Latest / Math Therapy / This will change the way you think about calculators w/ Curtis Brown

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This will change the way you think about calculators w/ Curtis Brown · Math Therapy

• 0:03
  Curtis Brown: I want students to be able to explore.
• 0:05
  Curtis Brown: I want students to be able to ask questions why, and I want'em to want to.
• 0:09
  Curtis Brown: we have to develop that curiosity.
• 0:11
  Curtis Brown: And where it's died, we need to find ways to rejuvenate it.
• 0:16
  Curtis Brown: 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.
• 0:33
  Vanessa Vakharia: Okay.
• 0:33
  Vanessa Vakharia: Hello.
• 0:34
  Vanessa Vakharia: Hi.
• 0:34
  Vanessa Vakharia: It's me, Vanessa, and welcome to your weekly hit of Math Therapy.
• 0:38
  Vanessa Vakharia: I need to start with a question that I know is gonna get some of you fired up immediately.
• 0:43
  Vanessa Vakharia: Are calculators actually making kids worse at math?
• 0:47
  Vanessa Vakharia: 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.
• 0:54
  Vanessa Vakharia: Because on one hand we have these incredibly powerful tools that can support thinking, reduce cognitive overload, and like open up access.
• 1:03
  Vanessa Vakharia: 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.
• 1:15
  Vanessa Vakharia: Are we even asking the right question.
• 1:18
  Vanessa Vakharia: 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.
• 1:28
  Vanessa Vakharia: The confidence, anxiety, identity, and whether or not the tools we're using are helping or hurting all of that.
• 1:35
  Vanessa Vakharia: 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.
• 1:43
  Vanessa Vakharia: You know what I'm talking about, that TI 81, 82, 83, 84.
• 1:47
  Vanessa Vakharia: You had one.
• 1:48
  Vanessa Vakharia: You might not have owned one, but you punched buttons into one.
• 1:50
  Vanessa Vakharia: Curtis is literally helping shape the tools that students are using every single day.
• 1:55
  Vanessa Vakharia: He also co-hosts the podcast Room to Grow, which you absolutely need to check out.
• 1:59
  Vanessa Vakharia: And he spends a ton of time working directly with educators, thinking about how we design math experiences that actually support learning.
• 2:06
  Vanessa Vakharia: And that is exactly what we're getting into today.
• 2:09
  Vanessa Vakharia: What role should calculators play in math class?
• 2:11
  Vanessa Vakharia: When do they support thinking, and when might they actually get in the way?
• 2:15
  Vanessa Vakharia: And how do we use them in a way that builds confidence instead of dependency?
• 2:19
  Vanessa Vakharia: 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.
• 2:31
  Vanessa Vakharia: Actually, you should probably block them right now.
• 2:33
  Vanessa Vakharia: Anyways, think of that person.
• 2:35
  Vanessa Vakharia: 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.
• 2:46
  Vanessa Vakharia: 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.
• 2:57
  Vanessa Vakharia: Let's get into it.
• 3:00
  Vanessa Vakharia: Curtis.
• 3:02
  Vanessa Vakharia: My dear pal from Texas Instruments.
• 3:05
  Vanessa Vakharia: Welcome to the podcast.
• 3:07
  Curtis Brown: Well, thank you.
• 3:08
  Curtis Brown: I'm super excited to be here.
• 3:10
  Vanessa Vakharia: I mean, we've had a series of very odd interactions up until this point, wouldn't you say?
• 3:16
  Curtis Brown: I would say we've had some odd interactions, some chance meetings at conferences.
• 3:21
  Curtis Brown: Uh, I didn't know you were gonna be here, what are you talking about?
• 3:25
  Curtis Brown: Coffee bar at 5:30 AM at Wisconsin Math Conference.
• 3:28
  Curtis Brown: You remember you came in and I was grinding my, coffee beans.
• 3:32
  Curtis Brown: The, um, getting ready to make my aeropress.
• 3:35
  Vanessa Vakharia: 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.
• 3:46
  Vanessa Vakharia: And actually, see it's funny that that's your core memory of our meeting.
• 3:48
  Vanessa Vakharia: '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.
• 4:02
  Vanessa Vakharia: And I was like, when I get famous enough, that's what I want.
• 4:04
  Vanessa Vakharia: And I think you said you were gonna make it happen.
• 4:07
  Curtis Brown: I mean, listen, I promise all kinds of things from time to time.
• 4:13
  Vanessa Vakharia: Okay.
• 4:14
  Vanessa Vakharia: 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.
• 4:21
  Vanessa Vakharia: One of them being that I am the biggest Texas Instruments fan, but I'm gonna save that gushing for later.
• 4:27
  Vanessa Vakharia: But I've, I really love the brand.
• 4:29
  Vanessa Vakharia: I love everything you guys do.
• 4:31
  Vanessa Vakharia: 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.
• 4:44
  Vanessa Vakharia: But they continue to be like this hot button topic in math education.
• 4:48
  Vanessa Vakharia: And now I have like the calculator guy.
• 4:53
  Curtis Brown: The calculator guy.
• 4:54
  Curtis Brown: Yeah.
• 4:55
  Curtis Brown: I mean, calculators have, they've been around for, so for quite a while.
• 4:59
  Curtis Brown: 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.
• 5:14
  Curtis Brown: And then you think about mechanical calculators that were even before that.
• 5:17
  Curtis Brown: I'm talking about digital
• 5:19
  Vanessa Vakharia: what's a mechanical calculator?
• 5:21
  Curtis Brown: Well, think about an abacus.
• 5:22
  Vanessa Vakharia: Ah.,
• 5:23
  Curtis Brown: But then this idea of the graphing calculator and the introduction of that was, early nineties, late eighties, early nineties.
• 5:31
  Curtis Brown: And that fundamentally changed the way we teach and learn mathematics, and I think that has real staying power,
• 5:38
  Vanessa Vakharia: okay.
