachers must listen. I’m so thankful my coworker directed me to this podcast. Our mission as teachers should be to excite and empower mathematics learners. I participated in the virtual summit back in November, and cannot believe it was free. Thank you for being a light in the mathematics education world. I hope the day comes when I have made a name for myself using what I have learned from this podcast, to have the opportunity to be a guest.” She says, #Goals.
Jon Orr: We can’t thank Bethany enough for taking the time out of her day to not only listen, but to help us increase our number of ratings to over 170 from around the globe, and over 75 written five star reviews.
Kyle Pearce: Wow, that is fantastic. If you haven’t taken a moment to go give us an honest rating and review on Apple Podcasts, or whatever podcasting platform you’re on, we would certainly appreciate it, and so what all of the other Math Moment Makers from around the globe.
Jon Orr: All right, now before we get to our discussion with Christie, we want to share with you our podcast big why. It’s providing teachers across the globe high quality, professional development on your schedule. We often talk about our three part framework on how to create resilient problem solvers, and a must for us when developing lessons using the framework is having our students discuss, and reason, defend mathematical ideas and a few routines that we use regularly in the classroom help us start these things. Math fights. No, they’re not a real fight. It’s a math fight. They get your students actively estimating, and questioning, and discussing, and defending their insights, not just with the teacher, but with each other.
Kyle Pearce: Awesome stuff, Jon. Well, we put together a one-page resource for you, a Math Moment Maker, that shows you how to encourage discourse and discussion in your classroom while giving you the resources to make it happen. Be prepared to have your students argue about math. So, head on over to makemathmoments.com/mathfight. That is makemathmoments.com/mathfight.
Jon Orr: All right, let’s jump into our conversation with Christie.
Kyle Pearce: Hey there, Christie. Thanks for joining us on the Making Math Moments that Matter podcast. How are things going over there? You are in, is it Pacific time?
Christina Marin: Yes.
Kyle Pearce: Awesome, where are you coming from?
Christina Marin: I’m in the San Francisco Bay Area, California. Things are great. I am in a town called Martinez, that’s where I live, but I teach in a town called Moraga, which is closer to Berkeley area. I don’t know if you know it. Berkeley is near there.
Jon Orr: A little, yeah. Awesome. Awesome stuff. While we get into this mentoring moment episode, why don’t you fill our listeners in a little bit about your teaching role, how long you’ve been teaching, and your teaching story? Like how you got into this profession.
Christina Marin: Sure. So, I’m currently in my eighth year teaching. I’ve taught middle school here at six through eight, and one year of high school in there, so I always knew I wanted to be a teacher. Originally, I thought I wanted to teach elementary education, and so I was getting my degree in elementary education, and we were required to take a math course. When I took the math course, it was like everybody was asking me questions, everybody felt like I was really good at math, and I was like, “Oh yeah, I like this. I can do this, it’s fun for me.” So I decided at that point to change my major to math education. I switched to math major, and then majored in math, and then did the courses for math teaching.
Christina Marin: When I graduated my undergrad, I took a year off, and in that year, I was a teacher’s aide in a school in a math classroom, and I really enjoyed it. And so, I ended up getting my masters in credential in secondary education, originally wanting to do high school math. I was like, “That’s what I’m going to teach, high school math, so I can coach at the same time.” Then I did part of my student teaching in middle school, and I loved it so much that I was like, “This is my calling. I want to be a middle school math teacher.” So when I applied for jobs, I applied at a middle school, and the middle school that I got hired at, that’s where I taught for my first six years. Then I had a baby, and I went on maternity leave, and when I went on maternity leave and came back, I was like, “The commute’s too far.” So my husband and I moved to another area.
Christina Marin: When we moved, I got a job at a private high school, and I realized that high school just wasn’t the right fit for me. I thought I would try it, just to see if that’s where I wanted to go back, and it wasn’t. Then I ended up having another baby, and went on maternity leave again. During that time, I applied for a job at another middle school, which is where I am now. I’m actually teaching the same classes I taught at my original middle school, which is just regular CCR8, Common Core Math 8, and then an accelerated seventh-grade pathway for students that want to accelerate to maybe do algebra in eighth grade instead of Common Core 8. That’s where I am now, and so I am just a classroom teacher at my school, and I really like it, and I love middle school.
Kyle Pearce: That’s fantastic. That’s such a great story. Jon and I really love the middle grade content, and I know that us being from Ontario, our curriculum or our standards are a little bit different in how they’re organized. So some of your grade seven year content comes up a little later or a little earlier for us, and Jon and I tend to really like hanging out in that six to eighth grade Common Core years, we’ll call it, here in Ontario a lot of that stuff comes up in grade nine as well. So, we can definitely relate on that level. I’m wondering if we can go back to your own experience in math class, and think about a Math Moment that you can remember from your schooling. When we say math class, what Math Moment pops into your mind?
