Episode #38: How to Move Beyond Answer Getting. A Math Mentoring Moment
In this Math Mentoring Moment episode we speak with a year 1 (first grade) teacher Sierra Classen in her second year of teaching from Melbourne, Australia. Listen in as we work through this common struggle we have all faced – either currently or in the past – related to students hyper focusing on answer getting over process.
- Strategies to help your students re-think the purpose of math class.
- How games can shape math lessons
- Why number talks are great culture builders
- Characteristics of effective math instruction
- Two Types of questions you should avoid answering
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Sierra Classen: Everybody struggles all throughout because their teaching degree or teaching whatever career because my network of schools is currently focusing on math. Things change. Teaching methods change and whatever. There’s been a lot of reticence and a lot of interest from different people and different approaches and reactions to us updating our teaching and talking about our struggles. That’s been very interesting for me. The kind of struggles that [crosstalk 00:00:30].
Kyle Pearce: You’re listening to, a fellow math moment maker, a year one teacher, Sierra Classen in her second year of teaching from Melbourne, Australia who’s joining us on this episode for a math mentoring moment.
Jon Orr: Listen in as we work through this common struggle we have all faced either currently or in the past related to students hyper-focusing on answer getting over process.
Kyle Pearce: Stick around as we work together as a team to unpack some strategies, not answers to this very common and challenging math teaching struggle. Here we go. Welcome to the Making Math Moments That Matter podcast. I’m Kyle Pearce from tapintoteenminds.com.
Jon Orr: I’m Jon Orr from mrorr-isageek.com. We are two math teachers who, together-
Kyle Pearce: With you the community of educators worldwide who want to build and deliver math lessons that spark engagement-
Jon Orr: Fuel learning and ignite teacher action.
Kyle Pearce: Welcome to episode number 38, How to Move Beyond Answer Getting in Math Class, a Math Mentoring Moment with Sierra Classen. Let’s do this.
Jon Orr: This is another math mentoring moment episode with many more to come where we have a conversation with a member of the Making Math Moments That Matter community like you who was working through a challenge and together brainstorm ideas and next steps to help overcome it. You can submit your challenge by visiting makemathmoments.com/mentor. That’s makemathmoments.com/mentor.
Kyle Pearce: Awesome stuff, Jon. Before we begin, we want to give a quick shout out to Sara Jane D who left us a five star rating and review on iTunes. Sara Jane D says-
Jon Orr: “Best summer PD! Over the summer, I am catching up on all the episodes I missed during the school year. I teach sixth grade math and every Making Math Moments That Matter episode offers new ideas and resources for inquiry-based instruction and conceptual learning. Thank you for all your hard work putting together this podcast and making summer PD possible, interesting and incredibly productive.”
Kyle Pearce: If you’ve been loving the podcast, please leave us that review on iTunes just like Sara Jane D did by outlining your biggest takeaway. Reviews help more educators hear about the show and in turn we can help make more Math Moments Matter for students.
Jon Orr: Also, the Making Math Moments That Matter podcast is excited to bring you another giveaway this time with Wipebook, our source for Wipebook Flipcharts. That’s right. You can easily post whiteboards anywhere in your room and easily bring them with you. Wipebook is offering you the Math Moment Maker community the chance to win one of five Flipchart packs. Yes, one of five Flipchart packs by visiting makemathmoments.com/giveaway.
Kyle Pearce: Not interested in chancing it? You can also take advantage of a special discount that they’re giving you the Math Moment Maker community 50% off Flipchart packs by simply entering the giveaway. Simply enter the giveaway by visiting makemathmoments.com/giveaway and you’ll also learn how you can take advantage of the 50% off discount.
Jon Orr: Don’t delay. The giveaway and 50% discount ends Wednesday, August 28, 2019. Head to makemathmoments.com/giveaway to get your name in that hat.
Kyle Pearce: Listening after Wednesday, August 28th, 2019? No sweat. We are always actively running giveaways. Check out, makemathmoments.com/giveaway regardless of what the date is today to learn more about what draw we have running for you right now.
Jon Orr: Remember you got to play to win. Dive in at makemathmoments.com/giveaway.
Kyle Pearce: That’s makemathmoments.com/giveaway. Now, here’s our chat with Sierra.
Jon Orr: Hey there, Sierra. Thanks for joining us here on the Making Moments That Matter podcast. How is winter going over there on the other side of the world?
Sierra Classen: Well, I have to tell you, it’s a bit chilly in these sort of non-insulating environments, not insulated houses, but it’s all good. It’s kind of refreshing.
Kyle Pearce: Fantastic. Fantastic. That’s awesome. Well, let’s hear a little bit about yourself, where are you coming to us from? We know where you’re coming from, but some of the people listening at home are thinking uninsulated environments? If they’re from Canada, like Jon and I are, they’re like, “There’s no way you are coming to us from Canada.” Tell us a little bit about where you’re coming from. How long have you been teaching and tell us a little bit about your teaching journey.
Sierra Classen: I am calling in from Australia, but I actually am Canadian originally and I’ve been teaching for two years and yeah, I teach primary schools. Well, I teach K to two, so kindergarten to grade two up to eight-year-olds and sometimes nine-year-olds, you never know. Yeah, teaching journey. Well, can I start like at my learning journey and then-
Jon Orr: Sure, absolutely.
