Curtis Brown from TI Calculators

Curtis Brown 0:03

I want students to be able to explore. I want students to be able to ask questions why, and I want 'em to want to. we have to develop that curiosity. And where it's died, we need to find ways to rejuvenate it. everybody is a math person, we all have the ability to be math people, Some of us find greater interest in mathematics, but I would argue that the majority of people who don't find great interest in mathematics haven't experienced it correctly.

Vanessa Vakharia 0:33

Okay. Hello. Hi. It's me, Vanessa, and welcome to your weekly hit of Math Therapy. I need to start with a question that I know is gonna get some of you fired up immediately. Are calculators actually making kids worse at math? I know that's a controversial statement, but I'm curious if you've ever thought that, or have you heard someone say it, or maybe you've seen it on Twitter. Because on one hand we have these incredibly powerful tools that can support thinking, reduce cognitive overload, and like open up access. And on the other hand, there's this very real fear that kids are becoming too reliant on them and like they're skipping the struggle and they're not actually understanding what they're doing and they're just like, boop, boop, boop, like punching things into the calculator without thinking. Are we even asking the right question. Because if you've been around for a while, you already know that I'm less interested in the "are calculators good or bad" argument, and way more interested in what's actually happening underneath that. The confidence, anxiety, identity, and whether or not the tools we're using are helping or hurting all of that. Today I'm joined by Curtis Brown, who is a former high school math and AP stats teacher, and now the math segment manager at Texas Instruments. You know what I'm talking about, that TI 81, 82, 83, 84. You had one. You might not have owned one, but you punched buttons into one. Curtis is literally helping shape the tools that students are using every single day. He also co-hosts the podcast Room to Grow, which you absolutely need to check out. And he spends a ton of time working directly with educators, thinking about how we design math experiences that actually support learning. And that is exactly what we're getting into today. What role should calculators play in math class? When do they support thinking, and when might they actually get in the way? And how do we use them in a way that builds confidence instead of dependency? Today we're digging into the big question, But before we do, I want you to think of that one person, the colleague, the department head, the parent, the very opinionated barista, the Twitter troll, actually, don't send it to the Twitter troll. Actually, you should probably block them right now. Anyways, think of that person. Send them this episode like right now, because this is one of those conversations that people think they've already made up their mind about until they hear a perspective that actually makes them rethink it. If you've ever felt conflicted about calculators or unsure about when to allow them, or just curious about how this connects to math anxiety and learning, this episode is going to give you a lot to think about. Let's get into it.

How tools can fuel learning

Vanessa Vakharia 3:00

Curtis. My dear pal from Texas Instruments. Welcome to the podcast.

Curtis Brown 3:07

Well, thank you. I'm super excited to be here.

Vanessa Vakharia 3:10

I mean, we've had a series of very odd interactions up until this point, wouldn't you say?

Curtis Brown 3:16

I would say we've had some odd interactions, some chance meetings at conferences. Uh, I didn't know you were gonna be here, what are you talking about? Coffee bar at 5:30 AM at Wisconsin Math Conference. You remember you came in and I was grinding my, coffee beans. The, um, getting ready to make my aeropress.

Vanessa Vakharia 3:35

And now what a full circle moment, because just two weeks ago, my friend made me a coffee in an aeropress, and it was superior to any other coffee I've had, and I was like, I'm, I'm converted. And actually, see it's funny that that's your core memory of our meeting. 'cause my core memory is NCSM two years ago when I accosted you, I think that was when I met you for the first time and told you that my dream was to have a Swarovski crystal Texas Instruments calculator like Lady Gaga has a Swarovski Crystal keytar. And I was like, when I get famous enough, that's what I want. And I think you said you were gonna make it happen.

Curtis Brown 4:07

I mean, listen, I promise all kinds of things from time to time.

Vanessa Vakharia 4:13

Okay. Well, I'm glad that our memories are fond and bizarre, and I'm so excited to have you on the pod for so many reasons. One of them being that I am the biggest Texas Instruments fan, but I'm gonna save that gushing for later. But I've, I really love the brand. I love everything you guys do. But the real reason I'm so excited is that I feel like calculators are like the hottest topic next to Ai, which is so bizarre 'cause AI is so much newer and calculators have been around for so much longer. But they continue to be like this hot button topic in math education. And now I have like the calculator guy.

Curtis Brown 4:53

The calculator guy. Yeah. I mean, calculators have, they've been around for, so for quite a while. And specific graphing calculators, like if we think about calculators, you think about the development of numeric calculators and the things back in the, in the late sixties, early seventies, right, and just this concept of calculation and being able to do that automatically. And then you think about mechanical calculators that were even before that. I'm talking about digital

Vanessa Vakharia 5:19

what's a mechanical calculator?

Curtis Brown 5:21

Well, think about an abacus.

Vanessa Vakharia 5:22

Ah.,

Curtis Brown 5:23

But then this idea of the graphing calculator and the introduction of that was, early nineties, late eighties, early nineties. And that fundamentally changed the way we teach and learn mathematics, and I think that has real staying power,

Vanessa Vakharia 5:38

okay. This is actually so interesting for you to just walk me down a little history, like a little gilded age vibe of what has happened in calculator land, because I've never, I don't think I've thought about really how long they've been around. You're saying digital calculators were created in the sixties or seventies and the graphing calculator was all the way back in the nineties. You're right. I had one.

Curtis Brown 6:01

Yes, yes,

Vanessa Vakharia 6:02

Oh my God.

Curtis Brown 6:03

did we've had them for a while, like a really long time.

Vanessa Vakharia 6:08

Okay, so then this is such a perfect segue into the first thing I wanted to accost you with really, which is, and, and this makes it, this makes it even crazier that they've been around for this long. Because as you are probably very well versed in, people love to say that calculators are making kids worse at math, right? People are like, calculators are the reason why kids don't know their math facts. Like, la la la, la, la. But hold on a second. If they've existed for this long, how are we still, how are we saying that now? Like, you know what I'm saying? Like, let me just ask you, do calculators make kids worse at math?