Christina Marin: So, there’s a couple that I really remember. The first one was in second grade. I went to a private school my whole life, except for college, and private Catholic, so I had the nuns as my teachers in some of my classes. The principal was a nun, that whole thing. I remember in second grade, they would drill the times tables. I remember that they would take us out in the hall, and they would just ask you, “Four times two,” or whatever it was, and you just had to spit them off. I remember one time, I was doing the sevens, and I was so nervous because I just had to memorize the sevens, and that was the hardest for me. I don’t even remember how I did. I just remember the moment leading up to it, and being so anxious about having to know my sevens times tables because that’s what I was being tested on that day.
Christina Marin: That’s one of them, and then the second of them was in third grade. I did not have a nun in this particular class, but I did have a teacher. She was Ms. Cunningham when I started, and Mrs. Oliveri went I finished, because she got married in the year. She was determined for her class to love math. And so, she taught us this “I love math” song that we would sing all the time before we started math class.
Jon Orr: Can you remember it? Can you sing it for us a little bit?
Christina Marin: I know.
Kyle Pearce: Exactly, I’m wondering.
Christina Marin: I don’t remember exactly, but I feel like it went, “I love math, yes I do. I love math, and so will you.”
Jon Orr: It’s like a chant.
Christina Marin: Just saying it, she wanted us to love math as much as she did, and so I feel like that’s really where my math interest started, in that class, because she was so passionate about it. I felt like that was a really cool thing to be passionate about.
Jon Orr: Awesome. Thanks for sharing that. So many of our guests, when we ask them to share a memorable moment, some of the negative ones usually tend to be memorizing math facts, and multiplication being one of those things that a lot of people say is either in that game format, or it’s a put on the spot kind of format. I was at parent-teacher interviews at my daughter’s school recently, and we walked in and they said that they had been working on their math facts, and they were making sure that they all knew them. I was like, “I wonder what’s going on here. I wonder if my daughter is going to have a memorable moment that’s good or bad out of this,” because so many people are having memorable moments that are negative about math facts and multiplying.
Jon Orr: My daughter was at a student-led conference, so she showed me what they were doing with multiplying facts. They actually were doing some really interesting things with using number sets to build strategies on multiplying, which I had never done when I was a kid. They were talking about when you’re multiplying by four, you can double the double, and when you’re multiplying by five, you can count by five. I found that there were nice strategies to help kids multiply with, which I never thought about as a kid. I just memorized my math tables. Let’s get into, are there any kind of struggles or challenges you have going with you right now? Is there anything on your mind that we can help dig into with you?
Christina Marin: Yes, there’s a lot on my mind. The things that I think that I want to focus on, that are really at the forefront of my mind right now are getting students to buy in, or try this type of teaching, and questioning, and notice, and wonder strategies that I have been trying out. Not just getting away from the direct instruction, and showing students how to do the problem, and then letting them try, because that’s what my students want. They’ve been very vocal about that, and I gave them a survey recently about how they want to see, or what their ideal math class is. If they could change one thing about math class, what would it be?
Christina Marin: I would say about 50% of them want me to stand up in the front and show them how to do it, and then try it on their own, and then start their homework so that they can ask me questions if they’re confused. That’s not really my style, and so I’m having a really hard time getting them to buy in. I think part of it is because they’ve been taught, in that method where they’ve been told how to do it, and then they try it. That’s how they’ve been taught for the last six or seven years. I’m struggling getting them to even try this method, and then I’ve been getting a few parent emails, or just concerns about me not teaching the students. I’m using the air quotes, “teaching,” because I am teaching, but I’m teaching differently than what they think teaching should be, I guess, how they view it.
Christina Marin: And then also, it’s an accelerated class, so they have to move at a faster pace. They’re learning more material in a certain amount of time, so it’s a very high stakes class. When they don’t understand something, it’s very concerning for them, and they get very stressed out. I’m struggling with that, and I don’t even know if I need to convince them or get them. I’ve been trying to convince them, but I think I need to stop doing that and just do my thing. I’m getting discouraged, I guess. At my old school, or my first school that I was at for six years, I never really had this problem. I don’t know if it was because I was just hidden from it, like my administrators got all the parent complaints and they just had our back, but my whole department, we all taught very similarly, so I think it was more like the students had seen it, so it wasn’t new to them. They knew what to expect going into math class. Does that make sense?