Sierra Classen: Yeah, because I like always wanted to be a math teacher or like some kind of teacher but I love math. In Australia, we say maths. I might slip up. I had a lot of interesting experiences in independent schools with math, especially in geometry. Yeah, I really wanted to share that. Now, I am doing that and yeah, I’m learning a lot and also having a lot of challenges, which was what all of the things I want to talk about.
Kyle Pearce: Well, it sounds like you must then be a relatively fresh teacher. For anyone who’s listening who is in year one, two, or maybe even year five or six, if they’re at home thinking, “I don’t have any challenges.” I’m going to assume that they’re either lying to themselves or maybe they’re just unaware that there’s some challenges that they’re facing. We can’t wait to dive into that but before we do, I want to hear more about your Canadian story. Were you born in Canada? Are you over on exchanged? Is it part of your family history? Tell us a little bit more about that.
Sierra Classen: Yeah, I was born in the BC in Canada and grew up there. I lived on the West Coast for a very long time in the mountains as well. I moved over to Australia about like 11 years ago. I did most of my schooling in Canada.
Jon Orr: Awesome stuff. Sierra, do you mind filling us in on a little bit of your backstory in the sense about your teaching role? Like for example, why did you become a teacher? How did you get into that teaching role? Where did that story come from?
Sierra Classen: My mom and dad are both teachers. At the moment, actually, my mom isn’t really a teacher. She’s a counselor but both my parents were teachers and school principals. My dad is actually a math teacher and the school principal as well, one of those teaching principals.
Kyle Pearce: Go dad.
Sierra Classen: Yeah. Yeah. Super cool. I always remember like when I was a kid, I always had really intriguing math-related toys. I don’t know if any of you remember those or use 10 Grams. That was a big one.
Jon Orr: Oh yeah.
Sierra Classen: Yeah or I think of rush hour as kind of a math-related game in terms of logic and puzzling and physical space. We had these games where you would get slices of solids and those, I can’t remember what they’re called, but they’re like these things that you use, they’re like circles and you put a pencil in a hole in the circle and then you spin it around the edge of this thing and you make a really cool design. I can’t remember what they’re called.
Kyle Pearce: What are those called? Those are, yeah.
Jon Orr: Pyrographs or spirograph.
Sierra Classen: [inaudible 00:08:53] spirographs. Anyway, I just remember always being doing little sort of investigations around those math toys early on. That kind of inspired me to want to share that. My sister and I were both like pretty keen. My sister was kind of brilliant in a lot of areas and we were both really keen on math together so we would kind of investigate things as kids in our lives. I guess we kind of came from more of that, like super keen in math class and liking to apply our stuff but things kind of came easier to us.
Sierra Classen: In some ways, I think, it might’ve been easier to do math teaching if I had a bit more experience struggling in math but actually I do remember early on in school, in maybe kindergarten to grade two being quite actually struggling a lot and that just in learning to write the numbers the correct way around and counting and stuff and then after that it’s when it just took off a bit later on. I never really had issues after that and just really enjoyed it but yeah, early on definitely had issues like dyslexia sort of things.
Kyle Pearce: That’s interesting too you had mentioned and we’ve talked about this on the show before, just this a bit of a struggle for those who didn’t have too much of a struggle. Like you said, you struggled early on, but it sounds like for the majority of the way through, you didn’t necessarily struggle too much and maybe that might have been something that was helpful to experience that to kind of put yourself in the student’s shoes.
Kyle Pearce: I’m wondering before we get moving along, now that you’re talking a little bit about some of the mathematical memories you’ve had from growing up, what is a math moment that mattered to you, something that popped out in your mind when you think about math class, what would be that memory?
Sierra Classen: My mom actually dropped out of math in grade six, I think. That made her know the value of math. She was really keen that my sister and I should both learn math and she got us like drugstore math books all the time and whatever. She was just like, she didn’t really know how exactly to facilitate math learning, but she was really keen that we would be good at math. That worked out well for her because we also help her out a lot with financial math and stuff now.
Sierra Classen: Anyway, one of the ways that she used to facilitate our math learning or especially mine when we were growing up is she would give my sister and I coins, maybe a few quarters or some dimes or whatever. She’d give us some spare change and she’d send us to the bakery or the diner and we could buy something that we wanted.
Sierra Classen: I remember on I think some days after school, she couldn’t pick me up right away from school. I would go to the diner and I was allowed to buy something off the menu. It was just that real excitement of being to count the coins and figure out what on the menu I could buy and then eating it and paying for it and calculating the, they call it like the GST. That was so exciting to me and that meant the change. Oh my God. I just, for some reason, just those simple arithmetic things but that power that I felt like I got from knowing from having those skills, it’s really memorable and made me really enthusiastic about math.
Kyle Pearce: Yeah, it sort of sounds like that was maybe one of the earlier, at least, one of the opportunities that you remember where math actually served you and it wasn’t just math for math’s sake, it was functional. It was something that actually you could see yourself sort of liking and needing maybe at some point.
Sierra Classen: Yeah, it was evident that it was really important and enjoyable and yet people were kind of like impressed that I was being so independent.
Jon Orr: I have a similar memory and I think a lot of us have memories about money as one of our first powerful moments in why math might be so useful. I don’t know about you guys but my parents used to throw all the spare change and I’m just remembering that memory jog into my memory. I hadn’t even thought about this since you said it about your spare change, but my parents would throw all the spare change in a bucket at home and that bucket would fill. They would dump it all out on the carpet and we would roll it like we would get the rolling papers out and we’d roll all the pennies and we’d sort all the pennies and sort all the quarters and count them all, make sure we have enough for a roll and then roll them all up.