Curtis Brown 6:46

No. Mean, blanket statement, calculators, no, they don't. And I would've said that when I was in the classroom, I would've said that even in my own high school experience, I mean, this predates me working, for Texas Instruments. This is a statement I would make any time, anywhere. Because calculator, if you think about calculators themselves, are a tool. A tool. And the way that you use that tool then can make a difference in the way that you build something, in this case, your understanding and learning of mathematics, right? and learning of mathematics, that's really what we can talk about, is the usage of graphing calculators or any kind of calculator for that matter. The type of usage and the way that somebody uses it, that's what can maybe kill someone's interest in mathematics, or not keep them interested in mathematics. Or the opposite of that. Like that could really get them engaged in mathematics. And so I think it's more about the execution of the tool. That, that's really what I'm thinking about whenever you ask that question, are calculators making kids bad at math? No, they're not. it's the way that we may use them or not use them that might make students not excited about math or not doing well in math.

Vanessa Vakharia 8:02

Well, it's so funny 'cause as you're saying that

When are calculators helpful?

Vanessa Vakharia 8:04

I'm like, yeah, if this is like the old adage like with great power comes great responsibility, like it's like the internet, right? Like it's like, is the internet doing like all sorts of bad things? Like, well the internet isn't, but the way we use it can either be to enhance a life experience or to detract from it, right? Like there are obviously like bad things you can do with the internet, right? Like, it's like anything. It's like the, the inanimate object itself is neither good or bad in a way. And with calculators, I think it's so important what you said that not only like you're kind of going a step further, you're like, well, not only is it, are they not bad for math learning, but they can actually be the tool that if used properly, help kids get into math in a way that they weren't before. And this is a podcast about Math Therapy. It's about math trauma, and so many anxiety around math. So I'd like to actually hear from you. Tell us when a calculator can be used. I don't wanna say like for evil, but it just sounds so like, good if I say that, like for good or evil, right? Like when is it appropriate to use a calculator and when is it not? When are we using the tool for good and when are we using it in a way that detracts, like give us some examples.

Curtis Brown 9:15

I'll, I'll give you an example. Here's a high school example. So background, first of all, I taught high school mathematics, right? So

Vanessa Vakharia 9:21

Yep.

Curtis Brown 9:22

is gonna kinda revolve around that, but I have some experiences in thinking about my children, also my own two boys, and the way that they have learned math and things that they've been exposed to. So maybe I'll, I'll get to that in a second. But I want to start with an example of using a calculator and specifically a graphing calculator. That maybe changes the way a student interacts with mathematics. I have a good friend of mine. his name is, Tom Dick. He works at, Oregon State University. You might know Tom, from other conferences and things. And Tom, told me, relayed me a story, for the first time that he ever used graphing calculators, with his students. His students were graphing a rational function. pick your favorite rational function that happens to have a, a hole in it. and he, had his students graph that function. and he had been doing those kinds of examples for years, having the students make pictures and think about limits and doing all of these things by hand. Right? students were more or less, engaged, but maybe not engaged. But this time. Using the graphing calculator, student happened to graph one such that, the hole actually appeared visually on the screen.

Vanessa Vakharia 10:32

Hmm.

Curtis Brown 10:34

so this student, as Tom was walking through the classroom, over to his buddy and said, my graph has a hole in it. does your graph have a hole in it? There's really important word there. My graph. Your graph, there's

Vanessa Vakharia 10:51

Huh.

Curtis Brown 10:51

that happened because these students created a picture on a graphing calculator. Okay. saw that picture and now there was an ownership that happened. That word never left their mouths beforehand. And I think there's something really, really important about students owning mathematics. I know we hear research and we hear talks. We go to trade shows and, and conferences and hear the, the teachers and the. Professors and the researchers talking about students owning mathematics. That ability to see something in my hand that I've interacted, that I've created, and now that math is mine, huge. That learning is huge. So using a graphing calculator, using a calculator in a way that allows me to explore mathematics, that gives me ownership. I think that fundamentally changes the way that I learn. And I think about the math. I own it now, right? So I can also draw, connections to things like same graph. If I wanted to make multiple examples of those things and I needed to do that by hand, it takes a long time to do that, right? I'm plotting points, I'm making tables, I'm making, and don't get me wrong, there's value in doing that. I think there's value in taking the time to do those things by hand. But, iteratively doing it multiple times in a row, recognizing a pattern, beginning to develop something happens a lot faster if I've got some technology in my hand to be able to do that. So there's some really nice pieces to the puzzle.

Vanessa Vakharia 12:26

Well, those I like weirdly was getting like goosebumps, like when you were talking about that first example, like I was like, oh my God. Like I was picturing that moment of like a student being like, why is there a hole in my graph? Like, and I, like, I, I could feel that with you, that excitement. And there's

Helping students take ownership of their learning

Vanessa Vakharia 12:42

a few things you really interesting, like I really like actually how you've positioned the idea of owning math because this is another one of those catch phrases. I think we have heard a lot, but. Seldom elaborated on. So I think we all think we mean the same thing when we're talking about students owning math. And I like the way you just explained it, that the ownership of math comes from them actually doing something, creating something, generating something, being a part of the process of the math that they're doing, and then being able to make an eye or a my statement to be like, this was something that, that happened as a result of me. It didn't happen to me. You know, like, Yeah, I think that's a really cool point. Like I was, as you were talking, I was thinking back to when I was in calculus and you know, I was graphing things and I was doing it all by hand. We weren't using the graphing calculators back then to graph in this way. Like I think I was still using my ti mostly for actually maybe we were doing some loose graphing, but just definitely not to this extent. And I think this is such a good point that like. What I'm hearing you say is there's two skill sets. Like there's the skill of being able to plot the points and graph that is skillset number one. And then there's a whole other set of skills, which is recognizing patterns, right? Like recognizing patterns, doing something iteratively to be like, if I change this factor, what happens to this? And that is just more efficiently done with the use of a tool.