Kyle Pearce: That totally makes sense, and I’m picturing a lot of guests that we’ve had on, and folks that we’ve worked with in our online workshop, and the academy oftentimes really struggle with these pieces. Just to make sure we’ve heard, I’m just going to restate a few things here, just to make sure that we’re on the same path here. It sounds like you’re trying to break free, or break away, and it actually sounds like since you had been doing this in your old school, that may be the culture of learning math in this new environment for you, it’s almost like it’s starting over, in a lot of ways, in terms of you’ve shifted your practice a little bit. Some students, about half of your students are saying, “Listen, I’d much rather if you just stood up there and did this for me, and I’ll just follow your lead.”
Kyle Pearce: You’re struggling, as well, because you’re feeling it, maybe hearing it from parents, as well. Does that summarize, in general, the struggle that you’re up against currently?
Christina Marin: I almost am doubting myself. Like, am I actually doing this right?? Am I doing this in a way that’s going to benefit them? Whereas I know I’ve been successful with it in the past, but it’s almost like me doubting myself because the students are so not on board with it. I’m like, “Maybe I’m not teaching them. Maybe I need to rethink how I’m doing things.” I’m a very reflective teacher, which is a good and a bad thing. But I’m very reflective, so I think a lot about how I’m impacting my students, and I think that’s also a big part of why I feel so frustrated.
Kyle Pearce: For sure. I’m wondering what sort of approaches have you done so far. Obviously, you’re aware of this, this is something, as you’ve mentioned, and I love how you mentioned being reflective is good and bad, because being reflective sometimes we beat ourselves up a little bit, right?
Christina Marin: Right.
Kyle Pearce: When someone who is not reflective, there’s less growth there. But at the same time, they are probably sleeping better at night, you know? There’s always that, which is kind of nice. But I would argue that being reflective is so important. So I’m wondering, to this point, what have you done so far to tinker with this, and try to, I guess you had mentioned convincing. Do you mind going a little deeper in that? You were mentioning as well, we heard you say that you’re not sure if you should be convincing. What might that look like, sound like?
Christina Marin: I like to start the school year with some stuff by Jo Boaler, like the week of inspirational math. We started the year with that, and doing, I have these brains in the back of my classroom where, when a student takes a risk, or supports somebody who takes a risk, or makes a mistake and learns from it, they can put a sticker and draw a synapse firing to show that they have grown their brain for doing these mistakes, or taking the risk. They really like doing that, and I think that’s helped a lot. I started it more part way through, I don’t know, October. The kids like doing that, so I think it’s helped one of my classes buying in a little bit. One of my other classes is still not on board. I’ve tried to retell them, it’s okay to struggle. It’s okay to make mistakes.
Christina Marin: I make mistakes as an example for them, and ask them questions, and try and get them to learn from each other. Tell them that I’m not going to give them the answer yet, those sorts of things. I do eventually help them out if they’re not getting there. If somebody doesn’t get there, I do eventually help them out. We do eventually do the notes piece, the direct instruction part that they want at some point, but it’s not at the beginning, and I am also wondering if because they know it’s going to happen at some point, they just don’t even try at the beginning. Yeah, but the brain has been, that’s been a good thing for one of my classes. It hasn’t really worked for my other classes yet.
Kyle Pearce: This just popped into my mind about one of the statements you just said about, you want to do the direct instruction, and you have this inkling that you might be saving them too quickly. I’m wondering what, and I know this is different based on lesson, and different based on what’s happening. I wonder if you could walk us through a lesson where, just give us a brief overview of what that looked like for you, where you felt that this is not going the way I wanted it to go, and I have to do something. It’s kind of like, you’re feeling that pressure of the kids aren’t buying into this, and I have to either give them what they need, or you have to adjust. Could you maybe just walk us through a lesson where you struggled with this mindset?
Christina Marin: Yeah. Recently, we did properties of exponents with both of my seventh grade and my eighth grade, but with my seventh grade, we started with the Andrew Siddall mistakes exponents. I don’t know if you’ve seen that before, or you’ve heard of it. It’s like he gives them eight problems, and they are all wrong for exponents.
Kyle Pearce: Maybe not that specific one, but I knew Andrew does a lot of work with error checking and that kind of stuff, yeah.
Christina Marin: Yes. So I gave them something where it was all wrong, and they knew basic properties of exponents, just like they know what the base, and the power, and the exponent mean. And so I tried to get them to use what they knew about exponents to figure out what was wrong with the other ones, and they just sat there. It was like, “No, you can do it. Keep trying.” And I would help a few of them, and they were working in teams, and I would help a few of them with, “What does it mean? Maybe put in expanded form and see if that helps you.” I basically gave them a day, and then we did a day of discussion. Then after that, we didn’t get through everything, so I was like, “Okay, we’re running out of time. I just need to give them the properties.”