Jon Orr: I remember, we’re doing that with my parents a lot. This is when I was probably, I had to be like maybe seven years old doing that and rolling the pennies and the quarters and then taking them to the bank, giving them to the bank and the bank handing the cash over and was like, like you said, it felt like so powerful and so amazing to feel like all of a sudden you’ve got this stuff that you could now spend and decide on how you want to spend this money.
Jon Orr: I remember walking out of that bank with $14 in my hand. I felt like the richest kid in the world with $14. I remember like I was waving it around. I was like, “Look at this. We got this from change,” and my parents were like, “Put that away. Don’t be waving that around.” Then we’d go into like Zellers, which is a, you’re in Canada, right? There’s no more Zellers but Zellers was like our Walmart and the toy section was spectacular, right? You’d go into the toy aisle and just be like, “Okay, I’m going to pick something.” Having those memories of trying to compare what the prices were to what you had was always such an amazing experience as a kid.
Jon Orr: I’m going to switch gears here into your teaching role and some of your teaching experiences right now and before we get into some of the challenges that you want to talk about with us here today, let’s talk about some successes first. Do you mind sharing a recent success that you’ve had in your role and give us a little story about that.
Sierra Classen: Well, I teach grade one. That’s five to seven-year-olds. I mean, I’m quite a positive person. I get a lot of joy out of just like seeing kids even just learning what the number two is and that really excites me when they just make any kind of progress but one really great moment for the whole class was one day one of the kids was going to have a birthday and he’d been counting down for a very long time. “Good morning. I’m really happy today because my birthday is in 26 days or my birthday is in like 22 days,” or whatever. Anyway, for ages it had been happening for a very long time. I guess, I was getting a little bit over it and I wanted to make sure that I wanted to have one final conversation about the birthday and then it would be done.
Sierra Classen: That conversation really turned into something really powerful in for math. Talking about calendars is great and everything, but this was really good. He ended up saying like, “Oh he wanted to bring in some lamingtons, which are this, you might know them or not, they’re this Australian sponge cake covered in coconut and chocolate. They’re pretty good and he wanted to bring in one for each kid in the class.
Sierra Classen: Then, I got him up in the front of the class to talk about that and then the kids were asking him, we kind of did a Notice and Wonder about I put up a picture of lamingtons and we did a Notice and Wonder about that packet in the context of this birthday treat thing. Then, we did a bit of a research project. Eventually, we talked about well everybody has a birthday and we all like to bring in birthday treats for our birthdays. We’re like how much would they cost? How many treats do we need? What if we want to include the class next door? What if we want to include the teachers? How many are we going to need? What if everyone gets two?
Sierra Classen: Then, the kids did kind of a personal, well, it was in pairs research project where they looked at where they could buy different birthday treats, how much they would cost or how much it would cost for them to get, because the lamingtons come in packets of eight or the cinnamon buns or whatever come in a certain number of, if they bought them from different places and yeah, it was really cool. They were super engaged.
Sierra Classen: I think the applicability of it and I guess that money thing of just the excitement of buying things that people get, we didn’t even actually get to buy them, but I guess we did eventually get to eat lamingtons from that student’s birthday. Yeah, it was just quite cool. The research aspect and everything with lots of outcomes.
Kyle Pearce: It’s interesting because I was thinking the exact same thing. It’s almost like taking your memory of all that spare change and going and being able to do something functional and being able to do something useful with the mathematics. It’s sort of like you’ve recreated that experience, which I think is really cool. I think the kids, especially young children, really thrive on that, in that environment where they get to investigate and inquire and just really kind of play around with mathematics in a very intentional way. It sounds like that’s worked well for you, which is awesome.
Kyle Pearce: I’m wondering, can we maybe now discuss and share any struggles or challenges you had mentioned early on that you are experiencing some of those challenges and we know that teachers all the way up to past year 30 continue to have struggles or challenges. It’s just whether we acknowledge them or not, right? It’s not that these will maybe ever go away completely, but new challenges will kind of pop up along the way. What current struggles or challenges do you or have you been experiencing along your teaching journey and what’s on your mind lately?
Sierra Classen: Yeah, it’s interesting that you say about struggles. Everybody struggles all throughout because their teaching degree or teaching whatever career, because my network of schools is currently focusing on math and things change, teaching methods change and whatever. There’s been a lot of reticence and a lot of interest from different people and in different approaches and reactions to us updating our teaching and talking about our struggles. That’s been very interesting for me.
Sierra Classen: The kind of struggles that, I guess, main struggles that part of it is like data collection in math but I think the main thing is this idea of I have a bunch of kids who or all my kids do this at some points where they’re just like, “Oh, just tell me the answer.” I’ll give them a problem and I’ll get all excited and like, “Oh, let’s solve this together.” They’ll just be like, “What’s the answer? Can you just tell me what number I’m supposed to say?” I’ll write that down.
Sierra Classen: I remember actually being quite annoyed by this in high school especially, when people would be like they would get out the syllabus and say, “Okay, all we need to know is this stuff. Can you just tell us the answers that we need to know here and then we’ll move on.” I feel like the teachers, my teachers anyway, didn’t really necessarily have solutions for this problem.
