Episode #67: How To Promote Reasoning and Proving Over Answer Getting – A Math Mentoring Moment
In episode 67 we speak with Karen Huber, a third grade math teacher from San Antonio Texas. Karen has taken a deep dive with us in our Full Online workshop, she’s a member of the make math moments academy and today in this Math Mentoring Moment Episode we talk about how to promote reasoning and proving with our students instead of focusing on just answer getting.
Stick around and you’ll learn strategies to get students to value math strategies over right and wrong answers, and …. what’s the 10-10-10 rule? and how you can help you think about student learning progressions so that you can give appropriate feedback
- How to help students dive deeper into their learning instead of just answer getting.
- How to use questioning to engage students.
- What’s the 10-10-10 rule and how it can help us think about student learning progressions.
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Karen Huber: We get through the notice and wonders. They turn and talk, do all that kind of stuff and then we get to the point where they do estimations and we’re still good but the estimations cause they really don’t have enough information to really launch into anything. But then as soon as I do the reveal of we talk about, “Okay, well today we’re looking for whatever it is,” and I reveal the information that they can use to start solving it, they go straight for the calculation without a thoughtful processing of why are they doing that calculation?
Jon Orr: [crosstalk 00:00:31] you are listening to the Karen Huber, a third grade math teacher from San Antonio, Texas. Karen has taken a deep dive with us in our full online workshop. She’s a member of the Make Math Moments Academy and today in this math mentoring moment episode, we talk about how to promote reasoning and proving with our students instead of focusing on just answer getting.
Kyle Pearce: Stick around and you’ll learn how to get students to value math strategies over right and wrong answers. What is the 10/10/10 rule? And how you can help think about student learning progressions so that you can give appropriate feedback. All right, let’s not waste any time. Let’s dive in. Welcome to the making math moments that matter podcast. I’m Kyle Pearce from tapintoteenminds.com.
Jon Orr: And I’m John Orr from MrOrr-isageek.com. We are two math teachers who together-
Kyle Pearce: We view the community of math moment makers worldwide who want to build and deliver math lessons that spark engagement, fuel learning, and ignite teacher action. Welcome math moment makers to episode number 67, how to promote reasoning improving over answer getting, a math mentoring 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 by leaving us reviews on Apple podcasts.
Kyle Pearce: This week we want to highlight a review from JJBMAW who gave us a five star rating and review that said, “This is a must listen to podcast for math educators. Each episode is a booster shot to keep my teaching spirits up and keep me going. I especially enjoy the math mentoring moment episodes.” He’s going to love this one then. “Really love hearing about other teachers who might have the same struggles as I do and listening to your analysis and advice on what we could do. Each episode gives me a chance to think about my role and how I can do better. Thank you for producing this great podcast. I’ve been telling my coworkers about your show.”
Jon Orr: We can’t thank JJBMAW enough for taking the time out of their day to not only listen but help us reach our current goal of over 500 ratings and reviews in the near future. We are well on our way with over 200 ratings and 100 written reviews on Apple podcasts.
Kyle Pearce: If you haven’t taken a moment to go and give us an honest rating and review on Apple podcasts, we would certainly appreciate it, especially if you’re listening from somewhere outside of North America just to let us know that you’re out there and listening.
Jon Orr: All right, now before we get to our math mentoring moment with Karen, we also want to take this moment to give you a quick heads up that our online workshop, Making Math Moments that Matter will open for registration next month in late April.
Kyle Pearce: We run the online workshop twice a year and we’re running our second cohort for 2020 this summer instead of the fall based on the feedback we’ve received from so many of you math moment makers, if you’re thinking about taking our online workshop during 2020 then you won’t want to miss registration this April, 2020.
Jon Orr: You can learn more about the workshop @makemathmoments.com/online workshop.
Kyle Pearce: That’s makemathmoments.com/online workshop. All right, my friends, let’s jump right into the conversation with Karen.
Jon Orr: Hey there, Karen. Thanks for joining us here on the making math moments that matter podcast. How are you doing today?
Karen Huber: I am doing fantastic. It’s a nice sunny day today.
Kyle Pearce: Nice. Excellent. That’s awesome to hear and if it’s sunny there, that must mean that you do not live around John and I. Where are you coming from? Tell us a little bit about yourself. How long have you been teaching, and maybe take us down a little bit of, I guess it’s memory lane with your teaching journey.
Karen Huber: Sure. Well, I am in San Antonio, Texas, so we are definitely not anywhere in near Canada.
Jon Orr: No.
