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Teachers in America
Innovative Math Teaching Strategies: Embracing Mistakes and Fostering Curiosity with Russell Hanes
Math mistakes can open up new learning opportunities.
Today we are joined by middle and high school math teacher Russell Hanes, who has been teaching for two decades in public and private schools in the U.S. and abroad. In this episode, Russell discusses how to help students step out of their math comfort zone and see themselves as “math people.” Plus, Russell shares teaching strategies to use in the math classroom, like helping students embrace and learn from their math mistakes.
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Let students see that there are actually multiple pathways that get them to the correct answer. And to honor different sorts of solutions, honor different ways of thinking about it, really honor that. Students have done a lot of the thinking. It just might not look exactly perfectly crystallized math right, but it's still mathematical thinking.
Speaker 2:From paper and pencil to Wi-Fi and AI. Education is ever evolving. On this new season of Teachers in America, we'll keep you on the forefront of what's new. We connect with teachers and ed leaders to talk trending topics and real issues, bringing you inspiring ideas that will influence the future of your teaching. Today, host Kaylee Rhodes connects with her former colleague, math teacher Russell Haynes. Russell has been teaching for two decades in public and private schools in the US and abroad. Throughout his career, he has taught public speaking, debate, civics and every math subject, from fractions in sixth grade to AP statistics in high school. Today, russell and Kaylee discuss how to help students step out of their math comfort zone and see themselves as math people. Plus, russell shares teaching strategies to use in the math classroom, like helping students embrace and learn from their math mistakes. Now here's Russell and Kaylee.
Speaker 3:Russell, welcome. I'm so glad that you're here. How are you?
Speaker 1:Very good, very good. Thank you so much for having me, kaylee. This is really awesome. Yeah, I love that you're doing the podcasting thing now. This is such an awesome stuff.
Speaker 3:It's a perfect fit, right, I like to talk and you're like I have to go teach.
Speaker 1:Yes, Well, I love that. I got a random text that was like, do you want to be on the math podcast? And I was like I can only be one person.
Speaker 3:Yeah, but then you, in true Russell form, had to don on talking about how to get students from their you know, very, very understandable math trauma into their math comfort zone, helping even teachers step more into that math comfort zone. And there's no better person to talk to than you, because you have been so formative in my journey as seeing myself as a math person, because I didn't start as a math teacher. You, I started in the English classroom and you were my first mentor as start as a math teacher. You, I started in the English classroom and you were my first mentor as I became a math teacher. Actually, one of the first conversations you and I had was about quote, not a math person. That was one of the first things we were in your office. So how do you? How do you respond? Let's just start with a student, because everyone says it right.
Speaker 2:But how do you?
Speaker 3:respond when a student says I'm not a math person.
Speaker 1:I mean, I think there's like sort of two flavors that you can get, right, like one is the student is saying it's just not really my interest, like it's not like something I'm super passionate about. And then you get the students who are saying that because they've been super traumatized by math. Right, this is a like just as a true story. I one time was getting my haircut and the lady said what do you do for a job? And I said math teacher. She hissed and jumped back Right, this is how traumatized some people people are about math, right. So I think the first thing that you have to do is figure out, like why the student is saying that. Are they telling you like they are afraid of math, or are they telling you that it's just not their thing, right?
Speaker 1:yeah which, if they're telling you that it's not their thing, like you know you want to connect them to all of the amazing things that you can do with math, all of the interesting properties that they can learn about, like connected to their interests, like the subject that they're. You know they're interested in science Great. They're interested in art Great. Like let's find the connections to math that they would find really interesting. Right, that's maybe just a function of they haven't had a teacher, like really look for projects and applications that they find interesting. But, as you well know, right from teaching sixth graders who many of them came into it like into your classroom, like really traumatized and upset, uh, like you have to figure out, like if that's what is going on and sort of help them start to unpack it, and that that's a whole different ball of black.