Sierra Classen: Now, I’m encountering this problem and I have found some things that have worked, but I haven’t found anything that has consistently meant that I don’t have this question of just tell me the answer. Yeah, that’s the main thing.
Jon Orr: I’m just going to repeat back a little bit. One of your main struggles is that kids are focused on answer-getting and not process or strategy on getting there, which I think you agree, we agree that, which is mainly the math part of math class is strategies that lead us to those answers. I think you know we’ve got some strategies I think we can share with you because this is a very, very common issue. We deal with every semester, every year. There’s kids coming in and they are focused on that answer-getting, and I think it’s natural. Most kids are viewing math class as a get-done-now kind of class. I just want to get this over. I wanted to get this done. I want, like you said, even the strongest kids are just looking at the, “What do I have to know to move on? Let’s get to it. Give it to me. I can memorize it,” that kind of stuff.
Jon Orr: This is a huge issue in mathematics right now because some people believe that math is about just, “Hey, let’s just get these strategies,” or they’re not strategies but procedures and ideas down and memorized and some people are viewing math as more of the how to get there and the struggles that are involved in there. There’s two kinds of views of what really math class is and I think teachers have a hard time too deciding what is really math class. What is the point of math class? I think we’ve got lots to chat about here.
Jon Orr: I’m wondering before we get into kind of our answer-getting, what have you tried so far and I guess maybe specifically I had been thinking about this a lot lately, what does the support look like in your school right now for helping each other out. You’ve got teachers to chat with or I guess what steps have you taken so far with people at your school? What do you guys chat about at lunch, that kind of stuff? Do you want to fill us in a little bit about that so far?
Sierra Classen: Yeah, sure. I have a really, really supportive K to two team. I feel like our team is kind of a dream team in some ways. Yeah, shout out to my great K to two team. Part of what’s really great about our team is that we have a lot of good open discussions about how we’re going in the classroom, what we’re doing. We share resources and all the people in K to two are also really committed and excited about implementing new strategies in math and in all subjects but in math because we’re talking about it.
Sierra Classen: I think that’s one structure that I can really rely on is knowing that my colleagues are excited to implement new things and try things and work with me in my class. We might swap classes or do a lesson together or our kids might share stuff that they’ve been doing. That’s really good.
Sierra Classen: We do network meetings in our school, talks with other schools and does professional development in conjunction with other schools. That often involves little group meetings or group chats about or we might learn about a new concept and then we’ll have little chats about something that we’re doing. It might be number talks or Newman’s analysis. Those are the main ones at the moment.
Sierra Classen: We’ve been trying to talk about some project-based learning in math, which is really good. Some schools have been more successful than others around that. There’s those groups and that’s really good as a reflection resource and also for like can go in and request to observe other people’s classes and what they’re doing.
Kyle Pearce: That’s great that you such a supportive team. I often find that we call the younger grades the early years or primary divisions. I often find that that tends to be pretty common for some reason. I don’t know if it’s because there’s such a drastic difference between the level at which the students are at and the teachers are at that you need to work together to be able to reach those students, right? It really could be a challenge, especially if students aren’t engaging in the learning and in the mathematics.
Kyle Pearce: I’m wondering, what sort of resources does your school/dream team have for teaching mathematics? What does that curriculum or those core resources look like, sound like? Are you sort of on your own to try to meet the standards or the expectations in the curriculum? Are you just sort of feeling like you have to go online to find all of that or is there something provided to you and how are you feeling about those resources that you have access to?
Sierra Classen: Well, oh man, there’s so much available. Sometimes it’s more about do you calling through the resources that are available online in order to figure out what’s the best thing to use in a particular moment with a particular class. There’s a lot available online. I have some favorites. Also, we collaboratively plan. I love that. It’s really great. I think it’s really useful to collaboratively plan to an extent or at least being in the same room with my colleagues to do. We have like programming afternoons and it can be just really good to bounce ideas off of colleagues to, and I don’t know, immediately share links and find units.
Sierra Classen: We’re in an area with a lot of first nations’ kids. I’m sure it’s similar in Canada and the U S where there are special techniques and stuff that are recommended for working with first nations’ communities but yeah, so we have that. It really helps to work with colleagues on integrating those kinds of techniques as well and there’s like a lot of specific websites around that as well.
Jon Orr: Okay. We’re wondering now, I guess is, you’ve got this great support team, you guys are co-planning and that sounds fabulous. I guess, what does your team think about this struggle of kids’ mentality towards answer-getting instead of the process? What have you guys tried so far?
Sierra Classen: Well, I found that number talks have been quite helpful and effective for getting kids talking about more than just a result. I guess, partially because it kind of disrupts that worksheet vibe or just like the equation, the idea that you have an equation and then there’s a little box at the end.
Sierra Classen: I guess that the way that number talks happen is it calls upon stuff that we do in English and history rather than routines that we’re used to doing in math. I won’t even say that now we’re doing math, we’ll just do like Notice and Wonder and they’ll come up with things that are used like mathematical thinking, but we won’t necessarily say, “Oh now, it’s math time.” I found that that’s been kind of helpful to like sneakily do, I guess, it’s kind of like a sneaky way, like sneakily getting kids to think about number instead of going, “All right, it’s math time.”