• 5:38
  Vanessa Vakharia: 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.
• 5:50
  Vanessa Vakharia: You're saying digital calculators were created in the sixties or seventies and the graphing calculator was all the way back in the nineties.
• 5:59
  Vanessa Vakharia: You're right.
• 6:00
  Vanessa Vakharia: I had one.
• 6:01
  Curtis Brown: Yes, yes,
• 6:02
  Vanessa Vakharia: Oh my God.
• 6:03
  Curtis Brown: did we've had them for a while, like a really long time.
• 6:08
  Vanessa Vakharia: 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.
• 6:20
  Vanessa Vakharia: Because as you are probably very well versed in, people love to say that calculators are making kids worse at math, right?
• 6:29
  Vanessa Vakharia: People are like, calculators are the reason why kids don't know their math facts.
• 6:32
  Vanessa Vakharia: Like, la la la, la, la.
• 6:33
  Vanessa Vakharia: But hold on a second.
• 6:35
  Vanessa Vakharia: If they've existed for this long, how are we still, how are we saying that now?
• 6:40
  Vanessa Vakharia: Like, you know what I'm saying?
• 6:41
  Vanessa Vakharia: Like, let me just ask you, do calculators make kids worse at math?
• 6:46
  Curtis Brown: No.
• 6:47
  Curtis Brown: Mean, blanket statement, calculators, no, they don't.
• 6:51
  Curtis Brown: 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.
• 6:59
  Curtis Brown: This is a statement I would make any time, anywhere.
• 7:02
  Curtis Brown: Because calculator, if you think about calculators themselves, are a tool.
• 7:06
  Curtis Brown: A tool.
• 7:07
  Curtis Brown: 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?
• 7:17
  Curtis Brown: 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.
• 7:26
  Curtis Brown: 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.
• 7:35
  Curtis Brown: Or the opposite of that.
• 7:37
  Curtis Brown: Like that could really get them engaged in mathematics.
• 7:40
  Curtis Brown: And so I think it's more about the execution of the tool.
• 7:44
  Curtis Brown: That, that's really what I'm thinking about whenever you ask that question, are calculators making kids bad at math?
• 7:50
  Curtis Brown: No, they're not.
• 7:52
  Curtis Brown: 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.
• 8:02
  Vanessa Vakharia: Well, it's so funny'cause as you're saying that 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?
• 8:10
  Vanessa Vakharia: Like it's like, is the internet doing like all sorts of bad things?
• 8:14
  Vanessa Vakharia: 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?
• 8:24
  Vanessa Vakharia: Like there are obviously like bad things you can do with the internet, right?
• 8:27
  Vanessa Vakharia: Like, it's like anything.
• 8:28
  Vanessa Vakharia: It's like the, the inanimate object itself is neither good or bad in a way.
• 8:33
  Vanessa Vakharia: 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.
• 8:51
  Vanessa Vakharia: And this is a podcast about Math Therapy.
• 8:53
  Vanessa Vakharia: It's about math trauma, and so many anxiety around math.
• 8:56
  Vanessa Vakharia: So I'd like to actually hear from you.
• 8:58
  Vanessa Vakharia: Tell us when a calculator can be used.
• 9:01
  Vanessa Vakharia: 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?
• 9:06
  Vanessa Vakharia: Like when is it appropriate to use a calculator and when is it not?
• 9:09
  Vanessa Vakharia: When are we using the tool for good and when are we using it in a way that detracts, like give us some examples.
• 9:15
  Curtis Brown: I'll, I'll give you an example.
• 9:16
  Curtis Brown: Here's a high school example.
• 9:17
  Curtis Brown: So background, first of all, I taught high school mathematics, right?
• 9:21
  Curtis Brown: So
• 9:21
  Vanessa Vakharia: Yep.
• 9:22
  Curtis Brown: 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.
• 9:32
  Curtis Brown: So maybe I'll, I'll get to that in a second.
• 9:34
  Curtis Brown: But I want to start with an example of using a calculator and specifically a graphing calculator.
• 9:42
  Curtis Brown: That maybe changes the way a student interacts with mathematics.
• 9:45
  Curtis Brown: I have a good friend of mine.
• 9:46
  Curtis Brown: his name is, Tom Dick.
• 9:48
  Curtis Brown: He works at, Oregon State University.
• 9:50
  Curtis Brown: You might know Tom, from other conferences and things.
• 9:52
  Curtis Brown: And Tom, told me, relayed me a story, for the first time that he ever used graphing calculators, with his students.
• 9:59
  Curtis Brown: His students were graphing a rational function.
• 10:01
  Curtis Brown: pick your favorite rational function that happens to have a, a hole in it.
• 10:04
  Curtis Brown: and he, had his students graph that function.
• 10:08
  Curtis Brown: 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.
• 10:16
  Curtis Brown: Right?
• 10:17
  Curtis Brown: students were more or less, engaged, but maybe not engaged.
• 10:21
  Curtis Brown: But this time.
• 10:23
  Curtis Brown: Using the graphing calculator, student happened to graph one such that, the hole actually appeared visually on the screen.
• 10:32
  Vanessa Vakharia: Hmm.
• 10:34
  Curtis Brown: so this student, as Tom was walking through the classroom, over to his buddy and said, my graph has a hole in it.
• 10:43
  Curtis Brown: does your graph have a hole in it?
• 10:46
  Curtis Brown: There's really important word there.
• 10:48
  Curtis Brown: My graph.
• 10:49
  Curtis Brown: Your graph, there's
• 10:51
  Vanessa Vakharia: Huh.
• 10:51
  Curtis Brown: that happened because these students created a picture on a graphing calculator.
• 10:57
  Curtis Brown: Okay.
• 10:58
  Curtis Brown: saw that picture and now there was an ownership that happened.
• 11:03
  Curtis Brown: That word never left their mouths beforehand.