Speaker 3:Right, yeah, I, um, for context, I have our, our group of sixth grade students, um, who need the most math support, and I think that what shocked me because I mean I'm going to say it like I'm not a math person and I'm not supposed to say that, like I'm not supposed to say that but I'm not a math person and like what I mean, what I mean when I say that is like math does not come by osmosis for me, like I can't just watch a teacher do it and like see it and just go replicate it or even be like what about this? And like get up there and ba-doop-boop-boop like jazz riff on whatever I just saw. I have to be like I need a lot more questions answered before I'm ready to really understand this, but I think that that's normal. But what I saw in school was just prodigies. It felt like prodigies and plebeians, Like and I was definitely a plebe and so I was just that.
Speaker 3:That equaled if you're not a genius, ergo you are not a math person Like that's what it felt like. Now I have to tell my students that I said that too. You and I have to reclaim our speed, because speed's a big trigger in math. We have to reclaim our speed and we have to reclaim that maybe I. This is something that I actually really love about the Common Core is it mandates that we have different ways of instruction, instructing the same concept, and I feel like that really like honors what I needed.
Speaker 1:And so what has also surprised me is that a lot of kids come into my class with uh, with the lowest math, uh, current like application ability, and they say they love math yeah, that's mean I think it's a testament to like your skills connecting with students, right, um, and I think what you're also saying is really important too about the curriculum, right, the way that we have taught math, right, where you're trying to go at the fastest possible speed, right, uh, does not work for a lot of kids. It doesn't particularly work for me either, like I don't find it really pleasurable to sit down and take a timed math test, right, no, um, and and there's also ways of like the ways that we have set up instruction, where we're like trying to get students to like replicate, like down a very specific narrow pathway, is not going to work really well for lots of students. And if you have a broader, open pathway, more open pathway, that's good for a lot of kids, that's good for more kids. That's good for a lot of kids. That's good for more kids. So I think a lot of the problem is that the way that we've taught creates a really stressful environment for kids. If we use timed tests, I don't particularly enjoy that. It's stressful. I recently have had to take a class where there were timed tests I, you know I didn't enjoy it like it's trying to recall stuff as quickly as possible, which doesn't work for every moment, for every learner right, and the way that we've done instruction too in the past has sort of limited the number of pathways that students can go down.
Speaker 1:Like we show them one pathway, we're like here's how to get to the answer, and we sort of expect students to be able to follow along that pathway and replicate it, whereas a better, I think, way of instruction is to let students see that there are actually multiple pathways that get them to the correct answer and to honor different sorts of solutions, honor different ways of thinking about it, really honor like that students have done a lot of the thinking. It just might not look exactly perfectly crystallized math, right, but it's still mathematical thinking, right. We kind of like fetishize, like a outcome, like students are supposed to write proofs or something when they're still learning material, right.
Speaker 3:Which is why in your class you do a ton of like group work, where maybe the mathematical thinking is crowdsourced and then maybe you've got the student that can kind of push it through to that distillation.
Speaker 1:Right. Right, and I think part of it is just not trying to rush the students to that point, right, part of it is that we want to have the students get to like this distilled, crystallized result in three weeks or four weeks or whenever we're wrapping up the unit, and we all know that that's like setting a timetable that like might not be realistic for certain kids, right, and it would be better to just sort of acknowledge, like okay, your understanding of this is still a work in progress, you're not like the most crystallized form, but you, you still understand the core concept, like recognizing that kids can still be in process, like at the end of the unit yeah, which makes uh grading really complicated oh, it's a mess, right?
Speaker 3:well, because if we're really if we're really like alive this idea of growth, it's not about achievement, it's about growth and if we're really therefore, nuanced about you have to understand each kid's kind of brain, not just what's on the paper, but what you know is going on back there, and that does make giving a score or a letter to that really, really tricky.
Speaker 3:And I'm actually going to I know that you and I could talk about grading all day, so I'm going to make sure that what I want to do is press pause and be like okay. So that moment that a student says I'm not a math person, you said just kind of suss out, what are they telling you? Are they telling you that they would rather be in art, or are they telling you that they have trauma or both? And then making sure that I've heard a lot of like speed. We've both been talking just a lot about speed and we've also both been talking a lot about like externalizing, um, this very conversation that we're having right now, kind of almost doing it in front of the kids.