Sierra Classen: That’s part of what’s being helpful. In that, I started getting kids to not mention any numbers. If it’s a diagram or something like that where there might be numbers involved, but I’d get them not to talk about the numbers and just tell them. Just talk about other things, just know numbers the rules are, and that’s been quite helpful in changing the talk, but still when I give them problems to solve more independently, it ends up deteriorating a bit into what’s the answer kind of chat.
Kyle Pearce: Nice, nice. I’m really liking this idea. It sounds like, so number talks have sort of been pushing students, it sounds like to get into that math talk, that mathematical discourse that we often refer to it as. I’m wondering as well with the number talks, inherently it sort of pushes this idea of multiple entries, multiple strategies instead of hyper focusing on efficiency or correctness.
Kyle Pearce: I try to be clear for those who are listening, we’re not suggesting that we don’t want to help students become efficient overtime or correct overtime. We want to make sure that those are important things too, but we don’t want to hyper focus on just those things. I recall earlier you mentioning about getting out of that worksheet funk, that fill in the blank or fill in the box or these little sort of really one-and-done sort of questions that aren’t super rich.
Kyle Pearce: I’m wondering in terms of as you’re engaging and I want to go all the way back to one of the successes you had, which it sounds to me like a lot of what you had done in that activity where you were discussing the students working with essentially food and the different baked goods and things like that where they were splitting them up and all of those different pieces and you had said that that was a success in your classroom.
Kyle Pearce: I’m wondering do you see a difference. I’m wondering if you feel like what some of those differences are if we were to compare and contrast maybe some of what you or I may have experienced in our own math classes. Not all of them, but in many of them in terms of that sort of answer-getting scenario where we might have been using a lot of worksheets or sort of really one-and-done sort questions where we didn’t really focus on strategies versus that experience you had as a success as well as what some of the things that we have to do with number talks.
Kyle Pearce: I’m wondering, are there some key pieces there that you feel you could pull out of that that might be one of the secret sauce as to why those things help you do things a little bit easier or better in your class than say a traditional worksheet or just a textbook problem. Any thoughts on that?
Sierra Classen: You’re saying what are the elements that really work in the project-based approach of the birthday treat thing or the [crosstalk 00:30:19]?
Kyle Pearce: Exactly. Are there some elements that sort of jump out at you as like, “Huh, I bet you that is something that’s really important.” Then, I guess the intent here is that if we reflect on those things, then we can say, “How can I try to pull these elements out of something else?” Because the one thing I hope you don’t do after we have this conversation is go and light all your old resources on fire, right? Sometimes we, we sort of tend to do that, right?
Sierra Classen: That’s a bit difficult nowadays in the digital age.
Kyle Pearce: You’re melting computers all over the place. That’s horrible. That tends to be what we, as humans, do, right? It’s like you try to change [inaudible 00:30:59] all the way out to the other side instead of making small shifts along the way. I’m wondering, are there any elements and obviously you don’t have to name them all, but are there any that sort of pop out at you as like, “I feel like this element is really important for trying to draw out some of those pieces you’re looking for.”
Sierra Classen: One thing I really liked about basically any math lesson that works is that kids put things into their own language, put ideas into their own language and use, make their own systems and symbols and processes. I think the fact that kids feel free feel like they have license to do that in these contexts, like the dialogical context helps. That’s one of the elements. I think I’ve actually like, because there’s always a place for practicing, practicing like addition, practicing things that the kids kind of know and they just need to practice and practice them with bigger numbers and whatever, which you could do with a worksheet or a textbook problem but also I found that to incorporate that dialogue, doing games helps a lot.
Sierra Classen: I think it’s because of that dialogue between the kids. Games with dice and manipulatives of any sorts of like paper clips or whatever, anything that involves like it doesn’t have to be winning, but just like any sort of stakes for the kids and where they’re motivated to explain to their peers how the game works, what they’re doing, what they’re not doing, giving feedback and stuff. I think that’s part of what works in both of those successes that I talked about and then that is how I’m starting to apply it is by using more games, especially for K to two, right?
Jon Orr: Yeah. I think that’s a great addition and the games are huge, especially at that level. Kids are just I’m sure you know, teaching that age group that they just view so many things as games and if you can structure them game-like or sneakily like you said, when you say, “It’s not math time. It’s game time,” or it’s this talk time, number talk time where they don’t actually think they’re doing mathematics. I think that’s a huge win there.
Jon Orr: In my high school class, I’ve done that somewhat successfully with students by been learning how to factor polynomial expressions without using the word factor initially. We don’t say, like we just say, “We’re solving puzzles in a certain way,” and then we’re using our manipulatives and there are tools like these little, our algebra tiles, which I didn’t even call them algebra tiles, but we just were using these shapes to make rectangles and it’s a puzzle. Can you make the rectangles using only these tiles or only these tiles?
Jon Orr: We do them at the beginning of class to start class and after a little bit, you all of a sudden we start throwing in a little idea here or there and how it relates to some of the math we’ve been working on. Then boom, you’ve got the major parts of that skill down without even calling it math but yeah, I think games can go a long way as I do that with my daughters. We play games all the time and there’s so many elements you can bring in for game like we talked with Dan Finkel. Kyle probably knows the episode number because he has the list probably on his wall.
Kyle Pearce: [crosstalk 00:34:07]. Sierra would love it.