Curtis Brown 14:06

Absolutely. It's more efficiently done. There's also another, another piece to that. so I talked about ownership, but there's also this explore exploration piece that happens, You can't explore as much, you can't be as curious, if you're having to do everything by hand, right? Like if, if, if I'm having to do everything by hand, I can't say, well, what happens if I change this? What happens if I do this? What happens if, those questions are a lot more difficult to answer when I'm doing a whole bunch of hand calculation and manipulation? Right? And you, it's difficult to begin to develop that reasoning about mathematics, I don't have the opportunity to do that in an iterative sort of space, right? Does that make sense? What I'm, what I'm driving at?

Vanessa Vakharia 14:57

No, it makes total sense. But what I'm thinking is I'm like, well, obviously like at, I'm actually like, so what has changed? 'cause obviously at a certain point, like you're talking about bringing this creativity and, you know, experimental, exploratory, adventurous nature to math, which like, number one makes it so much more fun. Number two puts the emphasis on exploration and discovery instead of answer getting, so cool. But what I'm thinking is obviously before calculators, like people did that, right? Like I, I'm kind of like, what were they doing in math classes before calculators? Like how did they have time to do this? What were they doing? Do you know? Like, not that you were alive, but like too many.

Curtis Brown 15:33

Yeah, I was alive before calculators. I mean, there is a little bit of gray hair up here. So I was alive before the graphing calculator was in, in classrooms. However, like my, freshman year of high school, I got, a TI 82, I think, was what I, what we had in my math classes. going through high schools was TI 82. So, yeah. I don't that I could speak with a ton of authority to be able to say, Hey, this is what people were doing before, 'cause I didn't experience it. I wasn't in the classroom, doing that before graphing calculators. But I can imagine, if you think about, like looking back at, these log tables and these, these things that these guys calculated by hand, over long decades of work, right? To be a mathematician in the 14, 16, 18 hundreds, and think about the work that went into that, the level of development by hand, of things, had to happen because the technology just didn't exist, I mean, I think the exploration was still happening. I think there was still curiosity, but it was probably for a far fewer number of people, and I think

Vanessa Vakharia 16:52

Um.

Curtis Brown 16:52

been able to do is, the graphing calculator being in every student's hand now gives me the ability to go, Hey, I can do this too. Like this is part of my exploration, this is my identity too. Right? I mean, there's only a few Isaac Newtons out there before, right. Like was one

Vanessa Vakharia 17:14

Yeah.

Curtis Brown 17:16

think about that for a minute. Like there was this isolated few that got to be able to do that, and now what we are able to do and generate, generations before us never got to see. things.

Why are calculators so controversial?

Vanessa Vakharia 17:28

I think it's so cool because in a way, like we're talking about accessibility, right? Like, it's like this idea of giving more people access to that type of thinking because they have this tool. And so I'm like, and I'm thinking too, like you brought up the abacus, you know, we've always had. Well, maybe we haven't always, but there's been many, many decades of tools progressively being introduced into a math classroom. Right. So I'm wondering why you, you, you think, in your opinion, like why are calculators such a hot button topic where we are so polarized in terms of people being like, calculators are the reason like kids can no longer, you know, multiply. Like they're the reason kids are, you know, our mask scores are low. Why are people so obsessed with calculators?

Curtis Brown 18:14

Okay, so that's an interesting question. Like thinking about, why then? Are calculators kind of still getting this, this question around them, right? Like, are, are they actually causing problems? So think about, I talked about earlier, the use of the tool, right? Like, you wouldn't wanna build a house without a hammer. You wouldn't wanna be, you wouldn't want to do those kind of like, there's, there's tools for jobs, right? But even in the building of the house, misuse of the hammer could result in, in challenges or problems or issues, right? So overdependence is the same thing here. My eighth grader taking algebra. and he and I get to lots of tutoring time together. this is a thing we do, on a nightly basis, which is great. I love it. I love the extra time and, and like my shirt says, math is my happy place. So we're good. Like, I enjoy that. Uh, all the, uh, I, I enjoy that. See, it's, I mean, it says, so math is my happy place,

Vanessa Vakharia 19:11

Yeah, we are on a podcast, Curtis, so people can't see you, but just for all the listeners to know, his shirt does in fact say, math is my happy place, can confirm.

Curtis Brown 19:20

There yet, um, you con confirm. Yeah, you could confirm that. I'm glad so, no, but thinking about overdependence though, on a tool. All right. So.

Vanessa Vakharia 19:30

Mm-hmm.

Curtis Brown 19:31

There's numeracy things that my eighth grader has now developed because over time he's been practicing, he's been doing the mental gymnastics. He's been doing this for quite a while that my fourth grader has not yet developed. So my fourth grader brilliant in mathematics. He's, he's snappy. I mean, his reasoning about math is ridiculous. But his memorization, his numeracy, his, his ability to recall facts fluently really, really fast, he's still growing. So he reasons about math really well. Okay, if I gave him, a calculator, let's say that I gave him a four function calculator

Vanessa Vakharia 20:13

Can you, sorry. Can you define a four function calculator?

Curtis Brown 20:17

So add, subtract, multiply, divide.

Vanessa Vakharia 20:20

Got it, because that's what I thought, but I just wanted to confirm. Okay.

Curtis Brown 20:22

Yeah. No, that's fair. So I give him, I give him a four function calculator and I begin to ask him questions, that the calculator really could just do for him. And I say, you can use it if you need to answer these questions. In a relatively short period of time. He's going to become pretty dependent on just. Because it's easy

Vanessa Vakharia 20:42

Hmm.