Speaker 1:Yeah, I think recognizing, like talking to kids and saying, you know, if you have been traumatized in a previous class, like I'm really sorry that that happened, like I don't think that that was right, like let's sit down and actually figure out what you really know.
Speaker 1:You know, let's figure out what you really can do, yeah, what you really can do without all of the stress, without all of the like you know, I mean, I've I've seen people, uh, you know, working with students who really just add to their stress, and I've seen people who like, take their stress away, right, and I think the whole thing that I would argue is that we need to, you know, as teachers, find ways to help take the stress off, because then you're going to get a more accurate read of, like, what the student really knows, what they actually really feel Like. Math doesn't have to be everybody's favorite subject, yeah, and that's okay, you know, but they can all do it, you know, we should figure out what they are actually capable of doing.
Speaker 3:Right, and we have a math pledge of allegiance in my class and the last line of it is just, I will go at my own pace and I will endeavor to see the beauty of math around me, me because if, even if you are not trying to go further with your math studies, which we're going to talk about in a second you can at least appreciate that math is probably, as you said earlier, they're interested in science.
Speaker 3:Math's everywhere in science, you know, um, but if you're, if they're interested in anime, math is all over anime. So just like it's everywhere, so just like let's, let's embrace it. So when we picture this math classroom that you and I are trying to like, kind of, maybe move away from a lot of people, the image that pops into their minds and they might even still be educators, but the image that pops into their minds is like a lot of bent heads over paper and pencil, doing these kind of repetitive tasks to get the algorithm down. Doing these kind of repetitive tasks to get the algorithm down, but teaching math? I was surprised, coming from, like the speech and rhetoric world, which you also occupy as a debate teacher, but coming from an English teacher. We talk so much in math. Math is so much discussion and argument, so how has your experience as a debate teacher shaped the way that you are able to hold space and facilitate that math discourse?
Speaker 1:Well, I think a big part of like what we need to do as math educators is actually thinking about entertaining hypotheticals. Right, Timmy might not have the correct answer, but has made an interesting mistake and we need to walk through that mistake and see where they slipped up and if other students made that mistake, and to understand why it's wrong and to understand how to correct it. Right, that isn't to say that like, like there is absolutely a place in math for like correcting students and saying what's right and what's wrong. Like there's absolutely a necessity for doing that, unless you are intentionally like leaving them with a cliffhanger, right. But I think that we should be able to entertain hypotheticals and like ask students to explain their reasoning. Like what's your argument for why this is true? Walk us through the logic. That's the key part that holds that math uh, has to like hang together by like logic, right?
Speaker 3:if the students can't explain the thinking that got there, it doesn't matter whether the answer is right or wrong it's kind of like when you're assigned a side in debate that you don't necessarily personally agree with and you still have to mine it for what's there, and there's definitely something there.
Speaker 3:I my favorite thing to do is, um, if a student has made an interesting mistake, like, say, on the board, number four, everybody take a look at number four. You know, and I've privately checked in with number four beforehand and been like, hey, I'm going to you have a really cool mistake, don't erase it, it's about to become the backbone of our lesson. Um, but one of my favorite things to do is, like, mute that kid. It they can't defend, like, and they're not being defensive, they literally are defending their math. But muting them and making the rest of the class try to explain what they thought happened not only enlivens the rest of the class but makes that one kid go insane. And you're like. I never thought I would see you writhe from wanting to talk about math. You're welcome, you're a math person.
Speaker 1:Exactly. Yeah, no, I think you're absolutely right. Like the issue is like you sometimes have to step into other people's shoes right and walk through the logic that they did, even when you can see that there's like a mistake. Like you have to be able to like articulate. I do think the problems that like being included more in curricula, where it's like here's what two students thought explain what their reasoning is, explain where they went wrong I think that's a really good exercise for students to see mistakes and see mistakes as normal right. That's a big part of we have to like see mistakes and see mistakes is like normal right.