Karen Huber: This is probably my third career, if you will. I came to teaching kind of sideways. I got a master’s degree in education and then I went back and got my teaching certification after I had both of my children. I actually ran their daycare. And through that kind of got into the teaching side of education. And the early childhood part of my experience has really informed how I go about learning about teaching because the early childhood is so foundational and it’s all about how to get kids to learn through play. And so that’s a big part of where my foundation came from. And then I just went back to through getting my certification and taught in various places. I’ve taught in Spokane, Washington, before we moved here to Texas. And so I taught fourth, fifth, and sixth gifted and talented students. I’ve taught second grade, I’ve taught fourth grade and I now teach third grade math and science. I am fortunate enough to departmentalize, so I get to focus
Jon Orr: Awesome stuff. I’m always very curious and in awe of teachers of early childhood education. And I also have had significant impact on my career and the way I’ve been teaching almost since the beginning. The way I think about learning, like you said, I have to relate to that because my wife was a Montessori trained teacher for 10 years. Or I guess is a Montessori trained teacher but taught in a Montessori school for 10 years. And has since moved to kindergarten in our local public school. And when I met her we were both teaching in the Caribbean. And what she taught me about early childhood education is what started immediately having me changed the way I’ve been teaching. And I had only been teaching for a couple of years then. But it just made me think about how learning occurs and the students and I’ve shared here that many times is that, I never took a lot of thinking into account about who kids were and what they were learning and how they learn, I just kind of taught the way I was taught.
Jon Orr: But even early in my career I had those thoughts too about different ways kids learn it. Some of that influence that early childhood learning has influenced my high school teaching career. I’m a high school teacher so I’m glad you said that because I think we should all have that early childhood experience. Not necessarily teaching because I don’t know if I could handle teaching little kids, but I think just understanding how little kids learn, like you said, through play. So important. You’ve kind of given us a little snapshot of your career, but I wonder if you could stretch back in time too. What’s a memorable math moment for you if you think about your schooling and the way you learn math, could you share a math moment for us?
Karen Huber: Sure. When I’m thinking about this, it’s hard for me to pinpoint one exact moment, but I think throughout my entire schooling I was good at math. I can make A’s in math. Like a lot of what you talk about, I was a great memorizer. I took calculus all the way through college. I could not tell you what the quadratic formula means or probably even use it right now, but I made A’s in my math classes. But I always remember feeling like I wasn’t good at math because I felt I had to struggle so hard to earn those A’s. And so I struggle in my teaching with how I was taught and what my education about teaching, how those kind of clash. And I have to unlearn how I was taught, if you know what I mean. And so I am never really thought, “Oh yeah, I’m great at math.”
Karen Huber: And I hear teachers all around me because I talk ad nauseum about math and they’re like, “Oh, you’re so good and you know all this and you know all that.” And even still, I’m like, “I’m good at math. I work hard at math.” And I’ve come to realize through readings, through Joe Bowler’s work that struggling doesn’t mean you’re bad at math. Struggling means you’re doing math and you’re exercising your brain. I talked to my kids about, when you’re struggling, that’s a good feeling. You should recognize that as your brain is actually working. It’s getting exercise. And when you come to that solution, when you’ve struggled and you get that there, that aha moment where you’re like, “Oh wow, I’ve got it.” And so I’ve really shifted my whole thought about who I was as a math student to who I am as a math person and that there is no such thing as a math person, but everybody is capable of doing math at whatever level they want to do it at. They just have to recognize easy doesn’t mean you’re good at it, if that makes sense.
Kyle Pearce: No, that totally makes sense. I often wonder because I always talk about this on the podcast as well, just this idea that I did well in math and it sounds like maybe a very similar experience to yours, Karen, where I could do these things but I never felt really good about it. I never necessarily felt super confident and I always wonder about that because even when you think about, you look at surveys on perceptions of mathematics and student perceptions of mathematics in particular and usually they tend to be kind of low even though there’s a lot of students who we would deem successful in math because they get good grades and it’s only recently when I really started diving into research around like the five mathematical proficiencies. This idea that just because you can get answers in math class doesn’t make you mathematically proficient.
Kyle Pearce: That’s like one small chunk, one small piece of a pie. And I wonder if maybe for you and for folks like myself and maybe a lot of students that have been taught in a sort of traditional fashion or a traditional setting where they were able to come up with answers but they didn’t truly have confidence, they didn’t have that productive disposition just because we didn’t have the necessary conceptual underpinning in order for us to actually feel like we knew what we were doing. I don’t know if that resonates with you at all, but for me, I know it certainly does.