Curtis Brown 20:43

and it's whatever. So I, 'cause I haven't given him any bound rail, boundaries. I haven't given him any guardrails as to how to use the calculator. As to how to use the calculator help him develop number sense. Right. Okay. Take that same scenario and I put it with my eighth grader who's now maybe, developed that number sense. He's recalling things quickly, but maybe we've got questions that, I don't know, there's decimals in the, in the answers or there's some weird fractions and things. And, and the point of the math that I'm trying to drive at is not, can you, do work with decimals or fractions, but can you find the zeros of a quadratic? What are the patterns and the things that you need? Now him having that, that calculator to be able to handle kind of the mathematics, the, the arithmetic stuff that he needs to be able to do to accomplish the questions that I've asked him in the context that I've asked him, it gives him a little bit more, access to that right? It, it speeds along the things that maybe his brain doesn't need to be thinking about. It frees up cognitive load, for him to be able to, Access the math that we were really caring about. Does that make sense? Like I'm driving towards this appropriate use

Vanessa Vakharia 21:55

Yeah. I want you to, I want you to talk a bit more about cognitive load though, because it's a term again that we've hear and throw like heard thrown around. But just for some of us who don't

Cognitive load & mathematical reasoning

Vanessa Vakharia 22:04

exactly know what that is, like tell us what cognitive load is and how calculators can help.

Curtis Brown 22:08

Well, my brain, your brain, all of our brains, we have capacities, some of the folks that I work with, I just can't believe all of the things that they can hold in their mind at one time. But that's, that's less, of us have that ability. Right? Like, not

Vanessa Vakharia 22:25

all have a.

Curtis Brown 22:26

we do, we all have different capacities, of things that we can hold in, in what I would, what, what might be termed short-term memory, right? Like the, this working memory that I'm able to kind of pull from and draw from really quickly. So if I overload that with calculations, arithmetic things that I can offload to a, to a piece of technology, my brain is no longer able to process the big things. The, the, what are the zeroes of this quadratic represent? How do I even factor this quadratic to come up with the zeroes and why, why is zero so important? Like, does that even help me with anything? Oh, zero product, property. What was that about? Like, there's so many things that I can't access because what I'm worried about is multiplying two thirds and three fifths, and being able to come up with some value for that. If I can offload that part to a calculator, then I can think about, oh, the zeros actually represent something. It's useful for me to find zeros because now I can, I can think about zero product properties. I can think about where this thing's gonna intersect axis. I can think about meaning behind the intersections of that aax axis as it applies to some projectile motion problem. Totally tried to make that up on the fly right there. But, like, does that make sense?

Vanessa Vakharia 23:47

It may. So let me, let me rephrase and tell me if you think that, or if this is what you mean. I'm thinking about? When I was in school, we used to have tests where you were allowed to use calculators on the first part of the test and not the second, or vice versa, whatever it was. It was, you know, whatever it was. And let's say we could use calculators on the part of the test that asked questions like that, where the calculations themselves were not the objective of the questions. They were secondary to the lesson that was being taught or the, or the knowledge that was being assessed. And the other part of the test that we were not allowed to use calculators on, the objective of that assessment was to test our calculation. So example if we're doing like six plus four, right? And the goal is, is we, we wanna see the student get the answer to six plus four. We wanna see what they're thinking, how they do it. A calculator should not be used for that because the objective is them doing the calculating themselves. But if the question is I don't know. I now, I am not gonna be able to make up something on the fly. I'm trying to think of like, you you know, if it's, interpret what the sum of six plus four could mean in this scenario where we are at a grocery store. I'm, I think this is gonna work, right? Like, like come up with, with a scenario where you would, where the sum of six plus four would represent something in a grocery store. Your job is to come up with this scenario. Then I'd be like, go ahead, ask, go, go to your calculator. See that six plus four is 10. I know this is, I know that elementary teachers are like, what is wrong with you? We do not want students to ever go on a calculator for six. Plus four. But I'm illustrating a point. I'm illustrating a point. So the point is I'd be like, fine, whatever. If, if you need to do six plus four on the calculator to see that it's 10, and then think about what quantity of 10 things you would buy in a grocery store, then fine. Am I, am I on the track here?

Curtis Brown 25:33

No, that's exactly, that's exactly what I'm thinking about. That even, well that example might be one that's like that. I mean, the elementary teacher's

Vanessa Vakharia 25:41

Sorry. Yeah, I'm That was, that was a lot. I know, It's true, but you're talking about zeros and quadratics and I was like, whoa, you've really gone off the deep end. We need to bring it down a notch here. Then maybe I went down, I overcorrected too far. You te You know what, if you're listening, if you're listening right now, text the podcast, hit the link in the show notes, text the podcast, and you give us a scenario when it's appropriate and not appropriate to use, uh, a calculator for a particular math concept. You do it. The listeners can do it. Curtis, we've, we've done enough work here. We've done enough today.

Curtis Brown 26:11

Love that. I was just gonna tell you, you could add in sales tax and all of a sudden now the calculator really becomes useful. All right, so the $6 item and the $4 item, and then you add in, you add in sales tax, now

Vanessa Vakharia 26:25

But shouldn't we be calculating the sales tax ourselves

Curtis Brown 26:28

no,

Vanessa Vakharia 26:29

the calculator

Curtis Brown 26:29

be going around doing eight and a half percent or eight and a quarter percent on my, in my head. Like I need, I, I, I can estimate it. Which I

Vanessa Vakharia 26:38

Sure.

Curtis Brown 26:39

the reasoning we want students to be able to develop. Right. But that's all

Vanessa Vakharia 26:44

How would you estimate that? I'm just now curious. Would you do 10? Would you just go to a 10?

Curtis Brown 26:49

a hundred percent. Start with ten

Vanessa Vakharia 26:50

Okay.

Curtis Brown 26:51

I know it'll be a little bit less than 10%. Right.

Vanessa Vakharia 26:54

Also, I'm sorry.