Speaker 1:Yes, that's a big part of like we have to normalize mistakes, we have to normalize disagreement. That's a that's a big part too that, like, the students look up to the teacher and think that the teacher never makes mistakes, and that's that's just not a good rhetorical stance to have as a teacher right.
Speaker 3:Right? No, it also makes you, as a teacher, feel so. I, as a math teacher, felt the same amount of pressure that I felt as an English teacher to answer everyone's grammatical question and I'm supposed to be able to spell every word that ever worded. So now, of course, I'm responsible for calculating everyone's taxes because I'm a teacher.
Speaker 1:That's terrible. No, I think it's like math teachers, like we should feel comfortable with ambiguity, like we should model that for our students, like I think it's perfectly OK to say that's a really interesting question.
Speaker 3:You've said that to me.
Speaker 3:I don't know if you remember this, but a couple years ago I couldn't figure something out and you were next to me teaching and I came over and interrupted you and I was like I have a problem, I don't know. Will you help me? I've done it to Chris too, another colleague of ours. I was just like I want them to watch two adults who are curious about a math problem and maybe they can't solve it. Like that is math in progress. A lot of the math that we're teaching is discovered math kind of like science.
Speaker 3:A lot of the science we're teaching is established science. But when you watch mathematicians math or when you watch scientists science it's because there's a question mark.
Speaker 1:Absolutely, and it doesn't have to be something that's like at the forefront of the limits of our research with math in order to be a valid question. Right, right, it's literally how much more parking do I need to?
Speaker 3:put in my meter if this is what they charge and, like Russell, can your phone reach my parking? Here's my phone. Go pay my parking Right. But that's silly.
Speaker 1:I'm excited to discover that there's so many parallels between what and that maybe you know, no one has the answer uh per se, or, like you know, we're we're going to figure out the answer together as a result of doing this process. Um, you know, I always tell, tell my students in debate that I have had students actually change my mind on a on an issue, and that it's not really important. You know what my position is. In a debate class, like, what is important is that you can actually justify and back up your own answer. Right, that you can. You can use research and explain your own reasoning. That's the important bit, and I think that's the same, exact same thing in math, right, you should be comfortable with ambiguity, like. The teacher doesn't have to be the final authority on every question.
Speaker 2:Hey teacher friends. If you're an HMH user, did you know you have access to Teacher's Corner on Ed Included with every HMH program? Teacher's Corner is a community of teachers, learning experts and instructional coaches gathered in one place to support you with a new kind of professional learning bite-sized, teacher-selected and teacher-driven, with on-demand sessions, lesson demonstrations, program support and practical resources. Teachers' Corner lets you choose how you interact with our content. I like to think about it as inspiration on demand.
Speaker 3:Okay, speaking of debate, there seem to be two schools of thought when it comes to math facts. A lot of people are still in this camp of we need to memorize them. And I'm saying a lot of people are still in this camp because I, on every other day I'm in this camp of we need to memorize math facts. And then others say to focus on the problem solving and the math facts will come, Like if a student just knows seven times eight, it doesn't necessarily tell us if they understand why. But what's your perspective on how students should build fluency with those math facts?
Speaker 1:So I think in this case both of the extremes are sort of caricatures that I think are not best practices for like helping kids. I'm sorry, what, what word did you?
Speaker 3:just say.
Speaker 1:Curricatures, curricatures.
Speaker 3:Oh my gosh, where are you from From? Where are you from From?
Speaker 1:Did I say it wrong.
Speaker 3:No. I don't just I say I say it wrong, I say caricatures.
Speaker 1:Can we write a song called caricatures, caricatures. I think they wrote one. You say potato, I say potato.
Speaker 3:Okay, that's just like the unknown verse. That's like the deep cut it's the deep cut, okay, sorry. So yeah, both extremes Not good. Like don't make students just like wrap them on the knuckles until they know all their their multiplication tables, but also like we need some kind of commitment to memory.