Jon Orr: We talked about a bit episode 11 with Dan Finkel about the elements of games. If you haven’t listened to episode 11, definitely check that one out. He has a lot of good tips about what are elements of good games because I think there’s some games in class that are better than others. I think the one that sticks with me that he talked about was this idea of choice can help kids make better decisions on strategy because that’s where so much thinking can happen is, I think the example I even gave in that episode was that my daughters brought home a math game that their school had sent home and to play and had a spinner and you spun the spinner and if it landed on a whatever number it landed on, like one to six, you’re supposed to double that number. It was about doubling. Then, you’d put a counter on that number from, I think, it was 2 to 12 on your space.
Jon Orr: Then, your opponent would do the exact same thing. They’d spend a spinner and then you’d double it and you’d put a counter and if you filled up your 2 to 12, first you won. They’re practicing doubling, but there was no choice, there was no actual strategy in that game. It was just kind of like whatever it landed on, I double it and then I put a counter on.
Jon Orr: My kids, we lost interest pretty quickly because there’s not actually anything to do other than double numbers. One of his big elements is including choice in the game. I think that was pretty useful. Check that episode out for sure.
Sierra Classen: Double it or half it and filling up the same… Everybody’s filling out the same number chart. You have to predict what numbers you want to get rolled or something.
Jon Orr: Right? For sure, you can modify that in many different ways. You’ve can have a hundreds chart or you could have the same numbers in different spots. You could have them double or half. You could have them go-
Sierra Classen: Yeah, cool.
Jon Orr: If you could double or you can add for. What [inaudible 00:35:56]? You’re going to do the math in both cases, right?
Sierra Classen: Do the math, cool.
Jon Orr: It’s forcing you to make some sort of different, yeah or you can cover one of your numbers or remove one of your opponent’s numbers.
Sierra Classen: That’s good.
Jon Orr: You could just have so many different choices…
Sierra Classen: Cool, yeah.
Jon Orr: … that you like to have to really think about what you want to do to win there. Yeah. That’s super exciting that you’d want to include some games aspect into your classroom. I’m wondering, I want to go back to something I was thinking about when you were talking about kids working independently. Sometimes your classroom discussions go well and they’re not focused on answer-getting, but then when you went to more an independent approach, when it was time to practice the result, practice what they’re doing or working independently, they were focused on getting answers at that point.
Jon Orr: I guess, what I’m wondering is put yourself in that position, the kids are working independently in your class, however you would do that and they’re at that moment where you’re like, “Oh, they just turned back to the answer-getting and they’re focused on that.”
Jon Orr: I guess, what I’m wondering is what do you do next? A kid comes to you and they’re in that mode where you’re saying they’re focused on answer-getting, what do you do next to that kid right now? Where do you go? What’s the language you use? What’s your suggestion to the student now?
Sierra Classen: Yeah. You’re the student. I might get you to explain how to do it to a friend. Usually, I get them to work in buddies. There’s very few times when I don’t because I find that it kind of encourages dialogue and other things. It’s good to work in buddies, accountability. I might get you to explain to your buddy how you did that question and sometimes that works and sometimes a student might be like, “My dad told me,” or something like that and that kind of devolves again but yeah, sometimes that can work or we might go to a similar puzzle or I don’t know, say if we’re working on addition, we might like, we’re like, “Six plus four equals 10,” and I might go, “Okay, well what’s six plus five then and then six plus six, et cetera, et cetera?” Then, why and just start to talk about why they’re related and then what did you do through that.
Sierra Classen: That’s one approach or I might start like we might start to apply it to you, apply the question to you because if it’s like to situation, a real life situation, if it’s not already in that content, if it’s not already a real life situation, I might go try to the kid to put it into apply the, explain this, I guess it’s like the opposite of abstract, apply it to their own life and that can work. But that’s much more difficult for kids who are struggling in math as opposed to that abstraction to concrete and concrete to abstract. That process can be quite difficult and needs a lot of practice.
Kyle Pearce: Yeah, for sure. I think you’ve highlighted something really important, especially at the grade level that you’re teaching. This would go for your entire dream team of K to two teachers but this idea of students building that abstract thinking, right? For young children, I always find it very interesting because their imagination is so wild, right? They can make anything become anything, right?
Kyle Pearce: My son will come up to me with something he’s created on paper or he’s created with Lego and I’m like, “Oh wow, that’s like a really nice truck.” He’ll be like, “No, it’s a dinosaur, silly.” I have no idea what he’s envisioning in his mind. They obviously have the ability to think abstractly, but when it comes to mathematics, there’s just so much going on under the hood that in order for them to see something abstract and then being able to connect it to the mathematics, that is a process.
Kyle Pearce: Beginning with that concrete is so important and I thought it would be a really good point to highlight some research from Anthony and Walshaw and we’ll include a link to one of the papers, but basically they go through and they highlight some of the characteristics of effective teaching of mathematics.
Kyle Pearce: This is something in my district, we’ve talked a lot about these different pieces and in particular something in their research that they highlight, they actually highlight, I believe it’s like what, 11 something like that. Let’s see, four, eight, it looks like 10, 10 different categories and they call them principles of effective pedagogy of mathematics. Here in Ontario, the Ministry of Education or a group from the Ministry of Education sort of took them all like all of these different principles and they sort of put them into four different categories.
Kyle Pearce: From this research are basically, it comes down to or I guess boils down to effective teaching of mathematics involves these four things. I think and I hear this first one automatically just in terms of who you are and how you discuss and talk about teaching and the students in your classroom is this idea of a nonthreatening classroom environment.