Karen Huber: It definitely resonates with me. I remember sitting in a training, and I think you said something like this in one of the podcasts or one of the things I was looking at, but it was teacher training for second grade math curriculum when we were adopting, which was very hands on, very spiraling is very good curriculum and we were working with tiles and I was like, “Oh my gosh, a square number makes a square. That’s why it’s called a square number. Oh my gosh.” And that was the first time I really thought, “What have I been missing? What are all the little nuggets and secrets about math that I just never uncovered and never realized.”
Jon Orr: We’ve talked about one specifically here. There’s a lot of us math teachers who had that same epiphany, “Like what else are we missing or was I not shown or what else did they miss out on that was like this amazing kind of surprising element that I just wasn’t shown in class?” And I have that same thought, we’ve talked about the Pythagorean theorem, like the idea that building on your example of squares is that A squared plus B squared equals C squared and if you draw this squares off the sides and then the areas of those squares add to the bigger area. Like that was mind blowing to me and I didn’t know that until I was a teacher and I didn’t know a lot of things until I was a teacher. I was often wonder, even though we’re showing our students these secrets that we see that as amazing, I still wonder if later on in life if they became math teachers, would they be like they would forget that and then all of a sudden being shown it again, it was like, “Oh, this is amazing. I didn’t realize this as a student. I often wonder if we missed it.” Just maybe I was shown that. I just don’t remember. I don’t know. And I’m hoping it, obviously we’re all hoping that that’s not the case.
Kyle Pearce: I wonder too if it’s just like sometimes you’re just not ready to experience something. It’s the timing just wasn’t right for you. It could have been maybe a time in your life or just maybe like your maturity. And was I develop mentally ready to experience that or to retain that or was I just distracted that day? There was something going on outside of class and I often wonder about that, how many things that now are realizations to me that maybe I’ve already bumped into 10, 20 times before, but they just never meant anything at the time. So that’s always an interesting piece for sure. So I’m wondering, Karen, why don’t we turn to and kind of get the wheels moving on this math mentoring moment and I’m wondering if you don’t mind sharing with us and the math moment maker community, maybe any struggles or challenges, maybe a problem of practice that you might currently be working on right now? Is there anything on your mind lately that we might be able to dig into as a three person team here and kind of hash out?
Karen Huber: Sure. I have a couple of things that are going on always. The main thing that I find I struggle with every year is twofold. I have students who come in from second grade because I’m a third grade teacher and they’re like, “I know all my math facts. I know all my math facts. I know my multiplication. I worked all summer long. My mom and dad worked with me and I know all my math facts.” And I’m like, “That is so great. That’s going to make some of what we do so much easier for you. But math facts are just a really small part of math and we’re going to learn a lot and you’re going to use those math facts as we learn them.” But then as we get down to learning the fact that they know their math facts impedes their willingness or their ability to not know that so they don’t get the discovery moment of the connection.
Karen Huber: So that connection of a square number makes a square because I already knew like two squared is four and three squared is nine, I wasn’t thinking in terms of, “What does that look like or how does that appear or why is that?” I just knew it. And so I have this resistance from those kids to backtrack because they see it as, and I’m making assumptions, wild assumptions, I’m not in their brain, but as taking a step backwards, like, “I already know my math facts. Why are you making me do all this silly work because I know my math facts?” As if that’s all you have to do when you learn multiplication is your math facts. And I struggle with that. So I looking always for tasks and problems for those students to do that require them to stretch what they know about their math facts. So for example, I did the massive mosaic three act today in class with my class. Started it because it takes us two or three days to actually get through these tasks.
Karen Huber: And I said, “You must use graph paper and manipulatives. You have to show me your work. As I’m walking around, I want to see what you’re doing and what you’re discovering and how you’re trying to solve this problem.” And I walked by two students and they’re sitting there, I’m like, “I don’t see anything. What’s going on? We already have the answer. We did all of it in mental math.” And I said, “Oh.” And I knew they didn’t because it was 24 times 24 and we are nowhere near that in third grade right now. And although these are really, really bright students, I picked this specifically so that those students would not be able to get the answer. And I said, “You know guys, one, this is what I asked you to do. Two, that’s not the right answer. You need to go back to the drawing board and let’s get some manipulatives out and let’s see what you can use to try and figure out where your thinking has gone off track.”