Christina Marin: So, I gave them my sheet that was, we filled in the properties together, and we went through it that way because I just felt like I was losing them.
Jon Orr: So, I want to go back a little bit. When you said, “Hey guys, do this,” what does that look like? What are the students doing? Are they at desks? Are they in partners? Are they in groups? Are they at the walls? Can you give me a little snapshot of that?
Christina Marin: In my classroom, there’s tables. It’s like desks put into groups of four, and normally when we do something like this, I always give them at least a few minutes by themselves to try whatever they can. I give them time to try alone. It’s almost like a think-pair-share in English. So they get time to do it by themselves, and then they work as a team and they try and figure out the problems asking each other, helping each other out. Then after that, we will have a class discussion about what they found, or what mistakes they saw and that sort of thing. When we do the class discussion, I usually take a step back and I have them come to the board, and show what they did, or what mistakes they made.
Kyle Pearce: Okay, so I’m wondering. You had mentioned one group. Do you find that they are actually utilizing one another in their groups, or are you finding that particular group of students is maybe not feeling so comfortable with that math discourse? How would you try to describe that, what that would look like, sound like, as the think-pair-share? Would you argue that strategy is working for that group, or are they not really turning, and talking, and actually collaborating with one another?
Christina Marin: They’re definitely collaborating, so it’s definitely working. I think the part that they’re struggling with the most is explaining to one another. If there’s a student in the group that has the right idea, or maybe has learned it before and already knows, they just are having a hard time explaining, and then the students are having a hard time understanding what the other student is saying. Maybe they are explaining, but because it’s not the teacher that’s explaining it to them. They are like, “I don’t get it.” Even if I explained it in the exact same way, because I’m the teacher, they feel more confident in what I have to say.
Kyle Pearce: I’m curious, what might that teacher move sound like when students are, I’m picturing in my mind and I’m not there, but I’m kind of reenacting this in my mind. I’m maybe feeling the tension in the room rising a little bit, because some students are maybe spinning their wheels a little bit. Then this puts me as the educator going, “What do I do next? Do I bail them out? Or what do I do?”
Christina Marin: Right.
Kyle Pearce: If you were to picture that scenario from your memory, what might that look like, sound like for you? What might you ask them, or have them do, in order to try to get out of that rut?
Christina Marin: A lot of times, I’ll ask them leading questions, or I will ask if they want somebody else to help them, or if they want me to help them. Sometimes, they will say yes, and sometimes they’ll be like, “Okay, somebody else can keep going, or help me out.” And it’s really hard for me, because I feel like almost the students tune out when another student is talking also, because they want to think of what they’re going to say if they wanted to respond, or argue, or whatever. I feel like they don’t listen to each other sometimes also. There’s kids that know what they’re saying, and then there’s also students who are totally confused, and they’re like, “I’m totally confused. I’m just going to check out and wait for Ms. Marin to go to the front and tell me what to do.”
Christina Marin: Which is also like, how do I get them to listen to each other better? Sometimes I will be like, “Okay, that was really great. Thank you for sharing. Did you guys hear what they said? Can someone rephrase what they said?” So that they can maybe try and listen to each other better. I don’t know if that answered your question.
Kyle Pearce: No, totally. Totally. I think rephrasing, it sounds like you’ve got a ton of strategies that you’re utilizing them. I’m wondering, do you ever find yourself where you feel like you get yourself to this point where maybe you step in? I guess I’m wondering, do students, are they depending almost too much on you to eventually come in and swoop and save the day for math class? What does that look like, or sound like to you? I know for me, I struggled in the classroom a lot, where I would have students problem solve, for example, but then I would sweep in, and then save the day. It was almost like I had some students in my room who knew that was going to happen, so it was like they never fully engaged. Do you find yourself struggling with that issue like I used to do? I mean, I still do. It’s always a struggle, but always working on it to get better.
Christina Marin: Yes, I think that’s definitely my biggest struggle right now. Me just wanting to swoop in and be like, “Here we go.” Some of the kids are just waiting for that, and then their complaint is, “Why didn’t you just do that sooner? Why did we waste all this time doing this thing? You should’ve just told us sooner.” And I’m trying to find a way to balance, to step back a little bit more so that I am not swooping in so soon, but then I am also worried about them still not being engaged and trying. I’m having a really hard time balancing, when do I swoop in so that they can still try and struggle, but not be frustrated with me as not teaching them?
Kyle Pearce: From what I’m hearing, I’m picturing again, I feel like maybe it’s more my story than your story, so forgive me if maybe I’m interpreting this incorrectly or if I’m off-base. But something that popped into my mind right away is, the antidote that I’ve been trying personally to work on and reflect on is this idea of purposeful questioning, which is one of the eight effective teaching practices in the principles to actions book by MCTM. It’s this idea of being able to go from group to group, and address groups more individually, versus me broadly stating things to the entire class. Something that I think about a lot now is, really using words like, have you convinced yourself? Have you convinced your community, or your neighbors of what it is you’re trying to say?