Curtis Brown 26:56

develop a little, logic around that.

Vanessa Vakharia 26:58

That makes sense. Are you are, your sales tax is only 8%?

Curtis Brown 27:03

Eight and a quarter, I think in Texas. Yeah.

Vanessa Vakharia 27:06

Well, in Toronto it's 13%. Okay. Anyways, so I, I do the 15, like I like do I estimate 10 and then I divide it by two, and then I'm like, okay, so I've got around approximately 15, which is approximately 13. Okay. No one needs to hear about this, guys. I'm sorry. Delete this, please. Okay.

Curtis Brown 27:21

though. That's it. that's the reasoning we want students to develop. Sorry, you just, you just did some real math reasoning right there, right? That like that's the stuff that we think about right. Now, would you have developed that on your own without having seen it and done it a few times? Hey, listen, the calculator gives you opportunity to develop that pattern that, hey, this, like, I can see this quickly. That reasoning you just did, that was it.

Vanessa Vakharia 27:48

Thank you so much. You're so good at affirming, like, wow, I feel really good right now. This is the thing is, I think this all really goes back to it's how you use the tool. Because when you were talking about your kid and you were like, well. If I was like, here's a four function calculator. If you want, you could use this. This is exactly what is happening to me with ai. It's like all of a sudden I'm just finding myself like, I could do it, but I could also just ask cha GPT to do it for me. And I've started doing it so much because I can, and it's right there. And I will tell you I am abusing the tool. Like it's like I, I'm because. I am, and I need a therapist for this because it's actually making me dumber. Like I'm, I know we're not supposed to use that word, but I can feel, I'm an adult, I'm a grown person, and I can feel that me using this tool in scenarios where it would actually benefit me to think about it, I would gain something from thinking about it. It's making me dumber. Whereas there's things that like, it makes sense to use the tool for, but I mean then we all have our own lines of like, when does it make sense? Like. And a calculator. I remember my high school math teacher who I love, and she is just like the smartest person on planet earth. She would always, I'd find, I'd catch her doing, like, she'd be adding up a student's marks like let's say like eight plus five plus three, and I would notice her doing it on her calculator and I'd be like, oh my God, you're using a calculator. And she would look at me and be like, yes, I can do it in my head, but for this particular situation, I have to do 30 of them in a row, I don't want, I guess she was talking about cognitive load before we were using the term, and she was like, I don't wanna make a mistake. It's a student's grade. I've gotta pump out 30 in a row. Like I basically have to do data entry. Like I'm just gonna use the calculator so that I don't mess something up. And that's fair. Right.

Curtis Brown 29:33

Yeah, that's, that's exactly Your teacher was doing exactly I'm thinking of. Right? Whenever it's an appropriate use of the calculator, even to do something really quick and fast like that. Right? Like in this scenario where you're adding up a whole bunch of student grades and maybe she was even gonna need to take, find an average right. Of course she could do that arithmetic in her head. Now, I know we're talking about arithmetic and calculators, especially graphing do a lot more than that, but the same rule applies to graphing scenarios or making lots of functions and, and conic sections and all of the, you know, upper level name, your favorite upper level mathematic, like there's by hand procedures that you can use to do those things. But often we get into a scenario where it is useful to use that tool to do the thing faster.

Vanessa Vakharia 30:28

Well, you know what? You're making me realize also, I'm talking about an adult. Who has already developed the skill and she's saying to herself, okay, I've already learned how to do it. Yes, I can do the arithmetic in my head. In this scenario, I'm gonna choose this tool. Versus a kid who is just learning how to add, let's say, and is given the, right, so we're talking about two different things here, like,

Curtis Brown 30:53

Yes.

Vanessa Vakharia 30:53

But I also, but I also think it's the same because it's like, sure. If you don't use it, you lose it. So yes, at a developmental stage, like when a kid is just, let's go back to graphing, 'cause I know I keep talking about arithmetic and you're like, just FYI. That's a different thing, which I know it's a, I know it's, but I feel like people, like when people are doing the hate on the internet, they're hating on the arithmetic part mostly.

Curtis Brown 31:17

Right, the, the,

Vanessa Vakharia 31:19

Right.

Curtis Brown 31:20

I think we have to be careful about that. Right. We, we should be careful because yeah. When people are hating on the internet about the calculator and people using them and students using them, they're hating on it because of the arithmetic part. And hey, students should be able to do that arithmetic part in their head or whatever. And, and the answer is okay. Sure. Yeah, they probably should. In fact, they should be able to do those things. But I'll even open up the door a little bit further since we're still on this arithmetic thing for just a

Vanessa Vakharia 31:46

Yeah.

Curtis Brown 31:46

Like, think about it for a second. Like, again, thinking about that cognitive load piece, let's suppose for a second, because it happens in the states often where, a student has for one reason or another, maybe not mastered those numeracy things. Okay. Hypothetically speaking, let's say that my eighth grader was struggling with the arithmetic part.

Vanessa Vakharia 32:11

Yep.

Curtis Brown 32:12

I do want to develop those in him. I do want to have time for him to, to develop that. however, should that be a barrier to him, beginning to try to develop those other algebraic ideas. I mean, his brain is mature enough at an eighth grade level that he should be trying to develop some of those abstract, algebraic concepts, those analytical concepts. And my question to you would be, should he be given a tool that gives him access, to those algebraic concepts? Taking, maybe getting that arithmetic piece off the table for a second. Like let me offload the arithmetic part so that I can try to develop that analytical part, that algebraic thinking like, can I do that for a minute? Like,

Vanessa Vakharia 32:57

A good point.