Speaker 1:Yeah, I mean, we know that like being like being unable to like draw from facts is going to hinder kids who are not able to like see a pathway through a problem, who are not able to like see a pathway through a problem right? So just to give an example, I had a student in a pre-algebra class who was still counting on their fingers, perfectly understood all the linear equations that we were doing, but every time this kid had to sit down and like simplify fractions, they were like counting on their fingers right In eighth grade and you could say, well, you could pull out a calculator. But the kid who's like able to look at a fraction and say, oh, six, sixteenths, I know that six is twice a three. I know 16 is twice an eight. It's going to be able to like simplify it much faster. They're going to be able to like simplify it much faster. They're going to be able to make insights and just not have the cognitive load Like this kid took like an hour to answer a question on a test because they were doing everything.
Speaker 3:Even though they're ready, they're ready, they get it, oh yeah.
Speaker 1:The abstract reasoning that we were doing with linear equations. This kid understood right. But their cognitive load was super high because and the way that I understand cognitive load.
Speaker 3:you taught me that term because I was coming to you and being like their gears are too frictious in their head and they get fatigued and you're like, yes, there's a word for that that's.
Speaker 1:That's exactly what it is, right. It's just you can only juggle so many balls and working memory and you need to be able to chunk things and working memory so that you can get to the bigger stuff, right? Yeah, if you're constantly managing small chunks of information because you haven't memorized something, then it's certainly going to slow you down and impair you when all these chunks are, like you know, need to be kept in mind at once.
Speaker 3:Yeah.
Speaker 1:I think that's the best argument.
Speaker 3:I think that's the best argument. It's just like it's not about turning our kids into into like a militant memorization thing. It's about smoothing the gears for later, when they are like ready to fly, and the small stuff isn't like gumming up their wings, exactly, exactly.
Speaker 1:It's ice on the wings, right, exactly, exactly. It's ice on the wings, right, right. But by the same token, there's good memorization and bad memorization. Like they can just sit there and memorize their times tables just completely rotely. You know, 7 times 9 is 63, right. Or they could actually memorize where they're looking for patterns, right. Oh, seven times nine. Well, I also know, seven times 10 is 70. Seven times nine must be less than 70, right. How much less. Well, it's one seven less. Then the chances that you can go and recall something when you need it just becomes exponentially higher, right? If you just memorize something as like a disconnected, isolated fact, your recall of it is going to also be kind of poor, right of it is going to also be kind of poor, right. You're going to have to like land the one pathway to recall that memory.
Speaker 3:But if you're like building an interconnected set of memories, yeah, if you're cultivating flexible agile, a playground of math in your head, rather than like one slide, one slide, one slide.
Speaker 1:Exactly. It's not just about cramming the stuff in and somehow recall happens magically, right? You want recall to be almost so. You want to have created so many pathways that it's almost hard not to recall it that they almost would have to like intentionally not wander across a pathway and recall it.
Speaker 3:Oh well, and you're, uh, there's a one of my tricks, one of my classroom tricks is that I buy like a ball and I write math, uh, multiplication problems all over it, and where we throw it around and wherever your right thumb lands, you have to answer that math, that problem. But there's no um, you don't have to play, you can sit down, um, you can say pass, like there's a lot of, there's a lot of uh safety nets, because I know that that that could sound. Not only have I entered some, that's some people's hell. Right, I have to catch and then do math, um, but but uh, I have a couple of things in place for my like high flyers too.
Speaker 3:When they catch a ball and they say a math fact, really fast, you know, like seven times nine, sixty three, and they like rear back to throw the ball to someone else, and I'm like wait, can you tell me another, can you tell me why? Like can you just walk me through? And they'll do your 71, because I'm all seven times ten minus seven, and I'll be like, can you do it any other way, a different way? And then they start getting like playful with 21. And so I asking people to like, asking students to like lubricate their gears externally and in front of other kids. Kids, like throwing a new pathway to even the high flyer, is essential to showing kids why it's not good enough to just know a 63. That's not, that's not the end goal. That kid, that would have intimidated Kaylee middle school.