• 11:06
  Curtis Brown: And I think there's something really, really important about students owning mathematics.
• 11:12
  Curtis Brown: I know we hear research and we hear talks.
• 11:14
  Curtis Brown: We go to trade shows and, and conferences and hear the, the teachers and the.
• 11:19
  Curtis Brown: Professors and the researchers talking about students owning mathematics.
• 11:24
  Curtis Brown: That ability to see something in my hand that I've interacted, that I've created, and now that math is mine, huge.
• 11:33
  Curtis Brown: That learning is huge.
• 11:34
  Curtis Brown: So using a graphing calculator, using a calculator in a way that allows me to explore mathematics, that gives me ownership.
• 11:43
  Curtis Brown: I think that fundamentally changes the way that I learn.
• 11:47
  Curtis Brown: And I think about the math.
• 11:48
  Curtis Brown: I own it now, right?
• 11:50
  Curtis Brown: So I can also draw, connections to things like same graph.
• 11:56
  Curtis Brown: 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?
• 12:02
  Curtis Brown: I'm plotting points, I'm making tables, I'm making, and don't get me wrong, there's value in doing that.
• 12:08
  Curtis Brown: I think there's value in taking the time to do those things by hand.
• 12:11
  Curtis Brown: 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.
• 12:23
  Curtis Brown: So there's some really nice pieces to the puzzle.
• 12:26
  Vanessa Vakharia: 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.
• 12:32
  Vanessa Vakharia: Like I was picturing that moment of like a student being like, why is there a hole in my graph?
• 12:37
  Vanessa Vakharia: Like, and I, like, I, I could feel that with you, that excitement.
• 12:41
  Vanessa Vakharia: And there's 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.
• 12:50
  Vanessa Vakharia: I think we have heard a lot, but.
• 12:53
  Vanessa Vakharia: Seldom elaborated on.
• 12:55
  Vanessa Vakharia: So I think we all think we mean the same thing when we're talking about students owning math.
• 12:58
  Vanessa Vakharia: 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.
• 13:17
  Vanessa Vakharia: It didn't happen to me.
• 13:18
  Vanessa Vakharia: You know, like, Yeah, I think that's a really cool point.
• 13:22
  Vanessa Vakharia: 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.
• 13:28
  Vanessa Vakharia: We weren't using the graphing calculators back then to graph in this way.
• 13:33
  Vanessa Vakharia: 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.
• 13:40
  Vanessa Vakharia: And I think this is such a good point that like.
• 13:43
  Vanessa Vakharia: What I'm hearing you say is there's two skill sets.
• 13:44
  Vanessa Vakharia: Like there's the skill of being able to plot the points and graph that is skillset number one.
• 13:49
  Vanessa Vakharia: And then there's a whole other set of skills, which is recognizing patterns, right?
• 13:55
  Vanessa Vakharia: Like recognizing patterns, doing something iteratively to be like, if I change this factor, what happens to this?
• 14:02
  Vanessa Vakharia: And that is just more efficiently done with the use of a tool.
• 14:06
  Curtis Brown: Absolutely.
• 14:06
  Curtis Brown: It's more efficiently done.
• 14:08
  Curtis Brown: There's also another, another piece to that.
• 14:12
  Curtis Brown: 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?
• 14:26
  Curtis Brown: Like if, if, if I'm having to do everything by hand, I can't say, well, what happens if I change this?
• 14:33
  Curtis Brown: What happens if I do this?
• 14:36
  Curtis Brown: What happens if, those questions are a lot more difficult to answer when I'm doing a whole bunch of hand calculation and manipulation?
• 14:43
  Curtis Brown: Right?
• 14:44
  Curtis Brown: 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?
• 14:54
  Curtis Brown: Does that make sense?
• 14:55
  Curtis Brown: What I'm, what I'm driving at?
• 14:57
  Vanessa Vakharia: No, it makes total sense.
• 14:58
  Vanessa Vakharia: But what I'm thinking is I'm like, well, obviously like at, I'm actually like, so what has changed?
• 15:03
  Vanessa Vakharia: '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.
• 15:14
  Vanessa Vakharia: Number two puts the emphasis on exploration and discovery instead of answer getting, so cool.
• 15:20
  Vanessa Vakharia: But what I'm thinking is obviously before calculators, like people did that, right?
• 15:24
  Vanessa Vakharia: Like I, I'm kind of like, what were they doing in math classes before calculators?
• 15:28
  Vanessa Vakharia: Like how did they have time to do this?
• 15:29
  Vanessa Vakharia: What were they doing?
• 15:30
  Vanessa Vakharia: Do you know?
• 15:31
  Vanessa Vakharia: Like, not that you were alive, but like too many.
• 15:33
  Curtis Brown: Yeah, I was alive before calculators.
• 15:36
  Curtis Brown: I mean, there is a little bit of gray hair up here.
• 15:39
  Curtis Brown: So I was alive before the graphing calculator was in, in classrooms.
• 15:43
  Curtis Brown: 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.
• 15:53
  Curtis Brown: going through high schools was TI 82.
• 15:55
  Curtis Brown: So, yeah.
• 15:56
  Curtis Brown: 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.
• 16:05
  Curtis Brown: I wasn't in the classroom, doing that before graphing calculators.
• 16:09
  Curtis Brown: 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?
• 16:24
  Curtis Brown: 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.
• 16:42
  Curtis Brown: I think there was still curiosity, but it was probably for a far fewer number of people, and I think
• 16:52
  Vanessa Vakharia: Um.
• 16:52
  Curtis Brown: 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.
• 17:04
  Curtis Brown: Like this is part of my exploration, this is my identity too.
• 17:09
  Curtis Brown: Right?
• 17:09
  Curtis Brown: I mean, there's only a few Isaac Newtons out there before, right.