Curtis Brown 32:58

And your podcast is Math Therapy, right? Like, think about what that does for a student who is, anxious about their mathematics. I'm coming into my eighth grade algebra class or my ninth grade algebra class, and I'm struggling still with that multiplication of fractions thing, it's a struggle for me. And yes, high school math teachers, I, I get it. I know there's rates of change all in that al in that multiplication of fractions, and that's a concept we need to be able to develop. I get it. I agree with you, but there's also an ability to be able to offload a little bit of that arithmetic to try to help develop those algebraic thinking concepts and maybe reduce a little bit of that anxiety walking in the door.

How tools can fuel learning

Vanessa Vakharia 33:40

Honestly, I think this is the most like important thing that I'm taking away from this because I don't know if this metaphor is going to work, but I actually think it is. This reminds me of, like, putting training wheels on a bike.

Curtis Brown 33:56

For sure it.

Vanessa Vakharia 33:57

Do you think, right, like it's like putting or putting floaties on when you're learning to swim or I even think I'm, I'm like in a, in a workout phase right now, so I'm, I'm actually thinking about fitness and I'm thinking about like, when I go to the gym, I can't jump up for the pull up bar, do you know what I mean? Like I can't jump up to get it. And I'm really stressed about that. I actually have this weird thing where I think I'm gonna jump up. I'm gonna, and I'm gonna grab it and I'm gonna fall. So I've been avoiding this pull up bar forever. Okay. And I think this might be trauma from the monkey bars when I was a kid, to be honest. But we don't have time to dig into that right now. 'cause this is Math Therapy, not like monkey bar therapy. But my point is, this is exactly like a kid going into the next grade of math, carrying a math trauma from the past, being like, oh my God. Those time tests, every time I had to do calculations and arithmetic in my head, I don't wanna face that again. And then I go to the gym and my trainer's like, oh, well you don't have to jump up to get to the bar. Just stand on the bench. And I'm like, what? And he is like, yeah, well you can just move a bench underneath the bar, grab it from there, and then do your pull up. We can skip the jumping part altogether. Now what has happened, Curtis, after two months of, so I, I get on the bench and I still do my pull up. Two months later, I'm like, you know what? Maybe I could jump up. And now I've started jumping up. So I, I feel like to your point, number one, you are literally removing a barrier so that the kid can continue along learning math skills, that they have the capacity to learn, but something is in the way they shouldn't be closed off or shut down from learning those math skills. And guess what? Once they build confidence learning those math skills, maybe they'll go back to the skill that they never felt fully developed and feel confident enough to tackle it again.

Curtis Brown 35:41

A hundred percent. A hundred percent. Like that. I love your analogy, by the way. I was trying to think about it for a minute. I was trying to tie into the work bench and jumping off, jumping off of the workout bench and, and grabbing that and yeah, I think that's exactly what we're we're talking about. Or at least, pretty closely related to talking what we're talking about, like this idea of giving the students, um, it's almost like a safety net. It's a little bit of a safety net, right? Like that idea that, hey, I've got a boost over here to manage this other part, so that my brain can focus solely on developing these other reasoning skills, that we have. Now, I wanna be careful, we're not totally couching the calculator and the usage of calculators and those as a tool, as offloading cognitive load. Because I think there's also an opportunity, for using the calculator and specifically the graphing calculator for exploration and development of concepts, right? So like we, you and I have been, we've been back and forth quite a bit on this idea of how do we help students who, are a spot where they're nervous about stuff that they didn't know that we can offload to the calculator. That's one space. And I think that's, there's a lot of value in that. There's a ton of value there. But I think there's also a ton of value in being able to, utilize the technology for exploration. And I can point right back to that story I started the podcast with, with Tom Dick and his student, with the hole in the graph and the, this idea that. what the heck is going on here? Like the, the exploration piece that happened because of that visual plotting out, and it's, it, it is a beautiful piece of the way that the graphing calculator works, graphing pixel by pixel, and the fact that the function is evaluated at this exact value and then. It either plots or doesn't plot, as a result of that calculation, right? So it's like, oh, I got a, I have an indeterminate value. I guess I can't plot a point. And so it just leaves that point blank and it, and so you see visually what is actually happening mathematically in the function. There's a really nice thing there. So you get an opportunity for exploration there that you wouldn't maybe have had if you, were doing this by hand and nobody being able to, nobody explaining it to you. Right? The calculator kind of shows that, and you go, oh my gosh, my, my graph has a hole in it. What about yours? Did yours

Vanessa Vakharia 38:13

Yeah,

Curtis Brown 38:15

Right.

Vanessa Vakharia 38:15

well.

Curtis Brown 38:16

Like what's going

Vanessa Vakharia 38:17

Well, there's even more, there's even more than that. I'm, I'm really glad you brought that up, ex because I think this is a good point. There is something so tangible. I have seen, like I've seen Michelle, your amazing social media person that refuses to come on camera or on the mic, but everyone, just so you know, she's amazing, follow Texas Instruments on Instagram, they're the best. But I've seen her posting like things like experiments teachers do where, for example, they like graphed, I think they graphed like clovers for St. Pat, is that what they're called? Clovers for St. Patrick's Day or like

Curtis Brown 38:49

like a

Vanessa Vakharia 38:49

four leaf clover for St. Yes, exactly. Or like hearts for Valentine's Day. And like the kids get so excited trying to figure out exactly how do I play around with all these variables to get the heart shape on my calculator? That's the perfect example of something where you're like, okay, if you were gonna do that by hand, like, like that would just take forever. You, because you, you, you need to be able to mess around with a bunch of factors and variables, like in quick succession to be like, okay, wait. I'm gonna increase this by one. Okay, I'm gonna decrease it by one. Okay, what if I do this? What if I do that? Like, whatever. And kids get so excited because they have this tool in their hand that is visually showing them the literal output of the inputs they're putting in and how adjusting these different variables like creates different graphs. I, I mean, I don't wanna say this so assuredly, but I, I like, you kind of need the calculator for that. Like you really can't be doing that by hand. Espe like, right? Like you, you need that and it's providing an experience that they're not gonna get otherwise. And then, yeah, they're creating, they're like, well, my heart has this, oh, I created this crazy clover. Like there's that ownership piece again, there's that visual, like there is everything. And I think this actually leads to an even bigger question, which is. What is mathematics? It isn't just arithmetic. It is not just you know, these fluency and these fast facts. That is a part of it, but part of it is exploration. It's problem creation, generation, and solution. It is patterns, it is trends. It is this curiosity. It's this wonder, it's this creativity, and that is what the tool can really bring to life.