Speaker 3:Kaylee Rhodes actually wasn't as as a maybe fluent as I thought.
Speaker 1:No, I, I totally agree. I mean, I think that that's an excellent activity and it's a really clear indication that like the stuffing memories in is not to like have all of these facts. It's to have like useful facts and connections and see the connections so that we can think flexibly Right, it's building. It's building muscles, like you play scales so that you can then play things that are not scales Right, but you need to know where your fingers need to go on the keyboard so that you can do the scale correctly, so then you can start jumping.
Speaker 3:Yeah, and the more like in your body the scale is, the the less friction you're going to have as you fly higher, as you, as you start composing Well, and so like this, this kind of like roteness versus rhythm, I guess is something that we see a lot in curriculum old curriculum, new curriculum because a lot of teachers swear by practice sets where students work on the same skill over and over again, just like get it in your body, get it in your body, which I understand. But there's also another school of thought where we're looking at these open-ended, rich, long math tasks that take whole class periods or longer. How do we strike a balance there, and what does a good math task look like in your opinion?
Speaker 1:So I think with like open-ended tasks, the same thing is true, that there can be good open-ended tasks and bad open-ended tasks. Right, if you threw a problem at students and basically said here you learn, you know derivatives on your own, like you need them to be able to answer this question, but I'm not going to teach you. I mean, that's just too much. Right, it's not scaffolded for the students it's a bad escape room yes, exactly, exactly.
Speaker 1:What you really need is an open-ended task where, like, they're bringing a motivation on their own, they're interested in the subject matter. Maybe it's the kid who's, like, passionate about art, getting to connect, uh, but where? Where you've scaffolded the math task for them, right? I think the question of, like, what defines a good activity versus a bad activity, like across the board, is, you know, number one is it something that's like in the appropriate zone for the kids, right? Is it something that they're actually able to understand and to do productively? Is it something where they will be able to think rich, make rich connections and think deeply about the problem? And have you set them up in a way where the clear onus of thinking is on them?
Speaker 1:And there's a whole gamut of activities, from, like, fun games, memorizing, to doing open-ended projects, to doing group work. All of those can meet those criteria. If you just are being really thoughtful about what my purpose is as a teacher, like, what is my pedagogical purpose? What do I want the students to accomplish here? So I think all of those can be set up as good tests.
Speaker 3:Do you have a favorite? Creating something? I know about me being a math teacher is inventing math problems is hard. Inventing whole class, rich task, perfect zone of proximal development, perfectly differentiated. I've created the. That is really tricky and so I have. I look to resources, right. What are some favorite? Like hey, if you are ready to engage your kids in some rich whole class tasks and your curriculum isn't maybe meeting that need, where would you direct one of your teachers? Aka, me.
Speaker 1:I would actually say I think a lot of the things that we need to do are pulling from those resources, just like you mentioned, from textbooks, from other resources that you have, from like websites. But I think the key thing is you, as a teacher, having the confidence to improvise and to adapt right. You know the. The saying is no battle plan survives contact first, contact with the enemy. Uh, and I think no lesson plan survives the first five minutes of class, like as soon as the students see the problem, you might as well just throw your lesson plan away right, because it's not going to go to plan.
Speaker 1:No, and I think the difference between an experienced teacher who's really focused on like the goals is that they know how to like, adapt and respond. They recognize where the students are struggling, where there's room for growth. So I don't, I don't think you have to come up with like here's the perfect lesson plan. I have defined this, I have pulled it out of the heavens and I've put it into paper form and it's going to, you know, amaze the students and wow my administrators.
Speaker 3:It's going to tap dance across the desk.
Speaker 1:Exactly right. That's not the goal. Like the goal is to say what do we need to do today? We need to talk about linear equations. Let me pull some lesson plans that I can find online and other textbooks. Where are my students going to struggle doing that? Pre-thinking makes a huge difference. And then, as soon as you get in the classroom, taking the opportunities and like like looking for the students who've made interesting mistakes, like looking for the uh, looking for the one-offs that just happened that one day and they don't happen again, right.