Kyle Pearce: And really allowing them to productively struggle through that process, and with that comes the tension that I think you have, which in some ways, I think initially that’s very scary. Like, it’s scary territory to be in, where there’s a little bit of this dissonance in the room. There’s a little bit of confusion, and I think we as educators, we want kids to have clarity, and we want them to have understanding. But I wonder if we’re so used to coming in and saving the day that, how many times I’ve saved students or I bailed them out of a tough situation, I wonder how many times that I literally just stole the thinking from the students, and I wonder whether they actually understood anyway, right?
Christina Marin: Right, I can picture the moments that you’re talking about.
Kyle Pearce: Yeah, it’s like all that tension immediately drops, and it’s sort of like, “Phew. We’re out of that situation. Now let’s just move on.” And in some ways, I wonder if maybe that might be where some of that reaction you’ve referenced earlier, where some students are like, “Why didn’t you just do that sooner?” Because it’s kind of like in their mind, the tension rose, but then all of a sudden it was gone, but I still didn’t actually gain the outcome that we were hoping for. We, as educators, were hoping for. I’m wondering, what are your thoughts on that? And I wonder, is there anything in your mind, if you are like, “If I had this magic wand,” Jon and I talk about it all the time. And if I could make this problem disappear, what might that look like or sound like if you were to have this productive struggle going on tomorrow? What might be maybe your strategy in your back pocket as, how can I maybe navigate this a little bit differently to see if maybe there’s some sort of change in behavior from our students?
Christina Marin: I think I would probably have more time in the class. Like, give me a whole day of math, and then we can definitely do this. But realistically, I would probably wait longer to help them. I really liked the purposeful teaching that you talked about, and going to individual groups and addressing them individually about what their struggles are, and giving each group the amount of time and attention that they need for whatever it is that they’re talking about, or struggling with in that particular problem. I think that would be ideal. And if I could do that, just maybe sit back and listen, and just ask students to repeat things if they’re headed in the right direction, and have students actually listening to what that student is saying. That would be great.
Jon Orr: I’ve got a few tips that I’ve used, Christina, in my classes to, I think help with a couple of the things that you’ve been talking about here. And also with this kind of pushback on students, which translates to parents. Parents push back because the kids are complaining at home, right? They’re like, “Oh, I’m not getting it.” Then the parents are like, “Okay, let me research this. What’s going on? Let me find out more.”
Christina Marin: And I think that’s the big thing, too. Kids are going home and they’re like, “My teacher’s not teaching me.” The parents are concerned because they are in this class, and they’re supposed to be accelerated, and they’re not accelerated, and they are supposed to learn, and be in high school next year, and you know all this material. Then they are like, “What is it that’s not being taught?” Every time I talk to a parent, it’s always positive, and the parents always totally understand where I’m coming from, and they get it, and they’re on board. I think it’s just like, they just want their students to be successful, and that’s what I want, too.
Kyle Pearce: Sure.
Christina Marin: And I think, I can’t remember her name, that wrote Adding Parents to the Equation. She talked about that when she came on.
Kyle Pearce: Hillary.
Jon Orr: Hillary, yeah.
Christina Marin: Yes, Hillary talked about that when she came on. Parents just want their kids to be successful, so they are trying to help them, and I get that. I totally get that.
Jon Orr: Yeah. The kids want to be successful, too, and sometimes when kids go home and tell parents that, her voice those concerns in class, they’re really saying, “I’m not getting what I need.” They only have to resort back to the way they were taught before, so I don’t think it’s a situation where you have to teach me the other way. I think it’s just like, they’re feeling like they’re not getting those mini successes that they would get. There’s something there that they’re walking out going, “I didn’t feel accomplished today.” Sometimes for me, because I had the same issues before. I think when I became very purposeful in the questioning, but also very purposeful in, what do you want to accomplish in that period?
Jon Orr: I’m always going into my lesson with, the same way I would have 10 years ago when I was teaching. It was like, “Today we’re going to learn about this.” I don’t specifically say that to the student, but this is in my brain. We need to get through, bring these concepts out, talk about this particular strategy, or practice on how to solve these types of problems. The same thing you would always think about for a lesson. When you have that learning goal in mind, it’s kind of like you have to remember that you’re going to get there. And so when you plan your lesson, I usually plan this lesson, it sounds like what you’re planning. It’s like, let’s get everybody to solve a particular series of problems, or a problem that’s going to generate different solutions that we can compare.