Curtis Brown 40:21

I love that you asked that question or that you even put that into that statement. That's the, the, fact that we can get to what is mathematics as a part of that conversation, that's huge. I'm going to point out my podcast partner, Joanie Funderburk, because we just, in our, podcast that we just released, I think it was two days ago. She actually talks about, that has changed for her about what is mathematics, right? And I, I don't know about your high school and, and grow going through school, experience, but I know my own and Joanie's, are are similar in that my understanding of what mathematics was, before I entered the classroom as a teacher, was that mathematics was an, an awful lot about just the procedures that we do to get right answers, right? That's what we kind of explored mathematics as, and it wasn't until I was in the classroom and utilizing technology for exploration and curiosity and teaching and understanding about mathematics that I, I developed a deeper understanding of what mathematics is, and it's all those things you listed. And the idea of reasoning, comes to mind also, like this tool gives me a place to do mathematical reasoning, and not just answer getting, right, like this idea that, that I can use the tool to explore, to ask the what if, to ask the, if I change this, this thing happens, uh, over there and I can develop that. That's huge. That's so,

Vanessa Vakharia 42:01

Ugh. I love this. Okay. I don't know how, but time has flown by and we need to, we need to get to our, LA

Why TI is so good at branding

Vanessa Vakharia 42:09

has to get to our last final questions, but before I ask you the final two questions I ask everyone, I have to let my like fangirling over TI just leak out a little. You know, I have been obsessed with Texas instruments since I was 17. I used to design my own face plates because at the time, the TI, you could remove the face plate and put different ones on there, just like the flip phone. And I wonder, and maybe you don't have an answer to this, but I'm curious, like to me, Texas Instruments has always been this like brand in the math ed space that has made math cool. And I don't wanna say it's the only brand doing that because that, but, but it definitely was the first brand to ever make math cool. To ever make like a calculator, like an accessory that like you want it to have. And I don't know, it's definitely the coolest brand in the math space. I'm sorry to everyone else listening, but it really is. Was that a conscious decision? Like, do you, like, do you know anything about that or are you like, yeah, I know we're cool and this is why, like, why is that such a core part of the TI ethos and like, I, I won't get you to talk about any other brand, but I'm curious why that choice was made and how like you feel about it or like if you're like, what are you talking about? Like, do you see what I'm seeing?

Curtis Brown 43:21

No, I see what you're seeing. And I think there's, there's potentially two answers, but, and Michelle is a, is a massive reason, uh, in all of her fantastic work. That's, that's one. Okay. Um, but I would say yes, the calculator play, okay. Yes, yes.

Vanessa Vakharia 43:36

Hugging my calculator plushie. Like who makes a calculator? Plushie guys, Texas Instruments.

Curtis Brown 43:43

that is, that's huge, right? So, okay. So there's that, I, and, and it's all the face plates and all those fun things. So those are great. But the, the real reason, and I think that the, maybe the biggest reason, is this, and I, and it's, it's the fact that, that teachers choose to use. Texas Instruments graphing calculators. and why do they choose to use them? Well, because we have spent a inordinate amount of time working with teachers, listening to math teachers, asking them, trying to draw upon their teaching expertise and what, what little thing could we help solve? What little thing could we help do? And we make intentional decisions about the features and the functionality and the things that we do and don't do for students, in our graphing experiences, in our calculation experience, in the functions and features that we offer, we make very intentional decisions about, what we can and can't do, what we will and won't provide, for a student. And I think, know, because we've listened to teachers, teachers actually chose us, teachers choosing us meant that, that every student had an experience to have us right in their, in their hands, right? So, so now students have them and just like you, other students in their, in their classrooms get an opportunity to personalize their calculator by putting a different face plate on it. They get to, have an experience with a sticker or a a, you know, something that a, that a teacher gives them that's calculator related. And, you know, the calculator part has become cool. I mean, the fact that you're sitting there holding, uh, the calculator plus you with a big old smile on your face, just makes me smile

Vanessa Vakharia 45:28

I sleep with her every night. Yeah.

Curtis Brown 45:31

No joke, like this idea that, that it, started with we listen to teachers and, and make pedagogical decisions about the things that we do, to make the tool useful for the teaching and learning of mathematics. And that kind of gave us the opportunity to be widely adopted. Because it was widely adopted, it became sort of a, A feature, right? I mean, tis been been in movies, you've seen calculators in clips,

Vanessa Vakharia 46:04

It's been in movies. Like what? What are you saying?

Curtis Brown 46:07

yes, it made a cameo in, in a, in a Spider-Man recently. So like, think about when you're trying to communicate things about a time period, the graphing calculator is a part of that time period. It's a part of, of our growing up. And it's part of high school. It's part of learning math, right? It's a thing. But it's there because the teachers made the decision and the teachers made the decision because ti listened. So I think that's, if you want to go back to why, I think that's a major reason why.

Vanessa Vakharia 46:35

Okay.

Curtis Brown 46:36

Okay.

Vanessa Vakharia 46:36

And Michelle. Okay, we'll take both answers. Um, we. Okay. Oh my God. Can't wait to see Texas Instruments on the red carpet next year. Make sure you invite me. We have to wrap up. You have 30 seconds to answer both of these questions. They're the last questions I always ask every guest. 30 seconds po. Okay.

Curtis Brown 46:52

I'll be

Vanessa Vakharia 46:52

question number.