• 17:12
  Curtis Brown: Like was one
• 17:14
  Vanessa Vakharia: Yeah.
• 17:16
  Curtis Brown: think about that for a minute.
• 17:17
  Curtis Brown: 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.
• 17:27
  Curtis Brown: things.
• 17:28
  Vanessa Vakharia: I think it's so cool because in a way, like we're talking about accessibility, right?
• 17:32
  Vanessa Vakharia: Like, it's like this idea of giving more people access to that type of thinking because they have this tool.
• 17:38
  Vanessa Vakharia: And so I'm like, and I'm thinking too, like you brought up the abacus, you know, we've always had.
• 17:43
  Vanessa Vakharia: Well, maybe we haven't always, but there's been many, many decades of tools progressively being introduced into a math classroom.
• 17:52
  Vanessa Vakharia: Right.
• 17:52
  Vanessa Vakharia: 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.
• 18:08
  Vanessa Vakharia: Like they're the reason kids are, you know, our mask scores are low.
• 18:11
  Vanessa Vakharia: Why are people so obsessed with calculators?
• 18:14
  Curtis Brown: Okay, so that's an interesting question.
• 18:16
  Curtis Brown: Like thinking about, why then?
• 18:19
  Curtis Brown: Are calculators kind of still getting this, this question around them, right?
• 18:24
  Curtis Brown: Like, are, are they actually causing problems?
• 18:26
  Curtis Brown: So think about, I talked about earlier, the use of the tool, right?
• 18:32
  Curtis Brown: Like, you wouldn't wanna build a house without a hammer.
• 18:34
  Curtis Brown: You wouldn't wanna be, you wouldn't want to do those kind of like, there's, there's tools for jobs, right?
• 18:39
  Curtis Brown: But even in the building of the house, misuse of the hammer could result in, in challenges or problems or issues, right?
• 18:46
  Curtis Brown: So overdependence is the same thing here.
• 18:49
  Curtis Brown: My eighth grader taking algebra.
• 18:52
  Curtis Brown: and he and I get to lots of tutoring time together.
• 18:56
  Curtis Brown: this is a thing we do, on a nightly basis, which is great.
• 18:59
  Curtis Brown: I love it.
• 19:00
  Curtis Brown: I love the extra time and, and like my shirt says, math is my happy place.
• 19:03
  Curtis Brown: So we're good.
• 19:04
  Curtis Brown: Like, I enjoy that.
• 19:06
  Curtis Brown: Uh, all the, uh, I, I enjoy that.
• 19:08
  Curtis Brown: See, it's, I mean, it says, so math is my happy place,
• 19:11
  Vanessa Vakharia: 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.
• 19:20
  Curtis Brown: There yet, um, you con confirm.
• 19:22
  Curtis Brown: Yeah, you could confirm that.
• 19:23
  Curtis Brown: I'm glad so, no, but thinking about overdependence though, on a tool.
• 19:29
  Curtis Brown: All right.
• 19:30
  Curtis Brown: So.
• 19:30
  Vanessa Vakharia: Mm-hmm.
• 19:31
  Curtis Brown: 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.
• 19:41
  Curtis Brown: He's been doing this for quite a while that my fourth grader has not yet developed.
• 19:47
  Curtis Brown: So my fourth grader brilliant in mathematics.
• 19:50
  Curtis Brown: He's, he's snappy.
• 19:52
  Curtis Brown: I mean, his reasoning about math is ridiculous.
• 19:55
  Curtis Brown: But his memorization, his numeracy, his, his ability to recall facts fluently really, really fast, he's still growing.
• 20:04
  Curtis Brown: So he reasons about math really well.
• 20:06
  Curtis Brown: Okay, if I gave him, a calculator, let's say that I gave him a four function calculator
• 20:13
  Vanessa Vakharia: Can you, sorry.
• 20:14
  Vanessa Vakharia: Can you define a four function calculator?
• 20:17
  Curtis Brown: So add, subtract, multiply, divide.
• 20:20
  Vanessa Vakharia: Got it, because that's what I thought, but I just wanted to confirm.
• 20:21
  Vanessa Vakharia: Okay.
• 20:22
  Curtis Brown: Yeah.
• 20:22
  Curtis Brown: No, that's fair.
• 20:23
  Curtis Brown: 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.
• 20:30
  Curtis Brown: And I say, you can use it if you need to answer these questions.
• 20:35
  Curtis Brown: In a relatively short period of time.
• 20:37
  Curtis Brown: He's going to become pretty dependent on just.
• 20:41
  Curtis Brown: Because it's easy
• 20:42
  Vanessa Vakharia: Hmm.
• 20:43
  Curtis Brown: and it's whatever.
• 20:43
  Curtis Brown: So I,'cause I haven't given him any bound rail, boundaries.
• 20:46
  Curtis Brown: I haven't given him any guardrails as to how to use the calculator.
• 20:49
  Curtis Brown: As to how to use the calculator help him develop number sense.
• 20:52
  Curtis Brown: Right.
• 20:53
  Curtis Brown: Okay.
• 20:54
  Curtis Brown: Take that same scenario and I put it with my eighth grader who's now maybe, developed that number sense.
• 21:00
  Curtis Brown: 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.
• 21:10
  Curtis Brown: 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?
• 21:21
  Curtis Brown: What are the patterns and the things that you need?
• 21:23
  Curtis Brown: 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?
• 21:40
  Curtis Brown: It, it speeds along the things that maybe his brain doesn't need to be thinking about.
• 21:44
  Curtis Brown: It frees up cognitive load, for him to be able to, Access the math that we were really caring about.
• 21:50
  Curtis Brown: Does that make sense?
• 21:51
  Curtis Brown: Like I'm driving towards this appropriate use
• 21:55
  Vanessa Vakharia: Yeah.
• 21:55
  Vanessa Vakharia: 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.