Jon Orr: Or maybe it’s a series of problems that lead you to talk about why a particular strategy is better than another. That might be the learning goal that day. For example, we’ve quoted Dan Meyer here lots of times, and he’s got that, if math is the aspirin, what’s the headache? Sometimes, you putting the students in a struggling situation where they do struggle, and get somewhat frustrated, and before that frustration boils over, you can come in and go, “Look, I’m going to be the guide. I’m here. I’ve got this other strategy that no one has created yet.” And you might have anticipated that. You might have anticipated them to do this, this, and this strategy, but the real strategy that you want to highlight today is this other strategy that you know probably no one was going to get to, but you now get to go, “This strategy is the aspirin.”
Jon Orr: This strategy helps us avoid that problem, and avoid that problem, and avoid that problem. Then you can practice that strategy, and that’s all done by the end of class. It’s like I wanted this to happen, and I got there. It’s all those many successes that happen along the way where the students were like, “Oh, she does have a better way to do this. Let’s listen in.” It’s the same as you swooping in, but I think it’s done a little bit differently if you’re going to set it up so that you know that’s going to happen. It’s kind of like you’ve orchestrated this whole ruse for them to lead to this nice move where you’re going to rush in. And sometimes, those lessons aren’t like that. The strategy pops out, and then you get to talk about it and then practice it.
Jon Orr: I think being very precise with what you want to accomplish in one period can give you the confidence to know what you’re going to talk about that day, and so that confidence will rub off on the students. It’s the confidence that we project to the kids about our learning goal that day, and what we want to accomplish, where they are going to go, “Oh, there’s a plan here.” And they can follow along with you, and know that you have their backs. It’s like if they get that feeling that my teacher is going to support me, my teacher is there every step of the way, and you’re going to give them those little successes along the way, they won’t walk out of the class going, “Oh, there’s something missing today.” I think there’s a lot of things going on in there, but these are the things I’ve thought about over the last few years about setting goals for myself, and making sure that we accomplish them.
Jon Orr: That one period, it kind of spills over. I try to make sure that we wrap it up before the period ends so that nobody is walking out going, “What did we just do?”
Christina Marin: Yeah, and I think that’s where I’m struggling, too, is the wrap-up. Wrapping it up before the period ends, because it’s like a 45 minute class period. It’s like okay, I’ve got to do all this stuff. Sometimes it does go into the next day, and I think that’s where they’re struggling because they’re like, “It wasn’t wrapped up. We didn’t talk about anything. I feel totally lost, still.”
Jon Orr: Yeah, they’re leaving class with these loose ends going, “I don’t have, what was the purpose today?”
Christina Marin: That’s really good to remember, the wrap up part.
Kyle Pearce: Yeah, that consolidation piece is really key. And it is hard, right? It’s hard because you are trying to plan it out, you’re trying to time things out. Sometimes it’s okay for a consolidation to go to the next day, but again, if there’s, let’s say the state of confusion, it just leaves a bad taste in some student’s mouths until they can figure things out. Or at least that they trust what’s actually happening. But something for me that’s popping into my mind, I think it’s how we were all taught. So many of us were taught by essentially watching teachers model a bunch of things, and essentially the kids who were successful were the ones who were pretty decent at memorizing it, and copying, and essentially mimicking what the teacher was doing.
Kyle Pearce: What you’re doing, and what we’re trying to do in our classrooms is really, we’re trying to put the thinking, and give the thinking to the students so that they can actually work through problems, and actually solve them. But the challenge with that is that in our minds, we go, “Well, when I used to model all these problems, I would model six of them. Then I would give kids a bunch of them to practice.” But at the end of the day, kids were essentially trying to behaviorally mimic what we were doing anyway, so it wasn’t like they were really understanding necessarily what was happening. They were essentially just following patterns, and hopefully they see a problem like that on their assessment, and we move on. Whereas now, if we’re actually going to put the thinking in their hands, and allow them to problem solve, we do have to allow for the time.
Kyle Pearce: Obviously, we don’t want it to just be like, “Hey, I’m going to go stand over here, and you just struggle right through.” That purposeful questioning is what keeps that moving, keeps that conversation going. At the end of the day, I just think to myself, how much more powerful it is when a student can solve, people call it a rich task, but essentially we give them a task, we haven’t told them how to do the task. But they have enough prior knowledge, and different strategies from things that they’ve done in the past, that they can work their way through, and essentially what we’re trying to do is to help emerge new models, help emerging new strategies like, take their thinking and make it connect to someone else’s thinking.