Karen Huber: And they were very, very resistant to that. And I don’t even think they got very far down the road today. And so that’s a very real struggle in third grade for me is to try and really get kids one to use manipulatives, graph paper pictures, show their work and to not cling so much as math facts.
Jon Orr: Thanks Karen for sharing that. Let me just restate what I’ve heard and just so that we are all on the same page and I usually like to restate anyway just so you’ve heard it back and then you can make any adjustments as to what I have heard. So I guess what I’m hearing is that you’re studying math facts or different ways of doing multiplication and you want your kids to be good with math facts. We all do. But some kids it may be because their parents influence or maybe because they’ve learned some of these math facts along the way and elsewhere, the kids feel pretty proficient at math facts, like knowing what times what is what answer. And are resistant and hesitant to actually value the deeper learning you’re trying to provide your students. And that is a huge struggle. So trying to get our students to see why we should represent things in different ways or try different strategies. You’re not alone in that, but did that kind of summarize your struggle that you’re currently having with your students accurately?
Karen Huber: Yes. That was very succinct. I like the way you put that.
Jon Orr: Yeah, I’ve experienced this in a high school level. I don’t think it’s something you’re experiencing yourself. So I’m wondering before Kyle and I kind of dig into this with you, is you recognizing this is huge already, right? You recognizing that you want to provide this deeper experience for them, but they’re just resistant to do that. What strategies have you put in place so far to kind of battle this?
Karen Huber: Well, the first strategy I’ve really tried this year that seems to be working a lot better is just we call them notice and wonder problems, but it’s your strategy for like three act tasks or [inaudible 00:18:42] stuff as well. It’s just getting kids to look beyond the numbers. So just withholding all of that information so that they’re just noticing things about the problem and they’re wondering what’s going on. And so they begin that thought process because they don’t have any numbers to work with. So they’re kind of forced in that into that curiosity realm of, “Well, I don’t know what’s going on,” and asking questions about what’s going on. And that’s really helped me to get past that first stumbling block of, especially in problem solving, because before I started using that strategy, we have a problem solving model that we use here at school.
Karen Huber: We use it throughout the district so that everybody’s kind of on the same page when they go from class to class or from grade level to grade level. But every time you present them with a problem, it’s a neat, tidy little problem. And it’s a word problem and the kids are already tackling the numbers without really thinking about the processing of the problem. And so the three act tasks have been a boon to me as far as just getting those kids to slow down and just think mathematically and have conversations with other students in the class. And so that’s really like that’s where I’m at strategically. The first thing that I’ve employed that seems to have worked really well. I am embarking on opening up or starting our rotations or our centers. And today the strategy I had for that, we haven’t started them, but I asked the students to tell me what they thought would be productive for them in centers.
Karen Huber: I asked them to think about, “What is it that you need to learn? What is it that’s difficult for you? What is it that you would want to practice? And here’s the things that you have to know before you leave third grade. There’s three main things you have to know, and so where are you in learning those three things and what would help you practice and learn those better?” And that’s kind of where we are in that progression.
Kyle Pearce: Yeah, I love that you’re seeing the value in doing like a notice and wonder routine and sounds like kind of following that curiosity path that Jon and I speak about in the early episodes, in episodes one to four of the podcast we take a deep dive into the spark fuel ignite sort of three part framework. I’m wondering after you were to intro a three act math task or any type of curious task and kids are engaging in that notice and wonder, we’re kind of withholding some of that information. Then can you kind of paint us a picture like then when to things start to head towards that math fact, “Here’s the answer,” kind of like, “Let’s move on and not really dive into the conceptual or the why behind it.” What does that look like, sound like?
Karen Huber: So what that looks like is we get through the notice and wonders, they turn and talk, do all that kind of stuff. Then we get to the point where they do estimations and we’re still good with the estimations because they really don’t have enough information to really launch into anything. But then as soon as I do the reveal of, we talk about, “Okay, well today we’re looking for whatever it is.” And I reveal the information that they can use to start solving it they go straight for the calculation without a thoughtful processing of why are they doing that calculation? Are they doing it correctly? Have they thought about how to use it? And so as soon as the numbers get introduced, that’s where the wheels fall off and it falls off for my really high kids and it falls off for my really low kids.
Karen Huber: The ones in between that are used to struggle on working hard are like, “Okay, I got this, let me get my manipulatives, let me get all the things that I’ve got. Let me see what I can do to try and figure it out.” And my highs and my lows, my lows are like, “I don’t know what to do with any of this.” And my highs are like, “I’ve got it, I’ve got the answer.” Even if the answers wrong, they really are very confident that they’ve got the right answer. And so my one strategy that I’ve tried to do recently is just pick problems that while they’re going to be really, really stretched for my lower kids, my higher kids, they’re not going to get the right answer because it’s something that they have to employ what they know about math facts to try and figure out how to answer the problem.