Speaker 3:So deviating from your script, making sure that you walk in with a rich thing that you've thought about. But if your goal is to watch them ignite with thinking and interacting with the problem, then they have about 100 different ways they can do that and you just need to follow them where they go.
Speaker 1:You're kind of a. Yeah, I was just going to say. If your goal is to get the students to think, how would you do that? By yourself shutting down in the classroom?
Speaker 3:Yeah, if your goal, what's your goal? To get them to think it's so and like what does that look? We haven't gotten to number three, which is when I show you this graph and you, like I, like we know we never got to number three because at number one there was enough for them to be thinking and that was my goal. But it is like letting go. So much of teaching is letting go. It's so, it's like a soap is in.
Speaker 1:You've heard the, the expression in editing, that you have to murder your darling yes that's the, that's the fundamental rule of teaching. I think too, it's like.
Speaker 3:But number three is so exciting to me I photocopied it front and back in the color printer. It was all across campus. Who am I making fun of Me? Okay?
Speaker 3:No, you'll recycle it, okay. So what you're recalling for me from the top of our conversation is this idea that, being honest about what thinking looks like and so it can't. Even if you have a kid that knows all the math facts, is there thinking? Even if you have a kid that's still counting on the fingers, is there thinking? And so, just um, coming back to this whole idea of not a math person, one of the things that I get, uh in my classroom are, you know, brand new little sixth graders who are not used to uh, not walking out of the classroom with an answer and or or knowing they did it wrong or well, this was your mistake. Okay, bye, see you tomorrow.
Speaker 3:And that they get very frustrated by that. They, they, a lot of people's frustration with math actually can lie in that open-ended stuff, because they are like just tell me the answer, just tell me how to do it, and I think that, like norming from day one, that part of undoing your math trauma is getting more comfortable with that ambiguity. I mean, all this is clicking for me. You already said this. You're nodding, you're like yes, I've been saying this the whole time and this is very true for us, this tracks, but just like it's all like coalescing for me, where I'm like oh, that's what you meant by ambiguity, and that is probably the most uncomfortable part, not only for us, but definitely for them.
Speaker 1:Yeah, no, I mean no other subject I think in middle school or high school puts kids on the spot as much. Right, at least in your science class there's a body of facts that you can sort of memorize and like same thing in your history class. Like, even if your thinking has not really developed in that subject, you can still get something down and get right for something. And it feels like in math, like everybody is expecting that there's just the right answer there. It doesn't matter what the thinking is, and I think we just have to get students a lot more comfortable with sometimes you're wrong, right. Sometimes the problem is outside of your ability to solve it, and that's okay. The problem is outside of your ability to solve it, and that's okay, right. And maybe we don't get an answer that day, but maybe we come back to it later in the semester. And we didn't.
Speaker 3:And that that's not the answer. The presence of or absence of an answer is not the presence or absence of success. That's not the those are. We have to break that and I think that's a myth that a lot of kids walk in with, and that's why they feel like a failure is because they're like that and I think that's a myth that a lot of kids walk in with, and that's why they feel like a failure is because they're like I didn't get the right answer, I'm a failure. But if we transform, if we alchemize that into, you came in here today. You were on your feet, you were engaged, you were thinking, you were making mistakes left and right because you were trying. You tried so much. Therefore, you failed some, and that is success in math class.
Speaker 1:You failed some, and that is success in math class.
Speaker 3:Well, I want to end on one last little question. Why are you so obsessed with statistics, Mr? I'm writing a textbook on statistics and you have to keep it short, I know, I know this is like its own podcast episode one of multi-season Russellsell's obsession with pot, with statistics I think that there are two main reasons.