• 22:02
  Vanessa Vakharia: But just for some of us who don't exactly know what that is, like tell us what cognitive load is and how calculators can help.
• 22:08
  Curtis Brown: 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.
• 22:19
  Curtis Brown: But that's, that's less, of us have that ability.
• 22:23
  Curtis Brown: Right?
• 22:23
  Curtis Brown: Like, not
• 22:25
  Vanessa Vakharia: all have a.
• 22:26
  Curtis Brown: 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?
• 22:33
  Curtis Brown: Like the, this working memory that I'm able to kind of pull from and draw from really quickly.
• 22:37
  Curtis Brown: 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.
• 22:54
  Curtis Brown: The, the, what are the zeroes of this quadratic represent?
• 22:58
  Curtis Brown: How do I even factor this quadratic to come up with the zeroes and why, why is zero so important?
• 23:04
  Curtis Brown: Like, does that even help me with anything?
• 23:05
  Curtis Brown: Oh, zero product, property.
• 23:07
  Curtis Brown: What was that about?
• 23:08
  Curtis Brown: 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.
• 23:19
  Curtis Brown: If I can offload that part to a calculator, then I can think about, oh, the zeros actually represent something.
• 23:27
  Curtis Brown: It's useful for me to find zeros because now I can, I can think about zero product properties.
• 23:32
  Curtis Brown: I can think about where this thing's gonna intersect axis.
• 23:35
  Curtis Brown: I can think about meaning behind the intersections of that aax axis as it applies to some projectile motion problem.
• 23:42
  Curtis Brown: Totally tried to make that up on the fly right there.
• 23:45
  Curtis Brown: But, like, does that make sense?
• 23:47
  Vanessa Vakharia: It may.
• 23:48
  Vanessa Vakharia: So let me, let me rephrase and tell me if you think that, or if this is what you mean.
• 23:53
  Vanessa Vakharia: I'm thinking about?
• 23:53
  Vanessa Vakharia: 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.
• 24:00
  Vanessa Vakharia: It was, you know, whatever it was.
• 24:01
  Vanessa Vakharia: 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.
• 24:13
  Vanessa Vakharia: They were secondary to the lesson that was being taught or the, or the knowledge that was being assessed.
• 24:20
  Vanessa Vakharia: 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.
• 24:26
  Vanessa Vakharia: So example if we're doing like six plus four, right?
• 24:30
  Vanessa Vakharia: And the goal is, is we, we wanna see the student get the answer to six plus four.
• 24:35
  Vanessa Vakharia: We wanna see what they're thinking, how they do it.
• 24:36
  Vanessa Vakharia: A calculator should not be used for that because the objective is them doing the calculating themselves.
• 24:42
  Vanessa Vakharia: But if the question is I don't know.
• 24:44
  Vanessa Vakharia: I now, I am not gonna be able to make up something on the fly.
• 24:47
  Vanessa Vakharia: 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.
• 24:59
  Vanessa Vakharia: I'm, I think this is gonna work, right?
• 25:01
  Vanessa Vakharia: 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.
• 25:07
  Vanessa Vakharia: Your job is to come up with this scenario.
• 25:09
  Vanessa Vakharia: Then I'd be like, go ahead, ask, go, go to your calculator.
• 25:13
  Vanessa Vakharia: See that six plus four is 10.
• 25:14
  Vanessa Vakharia: I know this is, I know that elementary teachers are like, what is wrong with you?
• 25:17
  Vanessa Vakharia: We do not want students to ever go on a calculator for six.
• 25:19
  Vanessa Vakharia: Plus four.
• 25:20
  Vanessa Vakharia: But I'm illustrating a point.
• 25:21
  Vanessa Vakharia: I'm illustrating a point.
• 25:22
  Vanessa Vakharia: So the point is I'd be like, fine, whatever.
• 25:24
  Vanessa Vakharia: 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.
• 25:31
  Vanessa Vakharia: Am I, am I on the track here?
• 25:33
  Curtis Brown: No, that's exactly, that's exactly what I'm thinking about.
• 25:36
  Curtis Brown: That even, well that example might be one that's like that.
• 25:40
  Curtis Brown: I mean, the elementary teacher's
• 25:41
  Vanessa Vakharia: Sorry.
• 25:41
  Vanessa Vakharia: Yeah, I'm That was, that was a lot.
• 25:43
  Vanessa Vakharia: 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.
• 25:48
  Vanessa Vakharia: We need to bring it down a notch here.
• 25:49
  Vanessa Vakharia: Then maybe I went down, I overcorrected too far.
• 25:53
  Vanessa Vakharia: 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.
• 26:06
  Vanessa Vakharia: You do it.
• 26:07
  Vanessa Vakharia: The listeners can do it.
• 26:08
  Vanessa Vakharia: Curtis, we've, we've done enough work here.
• 26:09
  Vanessa Vakharia: We've done enough today.
• 26:11
  Curtis Brown: Love that.
• 26:12
  Curtis Brown: I was just gonna tell you, you could add in sales tax and all of a sudden now the calculator really becomes useful.
• 26:18
  Curtis Brown: All right, so the$6 item and the$4 item, and then you add in, you add in sales tax, now
• 26:25
  Vanessa Vakharia: But shouldn't we be calculating the sales tax ourselves
• 26:28
  Curtis Brown: no,
• 26:29
  Vanessa Vakharia: the calculator
• 26:29
  Curtis Brown: be going around doing eight and a half percent or eight and a quarter percent on my, in my head.
• 26:35
  Curtis Brown: Like I need, I, I, I can estimate it.
• 26:38
  Curtis Brown: Which I
• 26:38
  Vanessa Vakharia: Sure.
• 26:39
  Curtis Brown: the reasoning we want students to be able to develop.
• 26:41
  Curtis Brown: Right.
• 26:42
  Curtis Brown: But that's all
• 26:44
  Vanessa Vakharia: How would you estimate that?