Kyle Pearce: I’m wondering like what might be a recent task that you’ve used, just so we can kind of get you thinking about that particular experience. I’m kind of curious, I want to sort of frame something out here and just sort of get your perspective on it. So what might be a recent task that you may have used in the class?
Karen Huber: Well, we did the massive mosaic today and which was really interesting. It showed me a lot of things about my students especially they’re wildly inaccurate and estimating, so they were really interested in what it was. They had a lot of questions. We are not at the point where we have used the notice and wonder enough for them to really be getting to the math questions when we do it. “There’s a lot of colors. It looks really pretty. I wonder who made it.” Sometimes we get some really good math questions and I’m like, “Okay, great. They’re asking some of the things that I need them to ask.” Today wasn’t quite one of those days, but we did come back from Thanksgiving break today, so maybe not the best data introduce, so I did say, “Well I’m wondering how many tiles there might be here.”
Karen Huber: And that’s kind of how I launched that part of it. Then they were all like, “Oh yeah, that’s a really big picture. I wonder how many tiles are on there.” And then they all rushed up to the board and started counting on the picture and trying to see how many. So they were all very interested in that’ll aspect of it. Then they’ve got their notebooks out, they have a partner and they’re talking with their partner and all the manipulatives are out and ready for them to use. And I showed them the reveal of the 24 by 24 and then that was where all three groups kind of did their normal business as usual kind of thing.
Kyle Pearce: Now that paints me like a really clear picture and I know you mentioned this earlier, so I should’ve clued in, I didn’t need to ask you what tasks you’ve done recently, but for this particular task, when students are now off to the races, and I can picture this like I feel I’m in your classroom right now and I can picture those three sort of groups of students, right? Those students who tend to take it and run and then you’ve got those students in that middle sort of ground and then you’ve got some students kind of throwing their arms up in the air. Let’s say it’s a student who goes straight to the standard algorithm or what we in North America call the standard algorithm.
Kyle Pearce: There are different depending on where you are in the world, different standard algorithms. So if I’m looking at that and they’re going, okay 24, they stack 24 and then they put a 24 underneath, they do the ones first, then they do the ones and the tens and the tens and ones, and tens and tens, and they do all of this stuff right. My wonder is what might we ask those students or what might that sound like if that student does come in and let’s say they do have the correct answer, what’s your thinking there? And I know sometimes it catches us off guard cause it’s like, “Oh you’ve got it now. What do I say?” I’m wondering, do you have any sort of ACEs up your sleeve there? When a student does do that to hope that the learning doesn’t stop there?
Karen Huber: Yeah, if a student comes up to me with the right answer, I do. A lot of times I’m like, “Okay wait,” but my normal response is, “Okay, that’s great. How did you get that? Can you show me how you got that? Could you show somebody else how you got that? Can you teach somebody else how to do what you did? Is there another way that you could show me how you got that answer.” And sometimes I’ll get a halfhearted response of like, “Yeah, I guess I could probably go do something else.” And some kids are like, “Yeah, I think I’ve got another way to show you.” Those are my kind of standard strategies is how else could you show this to me?
Kyle Pearce: Yeah, that sounds like a fantastic approach and I know for myself, and it doesn’t always work perfectly in some students, a little harder to kind of push than others, but something I’ve really found lately is really getting this idea of convincing your community meaning, “That’s great that you came up with this.” Something that I really try to do now is I try not to actually give the students any indication as to whether they’re on the right track or not. So, for example, that who comes running up to you with the standard algorithm, they’ve got it stacked and they’re sort of like, “Here look,” or sometimes they’re sort of looking to you for like, “Can you confirm that I did this correctly, that this is correct.” and it’s really hard to do, but I try my best to say, “I don’t know, is it.” And really it kind of like deflects this idea that, “Listen, if you’re coming to me to double check, then that means you haven’t even convinced yourself yet.”