Kyle Pearce: Through that work, that’s what really allows students to feel that confidence, that productive disposition around mathematics. I wonder if we give them a little bit more of that ownership, and then we focus in on that consolidation afterwards, to really try to help select and sequence student thinking, and really tie it together. Like if I’m thinking about how I could do that without just taking it and summarizing the whole thing, I wonder if that disposition will change, where students will start to see themselves as, “I can actually do this, because this is actually making sense to me.” Whereas if midway through that lesson, we flip-flop back to our more traditional style of, “Let me show you the answer, or how you could solve this problem,” but it doesn’t connect at all to my thinking that I’ve been using this entire class.
Kyle Pearce: Now I’m left almost worse off, where I’m like, “Geez, I was doing this over here. I was way off path.” Because look at it, she’s up there doing this. I’m over here doing that. I must be 100% incorrect, when meanwhile, that student might have had a really interesting and really effective strategy, but it just didn’t look like the strategy that we were sharing up on the board. Those are things like, it is some heavy, heavy thinking. Some heavy work, but I feel like just through the conversation and the different strategies that you’ve used in your classroom, I feel like you are right there. I feel like it’s right there for you. It’s going to take time to refine it, but I feel like you’re reflective enough, and you’re thinking deeply about it. You just keep on pushing that envelope, just a little bit further, and that trust from students will come.
Kyle Pearce: But I wonder if maybe you have to maybe trust yourself a little more, as well. Because sometimes we, as educators, that little voice in our mind, it’s always giving us bad ideas. It’s always giving us thoughts, and doubts, and at the end of the day, that doubt sometimes almost sabotages us, because now we half did something. Then we go back to this other way, and it’s almost like now we’ve done neither one as effectively as we could have, you know?
Christina Marin: Right. Even just while you’re talking, I’m already thinking, we’re doing percents next. Percent increase and decrease, and all of that, and I’m already thinking of, what am I going to use? How am I going to give them the productive struggle of doing percents, but give them tools that they can use? I’m already racking my brain of the things that I’m going to use, so it’s good. Listening to you guys, and hearing what you are saying, it gives me ideas to how to move forward and make sure that I’m still giving them.
Kyle Pearce: I’ve got a really cool task for you with percentages. I will email them to you. I’m going to make a note and include them.
Christina Marin: Perfect.
Kyle Pearce: It’s a problem of the week from the University of Waterloo, and I actually created some videos to re-create it 3X style.
Christina Marin: Awesome.
Kyle Pearce: I haven’t shared it with anyone, but I’ll forward you.
Christina Marin: I feel so honored to be the first.
Kyle Pearce: We’ll get you now. Yeah, and when it goes live, we’ll definitely let the rest of the Moment Maker community be aware of it, as well.
Christina Marin: I did use your stacking paper task. We just recently did predictions with the constant proportionality and all of that, and we did a notice and wonder, and the kids were like, “I wonder, what is tap into teen minds?” It just made me chuckle because I think some of them probably looked it up, just so that they knew after class was over.
Jon Orr: That’s funny.
Christina Marin: So they knew what tap into teen minds was, but I just thought that’s really funny. But it was great with my students, I did have to guide them on how to scale a graph and how to make a graph, because that was something that they knew how to do, but they weren’t very successful at it. It did present us with these really good discussions about graphs, and how to scale things, so that was really great.
Jon Orr: Yeah, I don’t know if you did this, but I used to make sure that wouldn’t have been an issue. I would be like, “I’ve got to make sure that we’re good at that before,” whereas now, I welcome that, like you’ve just welcomed that into your class, because it’s like a teachable moment in that moment to talk about why graphs, why the scales need to be adjusted, or why it’s important to think about that. That’s good.
Kyle Pearce: Yeah, why does your graph look like this, and mine look like that? Shouldn’t I be able to tell the same information?
Christina Marin: Yeah, and some of them did bars too, instead of plotting points and drawing lines, which was really fascinating, and that led to, “Okay, this is why we do a graph like this for this type of problem, because it helps us to make predictions and everything like that.” It was good. It was really good.
Jon Orr: Christina, you were mentioning some of the things that you’ve been taking away here from our conversation, but I wonder if you have any more big takeaways from our conversation that take back to class right away, or maybe even think about later on? Is there any kind of big takeaways that you would like to share with us?
Christina Marin: I think the two that I’m definitely going to, that are big takeaways that I’m going to do more with are the purposeful teaching and addressing the groups individually that you were talking about. I am going to do more of that, and definitely the wrap-ups every class period. I’m going to try and give myself at least five minutes at the end it to wrap it up, and to maybe give the students an overview of the things that we went over today, and the things that we learned, even if we didn’t totally close up, or make a solid understanding. I’d want to do some sort of wrap up so they are not feeling completely lost and out of the loop. I think for that too, I need to be okay with not assigning homework every night, so that if we didn’t wrap something up, they are not having homework on something they didn’t learn.