Speaker 1:The first is what other class has a greater claim to actually being useful in your adult life as, like a citizen right? Kids coming out of high school should understand how polling and surveys work. They should understand how you know research studies are done. They should understand how experiments are done. Do we think that you know, if people were more statistically literate that the pandemic would have unfolded the same way that it did? I don't. I think if people were actually statistically literate, I think they would have understood more and behaved differently.
Speaker 3:You know, and also questioned demanded good data, noticed flaws in the way that things are conducted sometimes, or sample sizes or things like that. Look at me trying to act like I know any of this vocabulary? I don't. I'm so sorry, russell.
Speaker 1:No, the sample size is the most important thing. Oh my God.
Speaker 3:I know, see, I know.
Speaker 1:There you go, there you go, you're right.
Speaker 3:Chapter one of your textbook. I'll write the foreword. You don't even have to ask.
Speaker 1:Thank you, I appreciate that. Yeah, I mean, I can't think of anything that's more important for students to understand graduating high school right.
Speaker 3:And you know you're making me think like what, speaking of real world fodder for your whole class? I mean you just must open the newspaper every day and be like this is today's lesson.
Speaker 1:I mean, we do this like with some regularity where I'm like all right, like today's lesson, I've brought in like this, you know, sample this survey that's just been done and we're going to talk about what went right, what went wrong, like why they got the results. And then I think the second reason that's super important for studying statistics is there are so many jobs where people encounter data and it is so, so easy to open up Excel and like to put numbers in a spreadsheet and have the spreadsheet do stuff, and everything that you do not see about how the data was collected is actually super, super important. And if you don't know something, you are so likely to be misled by data that looks like it supports your conclusion and actually doesn't. I was at a school and the head of school like made this announcement and like shared the dislike data with with the whole, uh, with all of the the three statistics teachers.
Speaker 1:We all just sort of heard this and we all go.
Speaker 3:Oh no, not the head tilt.
Speaker 1:Oh no, because we all immediately knew what the flaw was.
Speaker 3:Do you remember?
Speaker 1:what it was. It was basically, like I said, like, the data that you don't see is often what gets you right. So when you're saying like, oh, we've seen the sample increase, we've seen this population increase like it's average over time, the question is like why is it increasing over time? Is it because the population is changing? And that was exactly what was happening. It didn't actually indicate anything good was happening, it just indicated that the population was changing.
Speaker 3:Man, data is. You're right, it's everything I mean coming from the NWEA perspective of like needing those map growth scores to just you have to have data to know where you've come from and where you're going, and you have to have data. That's, we say, trustworthy data, and this is what this is. It's data that we're trusting is not being cherry picked to tell a certain narrative or left out a very big consideration or a big skew. Again, the incredible researchers are probably like stop, stop trying to use vocabulary, but you're right. And this idea of if we truly want to educate critical consumer kids, critical kids where is statistics? You're right. Well, when am when is your? When am I going to be able to take your textbook and read it before I go to bed every night?
Speaker 1:It's definitely bedtime reading it will. It will put you to sleep? No, I hope not. No, I'm like a couple months away from finishing it, but things keep happening. Life is life is busy.
Speaker 3:So it'll probably be another 10 years, but hopefully soon that is so exciting, russell, that you are like just I feel so lucky to know someone as mathy as you, because you, you do a, you do a great job of your. Math. Prowess never makes me feel inadequate and you, therefore, you, you do the opposite. You amplify my mathiness, you make me feel proud of my own like math speed and math journey. Um, and so you being my math department head when I came on and now being my math colleague, I just really really feel grateful. Um, so thank you so much for coming on and talking about all of this cool stuff today.
Speaker 1:Absolutely, absolutely. I really love the journey that you've been on. It's amazing to see someone start out and say I'm not a math person and then do the amazing work that you've been doing. So it's wonderful to see.
Speaker 3:Thank you. You know that if you ever want to like make me feel amazing, just tell me how the English teacher can become a math teacher and like, really I have a hard time picturing myself going going back to teaching not math. There's just something really beautiful about struggling with it as a student myself and stepping into not only reclaim that, but reclaim it with my kids. It's really big and, russell, thank you so much for joining us today.
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