Kyle Pearce: And really trying to come back to this idea of what are we valuing in our math class? What are we after? What do we want students to be able to do? And another thing too, that may or may not be happening, but in my classroom, anytime in this past year or two, I’ve really been a stickler. Every class I go into is a no calculator experience. So everything we’re doing today, we are not going to check with our calculator. We have to find a way that we’re going to be able to convince one another. And the way Karen does it might be very different than the way that I do it or the way that Jon does it. And that creates a great opportunity for them to practice that adaptive reasoning skill. That ability to justify and to conjecture to reason improve. And really when we do this, it sort of puts everybody in a place where it’s like, “You’re going to maybe have to really think that through.” And if you’re not certain that it’s correct or that you’re only looking to your neighbor to see if they got the same answer, like that’s not enough to give you that confidence, you know that you could actually stand up in front of a group of people and sort of advocate for this solution strategy.
Jon Orr: Something else I tend to think about a lot lately is the progression of learning. We got to know where they are. And when you do an activity, like you’ve described, you learn a lot about your students, you learn a lot about who is doing what strategy. You said you’ve got these other kids who are going straight to abstract or algebraic or just number sense or number crunching, but are skipping some of this things you want to see from them. But you’ve got kids who are diving into the manipulators, you got kids also who are struggling to get started. This is a lot of information that you learn about your students, which is awesome that you’re doing this because you know we’ve talked about this a lot here on the podcast is that when I didn’t do these kinds of activities, I didn’t know any of that information about my students.
Jon Orr: I wouldn’t know that until the test or the quiz or the assignment came back. And when I think about that, I think now because I see all of that, you want to think like what is the progression of where you want your students to go? Think of a timeline and not necessarily a timeline, but just a line of what are skills that they’re progressing at and where would we want those skills to end up eventually? And sometimes I think about this 10/10/10 rule. Where do I want their learning to go 10 minutes from now? Where do I want their learning to go 10 days from now? And then where should they be 10 months from now? And sometimes when I think about that in a classroom experience, when I’m seeing my students work and you’re doing some of these strategies, it gives me a lot of comfort about the 10/10/10 because some of the times I have to have a conversation with the kid to say, “I think I got this.”
Jon Orr: “In 10 minutes I think this learning is good, or I’m seeing what I think I need to see for where the student is at this point in the progression.” And then the 10 months gives me a lot of comfort to say, “I’ve got time to progress down this pathway for them.” And not everyone gets to the end of the pathway. We know that the learning doesn’t always work that way. And so that 10/10/10 rule helps me do all of that. But when you’ve got a student who you might think the end of the progression is this abstract multiplication, but you also want to do what you seem to be doing already is just, if you’re at the end of that progression, we should be able to move fluently from one side of the progression line to the other. We should be able to go back and go, “Okay, let’s draw a diagram to represent this multiplication. How can you represent this as an array? Or how can we represent this in a different way or in a number sentence or in a different way?”
Jon Orr: So I think knowing that progression and that landscape can help you decide where or what tip or what hint or what feedback to give the student to move them on that progression. If you think the 10/10/10 rule, you now know in 10 minutes I want them there, but in 10 days I want them there and in 10 months I want them there. So I think kind of knowing these kinds of things helps me in my class at a high school level, push them in the right direction and every kid’s different. So I think we want to think longterm. But I think short term you got the freedom to think longterm.
Kyle Pearce: Well and something else, as Jon you’re talking, and I’m thinking too, when we’re asking students during class to do some of this work and we go back to this idea of what we’re valuing sometimes we have to also sort of like zoom out a little bit and think about, so how am I going to assess and evaluate the students in my classrooms? So for example, let’s say my written assessments are, and I’m going to just kinda call myself out on this. When I started changing my practice and started pulling in more tasks that were filled with curiosity and were what I would consider to be rich because we can engage in these notice and wonder discussions and then actually get students into some powerful problem solving. I had those groups of students that were really kind of hard to shift away from this, like, “Listen, I got the answer.”
Kyle Pearce: Like, “Leave me alone,” is kind of the hunch that I had when you would talk to some of these students. And what I realized afterwards was that if I’m giving them any sort of formal assessment and evaluation, maybe it’s a quiz or a test of some type and in younger grades that looks different of course. But if what I’m evaluating with my students is sort of what some of those kids are doing. So if let’s say showing the standard algorithm is really all I’m after on any form of evaluation, then students kind of get that as sort of what I need to do and really all need to do in order to get some of this work done. And it reminds me of the classroom I was in today actually we were doing a context for learning math unit by Cathy Fasano. And this particular unit is called muffles truffles.