Kyle Pearce: Well, that’s fantastic. I will add into the show notes that purposeful questioning is one of those eight effective teaching practices, like Ed mentioned, from principles to actions. I’ll definitely include that in the show notes. Something you might want to consider when it comes to consolidation, like that wrap-up you were referencing is, John Van de Walle, to my knowledge, is the founder, the creative of the three part math lesson, which not to be confused with three active math tasks, like Dan Meyer three act math task, but the three part math lesson that has a minds-on, an action, and a consolidation. I’ll include some links in there, including a version that I did a little while ago. I called it the four-part math lesson, because I broke it up even into some smaller chunks.
Kyle Pearce: So, we’ll include those links, and then something else that could be helpful. I know this is a lot, lots of ideas here, but going back to episode 33, I believe it was, with Peg Smith and the five practices for orchestrating productive discussions in math class. That is a great episode to take this idea of, as kids are solving problems, what we as educators want to be doing before, during and after the lesson. I feel like those things could be three really big pieces that you could hone in on for your own professional learning over the next little while, and we just want to say thanks again for joining us on this episode. We’re wondering, would you be willing to come back in, say, I don’t know, 9 to 12 months to give the Math Moment Maker community an update on how things are going?
Christina Marin: Totally. I also want to say thank you to you guys, because I’ve got all these great resources that I am now using, and this whole list of books that I have to read. Some that I’m asking for, for Christmas, because I just have so many that I have to read now, that I’ve gotten from you guys on the podcast.
Kyle Pearce: Awesome, thanks for saying that.
Jon Orr: Fantastic. All right.
Kyle Pearce: Awesome. Thank you so much for joining us. We’ve had a blast. These conversations, we always talk about them. They’re our favorite because it really makes us be reflective. We’re envisioning what you’re describing and we’re saying, “Yeah, we’ve been there. We know what that feels like.” And hopefully between the three of us, hopefully that gives us all some new ideas as we move forward, in trying to help push student thinking forward, and evolving from that more traditional sort of sit back and mimic the teacher style that I did for so long in my classroom, I know for sure. So, thank you so much for joining us.
Christina Marin: Thanks for having me.
Jon Orr: Thank you.
Kyle Pearce: And hopefully we will get you back on in 9 to 12 months. We hope you have an amazing remainder of this next little bit of your semester, and we’ll go from there.
Jon Orr: All right, thanks so much.
Kyle Pearce: Have a great night.
Christina Marin: You took.
Kyle Pearce: As always, my Math Moment Making friends, both Jon and I learned so much by engaging in these conversations. But in order to ensure that we hang on to this new learning so it doesn’t wash away like footprints in the sand, we’ve got to reflect on what we’ve learned. An excellent way to ensure this learning sticks is to reflect and create a plan for yourself, so that you can take action on something. Maybe something even really, really small, just to get yourself started that you’ve learned here in this episode.
Jon Orr: A great way to hold yourself accountable is to write it down, or even share it with someone, your partner, colleagues, or with the Math Moment Maker community by commenting on the show notes page, or tagging us @MakeMathMoments on social media, or in our free private Facebook group, Math Moment Makers, K-12.
Kyle Pearce: As you know, our podcast’s big why is providing teachers like you across the globe high quality, professional development on your schedule. We often talk about our three part framework, and how to create resilient problem solvers. A must for us when developing lessons using this framework is having our students discuss, reason and defend mathematical ideas. A few routines that we use regularly in our classroom will help us to start these math fights. No, not a real fight, but a math fight. Get your students actively estimating. Getting them questioning, discussing and defending their insights, not with the teacher, but with each other.
Jon Orr: We’ve put together a one-page resource for you that shows you how to encourage discourse and discussion in your classroom while giving you the resources to make it happen. Be prepared to have your students argue about math. Head over to makemathmoments.com/mathfight. That’s makemathmoments.com/mathfight.
Kyle Pearce: And if you’re listening to this and you’re interested in joining us, just like Christie did today, for an upcoming Math Mentoring Moment episode, where you can share a big math class struggle, come on over, apply at makemathmoments.com/mentor. That’s makemathmoments.com/mentor.
Jon Orr: In order to ensure you don’t miss out on new episodes as they come out each Monday morning at 5:30 Eastern Standard Time, be sure to subscribe on your favorite podcast platform.
Kyle Pearce: Show notes and links, and resources from this episode can be found at makemathmoments.com/episode63. That’s makemathmoments.com/episode63. Well, until next time, I’m Kyle Pearce.
Jon Orr: And I’m Jon Orr.
Kyle Pearce: High fives for us.
Jon Orr: And high fives for you.
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