Kyle Pearce: Obviously, as you can imagine, students coming into the classroom, they have to feel comfortable in that space. I think you’ve got that tapped in. That’s a great one right there but then the other ones, one is a worthwhile mathematical task. Earlier in the conversation, what I was trying to get at when I asked you about resources is just that the task that we give students and what we ask them to do with it is so important.
Kyle Pearce: Some people refer to it as a rich task and it’s not even the task itself. It’s not like, “Oh, you can’t use any tasks from a textbook because it’s a textbook task.” It’s what we ask kids to do with the task. Thinking about what would make it mathematically rich. When we are asking them, “Am I framing the question to sort of lead them to this idea that the answer is all that matters or that we actually want to ask them something maybe a little more open, whether it’s open-ended, where there’s more than one solution possible or one entry point or maybe it’s open middle where there’s just different solutions, strategies in order to get there and really highlighting those things. Then, the other two, the first one is tools and representations. That’s something that I’m hearing when you talk about concrete to abstract.
Kyle Pearce: This idea that kids have the tools, especially in K to two having like that reckon wrecker, some call it the arithmetic rack out or the linking cubes, the connecting cubes, square tiles, the different types of mathematical manipulatives, those would be like the tools that they can use for thinking and then representing is where they’re actually either using tools or they’re using some sort of drawings or symbolic representation in order to represent their thinking to help explain it.
Kyle Pearce: Really, what I’ve tried to do in my own practice and it’s hard to remember to do, but it’s like anytime a student gives me any sort of solution or answer, I want to make sure that I’m asking them to convince me somehow whether it’s first with your elbow partners, your elbow partner has to understand why that works and I would argue that if it takes them two seconds to convince, then maybe that task or the way I framed the task wasn’t as rich as maybe it could have been had I maybe approached it some other way.
Kyle Pearce: Then finally, and you’ve already referenced this in your math talks or in your number talks earlier, is mathematical discourse. That’s this idea of getting kids talking. We know that we learn best when we’re actually talking and when we’re actually teaching.
Kyle Pearce: Those four things for me, nonthreatening classroom environment, rich tasks or what they call worthwhile mathematical tasks, tools and representations and mathematical discourse are all those four, they’re big, they’re huge and you might want to just focus on one and then maybe explore some of the others. I feel like when we frame that task and when we really push students to use tools and representations to share and explain their thinking, that’s where I feel like we start to move at least move a little bit further away from only doing the answer-getting, because I think in our heads we all think everyone thinks like us. It’s really easy for us to say, “Here’s how I did it,” and I’m going to assume that everybody else solved it the same exact way when in reality, someone might be thinking about it completely differently and until we allow those ideas to surface and bubble to the top, we’ll just kind of go on thinking that everybody did it the same way.
Sierra Classen: Yeah and Kyle, I think that’s like especially pertinent in K to two in the developmental stage that kids are at. It’s very much like a me, me, me and that idea that other people like have different things going on in their minds and they’re separate and it doesn’t necessarily dawn on people quite until a bit later on. It’s good to kind of tap into, I guess, harness that me, me, me and really understand that and recognize that in the classroom. I like that you’re saying that.
Jon Orr: I just want to throw in another thing to kind of think about too is we talked with Peter Liljedahl I think on episode 19 and Peter is a professor out of the Simon Fraser University in BC and he’s been doing a lot of work in the thinking classroom and I think something that he’s been researching right now can apply here and I always try to think about and include this in my classrooms, which is about the types of questions kids ask and then which questions you should answer and which ones you should not answer.
Jon Orr: He’s got three different types of questions kids will ask. One is called proximity questions. Proximity questions are like when you’re walking by a kid or when you’re standing close to a kid, they’re going to say like, “Can you check this?” A part of that might be like, “Is this right?” There’s those proximity questions when you’re close to a kid.
Jon Orr: The other type of question is the stop thinking questions and that’s probably more like, “Is this right?” These are questions that kids will ask that if you answer them, the thinking is over.
Jon Orr: Then, he’s got the third type of question, which are keep thinking questions. It’s pretty easy to kind of remember these types of questions, but keep thinking questions or questions kids ask that are about say a strategy that they’re on but if you answer that question, it doesn’t stop the thinking and actually keeps their thinking going.
Jon Orr: Peter’s suggestion about those types of questions is that a lot of us answered the proximity questions and the stop thinking questions quite regularly all day long. You’ll be walking by a kid and be like, “Hey, can you check [inaudible 00:46:48]? “Yup, good,” and you move on or the stop thinking questions. Kids will always want to ask those like, “Am I right?” Peter’s suggesting we have to resist answering those questions. He’s saying, “You only answer keep thinking questions.” You don’t even answer the other ones. I’m not saying ignore the students because I think especially [crosstalk 00:47:08].
Jon Orr: I like that idea.
Kyle Pearce: Yeah, in my class actually, my senior level students you can have the conversation with them about these types of questions that you will only answer keep thinking questions and you could easily ignore as high school students if they know that their answer is or you could just even say like, “Is that a keep thing in question or is that a stop thinking question,” but in your age group, you are not going to ignore those kids, but I think you could rephrase some of their, what you’d say next is I think what you tried to say before and what would you say next on those proximity questions and stop thinking questions to kind of redirect them to try to rephrase it as the keep thinking question instead.