Kyle Pearce: And it was the first day of this particular task. And it’s about essentially having all these truffles, it’s a bakery and the chef, his name is Muffles and he has all these truffles and we were working in a grade four or five class and the idea was he would have these different flavors like ones like vanilla, others, dark chocolate, this is raspberry, there’s all these different kinds. And they had different quantities and he had boxes and these boxes were five by two, so 10 chocolates per box. And the big thing here was to get this idea that like if you had 273 vanilla truffles that you could use 27 boxes. You could see it in the number based on our place value system.
Kyle Pearce: And really they’re taking these numbers and dividing by 10 and at that age, some students weren’t realizing that initially, but some of the students were able to pick up on this pattern that like, “If I just essentially took the ones number away,” and the kids were calling it things like crossing it out or just like pulling it to the side and then using the other digits. Like that’s how many boxes there would be. And some of these kids were really spinning their tires when I was asking them to convince me. And a lot of them couldn’t, they actually couldn’t because they didn’t have the tools, the representations, the mathematical models in order to actually convince me. And I also don’t think that they really were at this level where they could actually think of how to convince me.
Kyle Pearce: They’re still early on in their ability to reason improve. So for us, we were thinking like there’s two things we could do. We could continue nudging them to try to convince us somehow. I could propose ideas like, “Hey, I wonder if you were to draw a couple boxes would that be helpful?” And we’re not making any gains there on some students. The second thing we could do is like flip the script and by flipping the script it might be taking the context of the problem and changing it slightly. So now for these kids that are just looking at the number and covering up the ones column and saying, “That’s how many boxes,” but they can’t explain why it works. Now what we can do is maybe introduce a different box, like a box that fits eight. Like now what?
Kyle Pearce: So now by flipping the script it’s like now I’m putting them in this place where it’s going to cause them essentially to find the answer. They’re going to have to represent it either concretely or visually because they aren’t at the place yet where they have the standard algorithm like the long division algorithm, most of these students. So those are some things to maybe consider as well when you get stuck in this place where you’re really trying to push students for this convincing for. I always say to some kids like, “Hey, if I have $1 million here and you have this one opportunity and if I don’t believe you, you don’t get the $1 million, are you confident that you’ve explained it as clearly as you possibly have?”
Kyle Pearce: And some kids will say, “Yes I am.” And I’m like, “Sorry you don’t get the million dollars. I’m not convinced,” whatever you’re doing, that’s one way to do it. But then the other way is maybe I need to change something here. Maybe for this group of students or for this one student to get them to kind of get stuck in a place where their current understanding what they believe to be true about the mathematics might not work out so nicely. So what might that look like for the massive mosaic task where it’s a two digit by two digit? Is there a scenario where you could flip something there that might put them in a place where they go, “Huh, now I’m going to actually have to think about this and I can’t just turn to an algorithm to sort of save the day for me.”
Karen Huber: Right. Well, and that’s actually why I chose the massive mosaic a problem because we don’t do two digit by two digit here in Texas in third grade. That’s a fourth grade skill. And so I knew these students did not know how to do two digit by two digits. So I knew that they were going to have to do something else to convince me. And so that’s where we’re at. We stopped today, my stop with a couple of kids. I’m like Gia, I just flat out told him like, “No, that’s actually not the correct answer.” I do like the idea of saying, “Well I don’t know if that’s the right answer or not. How could you convince me?” I do like that. But for today, because I really wanted to try and have a conversation with them about what else could you do to show me?
Karen Huber: I was like, “I want you to understand that what you think you’re doing and the way the answer you’re getting are two different things.” Because when they multiply, they got like a thousand something. It’s like, “No, we need to have a conversation. Let me see what you’re doing.” Because they should be able to look at that and go, “Wow, that’s too much.” Even though they don’t know how to do two by two multiplication, they do have enough going on that they should be able to look at that picture and if they were using manipulatives, if for the using graph paper, they should be able to kind of see, “Hey, wait 1000, that’s way too much.” And so we’re on a pause of that because we did not get the test finished today and we were going to pick it up, but they did at the end of the day today we’re like, “Are we still going to get to work on this?”
Karen Huber: Because they knew they hadn’t finished it. They hadn’t come up with the answer, which they’re very keen on getting and I said, “Of course you’re going to have more time to work on this,” and so we’ll have more conversations. All of the kids jumped in and I did have a few that were really struggling as to where to start and so I was able to kind of launch them at each level wherever they were, “Here why don’t you use graph paper? Why don’t you use this?” Because they are third graders.
Jon Orr: Focus on this corner of the mosaic or something like that.
Karen Huber: Right. We are in third grade and they are eight and nine and so they do sometimes need a little bit of scaffolding to say, “Maybe if you start at this point based on what I know about them, I can kind of get them started,” and then they have conversations and they take off.