• 26:45
  Vanessa Vakharia: I'm just now curious.
• 26:46
  Vanessa Vakharia: Would you do 10?
• 26:47
  Vanessa Vakharia: Would you just go to a 10?
• 26:49
  Curtis Brown: a hundred percent.
• 26:50
  Curtis Brown: Start with ten
• 26:50
  Vanessa Vakharia: Okay.
• 26:51
  Curtis Brown: I know it'll be a little bit less than 10%.
• 26:53
  Curtis Brown: Right.
• 26:54
  Vanessa Vakharia: Also, I'm sorry.
• 26:56
  Curtis Brown: develop a little, logic around that.
• 26:58
  Vanessa Vakharia: That makes sense.
• 26:59
  Vanessa Vakharia: Are you are, your sales tax is only 8%?
• 27:03
  Curtis Brown: Eight and a quarter, I think in Texas.
• 27:05
  Curtis Brown: Yeah.
• 27:06
  Vanessa Vakharia: Well, in Toronto it's 13%.
• 27:08
  Vanessa Vakharia: Okay.
• 27:09
  Vanessa Vakharia: 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.
• 27:18
  Vanessa Vakharia: Okay.
• 27:18
  Vanessa Vakharia: No one needs to hear about this, guys.
• 27:19
  Vanessa Vakharia: I'm sorry.
• 27:20
  Vanessa Vakharia: Delete this, please.
• 27:20
  Vanessa Vakharia: Okay.
• 27:21
  Curtis Brown: though.
• 27:21
  Curtis Brown: That's it.
• 27:22
  Curtis Brown: that's the reasoning we want students to develop.
• 27:24
  Curtis Brown: Sorry, you just, you just did some real math reasoning right there, right?
• 27:28
  Curtis Brown: That like that's the stuff that we think about right.
• 27:32
  Curtis Brown: Now, would you have developed that on your own without having seen it and done it a few times?
• 27:37
  Curtis Brown: Hey, listen, the calculator gives you opportunity to develop that pattern that, hey, this, like, I can see this quickly.
• 27:44
  Curtis Brown: That reasoning you just did, that was it.
• 27:48
  Vanessa Vakharia: Thank you so much.
• 27:49
  Vanessa Vakharia: You're so good at affirming, like, wow, I feel really good right now.
• 27:53
  Vanessa Vakharia: This is the thing is, I think this all really goes back to it's how you use the tool.
• 27:57
  Vanessa Vakharia: Because when you were talking about your kid and you were like, well.
• 28:01
  Vanessa Vakharia: If I was like, here's a four function calculator.
• 28:02
  Vanessa Vakharia: If you want, you could use this.
• 28:04
  Vanessa Vakharia: This is exactly what is happening to me with ai.
• 28:07
  Vanessa Vakharia: 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.
• 28:15
  Vanessa Vakharia: And I've started doing it so much because I can, and it's right there.
• 28:18
  Vanessa Vakharia: And I will tell you I am abusing the tool.
• 28:21
  Vanessa Vakharia: Like it's like I, I'm because.
• 28:24
  Vanessa Vakharia: I am, and I need a therapist for this because it's actually making me dumber.
• 28:28
  Vanessa Vakharia: 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.
• 28:42
  Vanessa Vakharia: It's making me dumber.
• 28:43
  Vanessa Vakharia: 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?
• 28:50
  Vanessa Vakharia: Like.
• 28:51
  Vanessa Vakharia: And a calculator.
• 28:51
  Vanessa Vakharia: I remember my high school math teacher who I love, and she is just like the smartest person on planet earth.
• 28:57
  Vanessa Vakharia: 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.
• 29:09
  Vanessa Vakharia: 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.
• 29:23
  Vanessa Vakharia: It's a student's grade.
• 29:24
  Vanessa Vakharia: I've gotta pump out 30 in a row.
• 29:25
  Vanessa Vakharia: Like I basically have to do data entry.
• 29:27
  Vanessa Vakharia: Like I'm just gonna use the calculator so that I don't mess something up.
• 29:31
  Vanessa Vakharia: And that's fair.
• 29:32
  Vanessa Vakharia: Right.
• 29:33
  Curtis Brown: Yeah, that's, that's exactly Your teacher was doing exactly I'm thinking of.
• 29:40
  Curtis Brown: Right?
• 29:40
  Curtis Brown: Whenever it's an appropriate use of the calculator, even to do something really quick and fast like that.
• 29:46
  Curtis Brown: Right?
• 29:47
  Curtis Brown: 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.
• 29:54
  Curtis Brown: Of course she could do that arithmetic in her head.
• 29:57
  Curtis Brown: 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.
• 30:20
  Curtis Brown: But often we get into a scenario where it is useful to use that tool to do the thing faster.
• 30:28
  Vanessa Vakharia: Well, you know what?
• 30:29
  Vanessa Vakharia: You're making me realize also, I'm talking about an adult.
• 30:33
  Vanessa Vakharia: Who has already developed the skill and she's saying to herself, okay, I've already learned how to do it.
• 30:38
  Vanessa Vakharia: Yes, I can do the arithmetic in my head.
• 30:40
  Vanessa Vakharia: In this scenario, I'm gonna choose this tool.
• 30:43
  Vanessa Vakharia: 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,
• 30:53
  Curtis Brown: Yes.
• 30:53
  Vanessa Vakharia: But I also, but I also think it's the same because it's like, sure.
• 30:58
  Vanessa Vakharia: If you don't use it, you lose it.
• 30:59
  Vanessa Vakharia: 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.
• 31:07
  Vanessa Vakharia: 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.
• 31:17
  Curtis Brown: Right, the, the,
• 31:19
  Vanessa Vakharia: Right.
• 31:20
  Curtis Brown: I think we have to be careful about that.
• 31:22
  Curtis Brown: Right.
• 31:23
  Curtis Brown: We, we should be careful because yeah.