Kyle Pearce: I think those three things are good to think about in how you can structure what they say because I think if we are answering the proximity questions regularly and stop thinking questions regularly, then kids are just going to keep asking them. I think if we start changing what we answer and it’s kind of like that positive feedback that kids will only start gravitating towards that because that’s what you’re going to engage with them on and they will limit those other kinds of questions because you’re not going to engage with them on those things. I think you will condition them to start asking the keep thinking questions. Those are a couple of things to think about while you’re thinking about getting kids to not focus on answer-getting.
Sierra Classen: Yeah. Well, I think that we could talk about the different kinds of questions. We definitely talk about it enough in literacy. I mean, I would counter that it could be quite a powerful thing to have the kinds of discussions and also that language is quite nice that you bring up that framework of the different types of questions. I mean, I’ll have a think about how I can introduce that with my kids, at least some of them. Also the, I think it was Kyle was mentioning all those different, the powerful techniques for math teaching or that seems really fantastic.
Sierra Classen: I think when you think about rich tasks, I guess I was talking about games, using games in the classroom and what’s like I guess that’s been really good and then the extension of that that’s been, I mean, those are kind of like could be rich tasks in themselves, but like what has been even better with the games is getting the kids to make up their own versions of the games of their own new rules and write down the strategies, how to win and stuff like that. I feel like that’s kind of being the other success angle of that stuff that’s been happening in the classroom but so I’m really keen to explore that, explore those more and when you give me the articles as well, I’ll definitely read through.
Kyle Pearce: Fantastic. Well, I just want to let people know that Landon Pearce has joined us in this episode. You might hear him in the background a little bit. Landon say hello.
Landon Pearce: Hello.
Kyle Pearce: This is Landon and he really wants to play [inaudible 00:49:56]. He’s going to have to wait a few minutes, but I did want to also reference him. We’ll put this link in the show notes for you. It sounds like you-
Landon Pearce: Super hero.
Kyle Pearce: Thanks buddy. It sounds like you had some big takeaways from this episode so far, which is fantastic. One more resource we’re going to put in, we won’t talk about it here, but we do discuss it at length in our four-part video series. We’ll put a link to that in the show notes. We also go in depth into it in our online workshops. We’ll put links in the show notes that for everyone who’s listening at home as well as for you there, Sierra.
Kyle Pearce: We’re wondering, is it okay if maybe we touch base with you in like say 8 to 12 months just to kind of see how things are going before we start wrapping up for this episode?
Sierra Classen: Yeah, that would be awesome. I’d love that. Yeah, share some more ideas and successes.
Jon Orr: That’d be great to touch base so we can chat about some of the strategies you’ve tried and see how they went. Sierra, we want to thank you so much for joining us here on the Making Math Moments That Matter podcast and we hope you enjoy the rest of your evening. We are just waking up but you are just about to go to bed.
Sierra Classen: Thank you. Yeah, thanks guys. I really, really enjoyed this and I think I’ve got a lot of really good ideas to mull over as I sleep, I guess.
Kyle Pearce: Awesome. Thanks again for hanging out with us and we will chat with you soon. Hopefully, you’ll have a fantastic evening and Jon and I are ready to engage in the rest of the day. Take care.
Sierra Classen: Thanks.
Kyle Pearce: As always, both Jon and I learned so much from these Math Mentoring Moment episodes, but in order to ensure we hang onto the new learning, we must reflect on what we’ve learned. An excellent way to ensure this learning sticks is to reflect and create a plan for yourself to take action on something that you’ve learned from this episode.
Jon Orr: A great way to hold yourself accountable is to write it down or even better, share it with someone, your partner, colleagues or with the Math Moment Maker community by commenting on the show notes page, tagging Make Math Moments on social media or in our free private Facebook group, Math Moment Makers K through 12.
Kyle Pearce: Also, don’t forget the Making Math Moments That Matter podcast is excited to bring you another giveaway. This time it’s with Wipebook, our source for Wipebook Flipcharts. That’s right. You can easily post these whiteboards anywhere in your room and bring them with you anywhere you go. Wipebook is offering you the Math Moment Maker community the chance to win one of five flipchart packs. Yes, one of five flipchart packs by visiting makemathmoments.com/giveaway.
Jon Orr: Not interested in chancing it? You can also take advantage of a special 50% discount on flipchart packs by simply entering the giveaway. Simply enter the giveaway by visiting makemathmoments.com/giveaway and you’ll also see how you can take advantage of the 50% discount.
Kyle Pearce: Don’t delay. The giveaway and the 50% off discount ends on Wednesday, August 28th, 2019. Head to makemathmoments.com/giveaway to get your name in the hat.
Jon Orr: Listening after Wednesday, August 28th, 2019? No sweat. We are always actively running giveaways. Check out makemathmoments.com/giveaway to learn about the draw we have running now. Remember, you got to play to win. Dive in at makemathmoments.com/giveaway.
Jon Orr: That’s makemathmoments.com/giveaway. Are you interested in joining us for an upcoming Math Mentoring Moment episode where you could share a big math class struggle? Apply over at makemathmoments.com/mentor, that’s makemathmoments.com/mentor.
Kyle Pearce: 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.
Jon Orr: Show notes and links to resources from this episode can be found at makemathmoments.com/episode 38. Again, that is makemathmoments.com/episode 38.
Kyle Pearce: Well, until next time, I’m Kyle Pearce.
Jon Orr: I’m John Orr.
Kyle Pearce: High fives for us and high fives for you.
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