Jon Orr: Well we’ve chatted about a few different things here this evening and Karen you mentioned one take away already. I think just in passing just then about you really liked the idea of not telling them that they’re right right away. And that’s something I’ve specifically learned from Peter Little at all who call those proximity questions. Like if you’re close, kids will say, “Am I right?” And then you just keep walking away. Just don’t let them know that they’re right or wrong. Let them think like Kyle suggested there. So are there any other big takeaways that you’re thinking of now either trying in your classroom or you’re like, “Ah, I want to do that,” or any other kind of a big takeaway for you this evening?
Karen Huber: I think one of the things just is that 10/10/10 really kind of helps me get a little more perspective. I feel like as teachers, a lot of times we have the standards that we have to get done and we have this end of the year and that’s always looming. But if I can just parse it down to, “Oh, you know what, let’s see where we are in 10 minutes, 10 days.” It just gives a little freedom to relax a little bit. And realize it doesn’t have to all be done immediately. They can’t and don’t have to know everything. The instant you introduce it to them. I really like that idea. And then again, just the idea of I’m not giving that answer away of just, I think that’s the one of the hardest things I struggle with is to remember they don’t need me to tell them whether the answer is right or not. They need to be the ones to feel confident in that. And so those are the two really big ones that I’m taking away tonight. I’m sure as I reflect, there’ll be other ones that come to mind, but those are the ones that are resonating me right now.
Kyle Pearce: Well, you know what? It’s so encouraging to hear someone who has taken and participated in the online workshop and is a part of the Academy. Putting that curiosity path to work and continuing to work through some of our current problems of practice and like we mentioned in the online workshop and throughout everything we do, this is a process that takes time and it sounds like you’re making some headway, which is great. And I think even changing a little bit about how much and how quickly we come in to save students I think is so important. It’s something I still really struggle with because we’re so driven to try to get through stuff, right? We want to get through curriculum and we want to make sure that we’re on track or if you have a pacing guide or all of these things, but at the end of the day it’s like when we come in and save students, how often are students actually benefiting from that anyway? We feel this sense of relief and maybe even they feel a sense of relief, but it doesn’t necessarily mean that learning actually has solidified with those students.
Kyle Pearce: So I’d really love if it’s possible, if you can kind of keep us up to date in between for the next little while inside the academy in the community area. Keep us up to date, let us know how things are going and hopefully can continue this conversation and if it’s okay with you, can we possibly invite you back maybe nine to 12 months from now to kind of see how you’re progressing, how things are shifting in the classroom and basically kind of carry on from where you are at that point?
Karen Huber: That would be great. I would love it.
Kyle Pearce: Fantastic. Fantastic.
Jon Orr: Awesome stuff. Awesome stuff. Thanks so much Karen, for joining us here on the Make Math moments podcast and we look forward to keeping this going and have a good rest of your evening.
Karen Huber: Thank you so much. I enjoyed it.
Kyle Pearce: As always, both John and I learned so much from these math mentoring moment episodes. They happen to be some of our favorite of these podcast episodes that we record, but in order to ensure we hang onto our new learning so it doesn’t wash away like footprints in the sand, make sure that you’re doing some reflecting on what you’ve learned here today. An excellent way to ensure this learning sticks is to reflect and create a plan for yourself to take action on something you’ve learned here.
Jon Orr: A great way to hold yourself accountable is to read it down or even better share it with someone, your partner or your colleague, or even a fellow math moment maker in the community over on Facebook. And you can tag us on social media @makemathmoments.
Kyle Pearce: We also want to take this moment to give you a quick heads up that our online workshop, Making Math Moments That Matter, will be open for registration next month in late April.
Jon Orr: We run the online workshop twice a year and we’re running our second cohort for 2020 this summer instead of the fall. And if you’re like Karen here and you are thinking about taking the workshop during 2020 then you won’t want to miss registration this April of 2020.
Kyle Pearce: Are you interested in joining us for an upcoming math mentoring moment episode where you can share a problem of practice? Apply over @makemathmoments.com/mentor, and we’ll work together as a three person team to help you overcome that problem of practice and develop some next steps.
Jon Orr: In order to ensure you don’t miss out on new episodes as they come out each week. Be sure to subscribe on your favorite podcast platform.
Kyle Pearce: Show notes and links to resources from this episode can be found @makemathmoments.com/episode67. Again, that’s makemathmoments.com/episode67. Well, until next time math moment makers, 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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