• 31:25
  Curtis Brown: 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.
• 31:32
  Curtis Brown: And hey, students should be able to do that arithmetic part in their head or whatever.
• 31:36
  Curtis Brown: And, and the answer is okay.
• 31:37
  Curtis Brown: Sure.
• 31:38
  Curtis Brown: Yeah, they probably should.
• 31:39
  Curtis Brown: In fact, they should be able to do those things.
• 31:41
  Curtis Brown: But I'll even open up the door a little bit further since we're still on this arithmetic thing for just a
• 31:46
  Vanessa Vakharia: Yeah.
• 31:46
  Curtis Brown: Like, think about it for a second.
• 31:48
  Curtis Brown: 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.
• 32:03
  Curtis Brown: Okay.
• 32:04
  Curtis Brown: Hypothetically speaking, let's say that my eighth grader was struggling with the arithmetic part.
• 32:11
  Vanessa Vakharia: Yep.
• 32:12
  Curtis Brown: I do want to develop those in him.
• 32:14
  Curtis Brown: I do want to have time for him to, to develop that.
• 32:17
  Curtis Brown: however, should that be a barrier to him, beginning to try to develop those other algebraic ideas.
• 32:24
  Curtis Brown: 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.
• 32:34
  Curtis Brown: And my question to you would be, should he be given a tool that gives him access, to those algebraic concepts?
• 32:42
  Curtis Brown: Taking, maybe getting that arithmetic piece off the table for a second.
• 32:46
  Curtis Brown: 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?
• 32:56
  Curtis Brown: Like,
• 32:57
  Vanessa Vakharia: A good point.
• 32:58
  Curtis Brown: And your podcast is Math Therapy, right?
• 33:01
  Curtis Brown: Like, think about what that does for a student who is, anxious about their mathematics.
• 33:07
  Curtis Brown: 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.
• 33:16
  Curtis Brown: And yes, high school math teachers, I, I get it.
• 33:19
  Curtis Brown: 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.
• 33:25
  Curtis Brown: I get it.
• 33:26
  Curtis Brown: 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.
• 33:40
  Vanessa Vakharia: 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.
• 33:50
  Vanessa Vakharia: This reminds me of, like, putting training wheels on a bike.
• 33:56
  Curtis Brown: For sure it.
• 33:57
  Vanessa Vakharia: 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?
• 34:13
  Vanessa Vakharia: Like I can't jump up to get it.
• 34:14
  Vanessa Vakharia: And I'm really stressed about that.
• 34:16
  Vanessa Vakharia: I actually have this weird thing where I think I'm gonna jump up.
• 34:18
  Vanessa Vakharia: I'm gonna, and I'm gonna grab it and I'm gonna fall.
• 34:20
  Vanessa Vakharia: So I've been avoiding this pull up bar forever.
• 34:22
  Vanessa Vakharia: Okay.
• 34:23
  Vanessa Vakharia: And I think this might be trauma from the monkey bars when I was a kid, to be honest.
• 34:26
  Vanessa Vakharia: But we don't have time to dig into that right now.
• 34:28
  Vanessa Vakharia: 'cause this is Math Therapy, not like monkey bar therapy.
• 34:30
  Vanessa Vakharia: 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.
• 34:38
  Vanessa Vakharia: Those time tests, every time I had to do calculations and arithmetic in my head, I don't wanna face that again.
• 34:43
  Vanessa Vakharia: 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.
• 34:48
  Vanessa Vakharia: Just stand on the bench.
• 34:50
  Vanessa Vakharia: And I'm like, what?
• 34:51
  Vanessa Vakharia: 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.
• 34:56
  Vanessa Vakharia: We can skip the jumping part altogether.
• 34:59
  Vanessa Vakharia: Now what has happened, Curtis, after two months of, so I, I get on the bench and I still do my pull up.
• 35:07
  Vanessa Vakharia: Two months later, I'm like, you know what?
• 35:09
  Vanessa Vakharia: Maybe I could jump up.
• 35:11
  Vanessa Vakharia: And now I've started jumping up.
• 35:12
  Vanessa Vakharia: 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.
• 35:30
  Vanessa Vakharia: And guess what?
• 35:32
  Vanessa Vakharia: 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.
• 35:41
  Curtis Brown: A hundred percent.
• 35:42
  Curtis Brown: A hundred percent.
• 35:43
  Curtis Brown: Like that.
• 35:44
  Curtis Brown: I love your analogy, by the way.
• 35:46
  Curtis Brown: I was trying to think about it for a minute.
• 35:47
  Curtis Brown: 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.
• 35:55
  Curtis Brown: 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.
• 36:04
  Curtis Brown: It's a little bit of a safety net, right?
• 36:05
  Curtis Brown: 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.
• 36:19
  Curtis Brown: 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.
• 36:30
  Curtis Brown: Because I think there's also an opportunity, for using the calculator and specifically the graphing calculator for exploration and development of concepts, right?
• 36:42
  Curtis Brown: 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.
• 36:52
  Curtis Brown: That's one space.
• 36:53
  Curtis Brown: And I think that's, there's a lot of value in that.
• 36:55
  Curtis Brown: There's a ton of value there.
• 36:56
  Curtis Brown: But I think there's also a ton of value in being able to, utilize the technology for exploration.
• 37:04
  Curtis Brown: 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.
• 37:15
  Curtis Brown: what the heck is going on here?
• 37:16
  Curtis Brown: 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.
• 37:34
  Curtis Brown: It either plots or doesn't plot, as a result of that calculation, right?
• 37:39
  Curtis Brown: So it's like, oh, I got a, I have an indeterminate value.
• 37:43
  Curtis Brown: I guess I can't plot a point.
• 37:44
  Curtis Brown: And so it just leaves that point blank and it, and so you see visually what is actually happening mathematically in the function.