Q1

Vanessa Vakharia 46:54

Question number one. If there's one thing you could change about the way math class is taught, what would it be? Go.

Curtis Brown 47:00

Uh, curiosity. Engagement, I want students to be able to explore. I want students to be able to ask questions why, and I want 'em to want to. so we have to do things to help students want to ask the questions why. We have to ask, we have to develop that curiosity. And where it's died, we need to have, find ways to rejuvenate it. Um, so your 45 second answer to that question.

Vanessa Vakharia 47:27

That was good. That's good enough. Okay.

Q2

Vanessa Vakharia 47:29

Final question. Someone's listening to this, they're like, cool, cool. I get it. Like, I guess a calculator could help me maybe, but honestly I'm, I've just, there's no hope for me because I'm just not a math person. What do you say?

Curtis Brown 47:42

It makes my heart hurt, first of all. I just wanna hug them. I, because everybody is a math person, we all have the ability to be math people, okay? Some of us find greater interest in mathematics, but I would argue that the majority of people who don't find great interest in mathematics haven't experienced it correctly. Like they haven't gotten a good experience, they haven't been exposed to the, to the fun. And, and it goes right back to my previous answer, which is if they haven't been given an opportunity to be curious, if they haven't been given an opportunity to engage, that's potentially the reasons why they have that,

Vanessa Vakharia 48:22

Yeah.

Curtis Brown 48:23

And so it just makes me wanna hug them.

Vanessa Vakharia 48:25

Okay. Well they probably need a ti plushy.

Benefits of a handheld tool

Vanessa Vakharia 48:29

Um, Okay. Curtis. Oh my god, this has been wild that we could talk forever, but we have to wrap up. David is giving me the wrap up eyes, but Curtis, if there's anything else you wanted to say, this is your chance to say it. So spit it out.

Curtis Brown 48:43

So I do think there's one thing that we haven't gotten a whole lot of chance to talk about, and that is this idea that, Thinking about this, this handheld calculator. So we talked about why do teachers use these things in their classrooms? Why is this here? This is another piece of the puzzle. Um, and that is the idea of focus. Have lots of tools that are out here. That exist in the world today, right? Like you mentioned the internet earlier this morning about like being a tool, and then it's the appropriate usage of that tool. Like think about for a minute, all of the things that are out there on the internet, like there's a ton, right? And so this concept of being able to use a handheld calculator a purpose-built device, a device that is for at learning and exploring mathematics. Like there's a keypad that's designed, it's all keys that are math tools and keys, right? Like, think about for a minute the focus that that gives you. When I'm using this thing, I'm using it for doing math. I'm using it for exploring mathematics. I'm not using it, and then switching to another tab really quick when my teacher isn't looking and then switching back. Like, I can't do that. This is a purpose-built device. It's my thinking space about mathematics. So like I think there's another piece to the puzzle that maybe I didn't mention earlier, which was that this idea that this is a focus driven tool, right? And that's another reason why teachers love and that's another reason why the longevity is there. Does that make

Vanessa Vakharia 50:17

Well, well, it makes so much sense. I'm actually kind of like, oh my God. Like this is like the answer to the argument of people being like, well, we have phones in our pockets. It's like, yeah, you do, but

Curtis Brown 50:30

Like, oh my gosh, we got all these other tools that we could have access to. They're out here. Everything's all over the place. Why? Why do we need this thing? And the answer to that question is I need this thing because it's my thinking space, it's my focus space. It doesn't have access to all those other things that could be distractions, right? I'm not getting notifications on my graph calculator. I'm not getting that Facebook, right? I'm not getting that friend invite just now. Oh my gosh, 10,000 people love my post, I don't get that little post. I don't get that on my graphing calculator. It doesn't come up and cover my parabola.

Vanessa Vakharia 51:09

Yeah. Oh my God. Please, like, I know you guys are cool, but Texas Instruments, please, this is my public call out to never get to the point where it's like, and as soon as you get to the vertex, like TikTok opens, like, no.

Curtis Brown 51:25

No, exactly. We can't do that. We choose not to do that.

Vanessa Vakharia 51:31

Perfect. And

Outro

Vanessa Vakharia 51:33

now we're gonna say goodbye and there's a little someone special who would like to say bye to you today, Curtis.

Curtis Brown 51:39

Ah, bye-bye. Calculator buddy.

Vanessa Vakharia 51:42

Oh yeah. Sorry guys. This is my calculator plushie, who I've named Calcie. I was given her at NCTM two years ago, and

Curtis Brown 51:51

Hold

Vanessa Vakharia 51:51

Sorry. You're gonna take it back. Michelle gave me one actually.

Curtis Brown 51:55

No, I don't have one. I didn't get

Vanessa Vakharia 51:59

Oh.

Curtis Brown 51:59

What? Michelle? For real.

Vanessa Vakharia 52:03

And that concludes our interview today.

Curtis Brown 52:05

Even.

Vanessa Vakharia 52:06

Goodbye. Shut it down. Shut it down. Whew. Okay. If this episode made you think differently about calculators, even a little tiny bit, I want you to send it to someone who needs to hear it. Someone who needs to have their view challenged, and maybe someone who you want to have a discussion with, and this might be the thing that opens the door. By the way, we're taking a quick break next week, so this is the perfect episode to share while we're off, and actually now that I'm thinking about it while we're off, if you need something to listen to next week, you could throw on a episode of Curtis's Podcast Room to Grow. And if you have thoughts, reactions, or strong opinions, which I'm sure you do on this topic, text me through the link in your podcast app. You can also DM me on Instagram at the Math Guru or email me at vanessa@themathguru.ca. That was a wild ride, but honestly, I know I'm thinking a lot differently now, and I'm really curious how your mind has changed or maybe hasn't changed at all. Maybe you've doubled down on something you already thought. So get in touch and I will see you not next week, but the week after that. And until then, I'm sending you all the peace, love, and pi