• 37:53
  Curtis Brown: There's a really nice thing there.
• 37:54
  Curtis Brown: 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.
• 38:07
  Curtis Brown: Right?
• 38:07
  Curtis Brown: The calculator kind of shows that, and you go, oh my gosh, my, my graph has a hole in it.
• 38:12
  Curtis Brown: What about yours?
• 38:13
  Curtis Brown: Did yours
• 38:13
  Vanessa Vakharia: Yeah,
• 38:15
  Curtis Brown: Right.
• 38:15
  Vanessa Vakharia: well.
• 38:16
  Curtis Brown: Like what's going
• 38:17
  Vanessa Vakharia: Well, there's even more, there's even more than that.
• 38:19
  Vanessa Vakharia: I'm, I'm really glad you brought that up, ex because I think this is a good point.
• 38:23
  Vanessa Vakharia: There is something so tangible.
• 38:25
  Vanessa Vakharia: 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.
• 38:36
  Vanessa Vakharia: 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.
• 38:44
  Vanessa Vakharia: Pat, is that what they're called?
• 38:46
  Vanessa Vakharia: Clovers for St.
• 38:47
  Vanessa Vakharia: Patrick's Day or like
• 38:49
  Curtis Brown: like a
• 38:49
  Vanessa Vakharia: four leaf clover for St.
• 38:50
  Vanessa Vakharia: Yes, exactly.
• 38:51
  Vanessa Vakharia: Or like hearts for Valentine's Day.
• 38:53
  Vanessa Vakharia: 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?
• 39:01
  Vanessa Vakharia: 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.
• 39:08
  Vanessa Vakharia: 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.
• 39:15
  Vanessa Vakharia: I'm gonna increase this by one.
• 39:16
  Vanessa Vakharia: Okay, I'm gonna decrease it by one.
• 39:17
  Vanessa Vakharia: Okay, what if I do this?
• 39:18
  Vanessa Vakharia: What if I do that?
• 39:19
  Vanessa Vakharia: Like, whatever.
• 39:19
  Vanessa Vakharia: 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.
• 39:31
  Vanessa Vakharia: I, I mean, I don't wanna say this so assuredly, but I, I like, you kind of need the calculator for that.
• 39:38
  Vanessa Vakharia: Like you really can't be doing that by hand.
• 39:41
  Vanessa Vakharia: Espe like, right?
• 39:42
  Vanessa Vakharia: Like you, you need that and it's providing an experience that they're not gonna get otherwise.
• 39:47
  Vanessa Vakharia: And then, yeah, they're creating, they're like, well, my heart has this, oh, I created this crazy clover.
• 39:51
  Vanessa Vakharia: Like there's that ownership piece again, there's that visual, like there is everything.
• 39:56
  Vanessa Vakharia: And I think this actually leads to an even bigger question, which is.
• 39:59
  Vanessa Vakharia: What is mathematics?
• 40:00
  Vanessa Vakharia: It isn't just arithmetic.
• 40:02
  Vanessa Vakharia: It is not just you know, these fluency and these fast facts.
• 40:05
  Vanessa Vakharia: That is a part of it, but part of it is exploration.
• 40:08
  Vanessa Vakharia: It's problem creation, generation, and solution.
• 40:12
  Vanessa Vakharia: It is patterns, it is trends.
• 40:14
  Vanessa Vakharia: It is this curiosity.
• 40:16
  Vanessa Vakharia: It's this wonder, it's this creativity, and that is what the tool can really bring to life.
• 40:21
  Curtis Brown: I love that you asked that question or that you even put that into that statement.
• 40:25
  Curtis Brown: That's the, the, fact that we can get to what is mathematics as a part of that conversation, that's huge.
• 40:33
  Curtis Brown: 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.
• 40:40
  Curtis Brown: She actually talks about, that has changed for her about what is mathematics, right?
• 40:49
  Curtis Brown: 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?
• 41:10
  Curtis Brown: 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.
• 41:33
  Curtis Brown: 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.
• 41:59
  Curtis Brown: That's huge.
• 42:00
  Curtis Brown: That's so,
• 42:01
  Vanessa Vakharia: Ugh.
• 42:02
  Vanessa Vakharia: I love this.
• 42:04
  Vanessa Vakharia: Okay.
• 42:04
  Vanessa Vakharia: I don't know how, but time has flown by and we need to, we need to get to our, LA 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.
• 42:18
  Vanessa Vakharia: You know, I have been obsessed with Texas instruments since I was 17.
• 42:22
  Vanessa Vakharia: 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.
• 42:32
  Vanessa Vakharia: 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.
• 42:42
  Vanessa Vakharia: 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.
• 42:50
  Vanessa Vakharia: To ever make like a calculator, like an accessory that like you want it to have.
• 42:54
  Vanessa Vakharia: And I don't know, it's definitely the coolest brand in the math space.
• 42:57
  Vanessa Vakharia: I'm sorry to everyone else listening, but it really is.
• 42:59
  Vanessa Vakharia: Was that a conscious decision?
• 43:01
  Vanessa Vakharia: 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?
• 43:19
  Vanessa Vakharia: Like, do you see what I'm seeing?
• 43:21
  Curtis Brown: No, I see what you're seeing.
• 43:22
  Curtis Brown: 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.
• 43:30
  Curtis Brown: That's, that's one.
• 43:31
  Curtis Brown: Okay.
• 43:32
  Curtis Brown: Um, but I would say yes, the calculator play, okay.
• 43:35
  Curtis Brown: Yes, yes.
• 43:36
  Vanessa Vakharia: Hugging my calculator plushie.
• 43:38
  Vanessa Vakharia: Like who makes a calculator?
• 43:40
  Vanessa Vakharia: Plushie guys, Texas Instruments.
• 43:43
  Curtis Brown: that is, that's huge, right?
• 43:44
  Curtis Brown: So, okay.
• 43:45
  Curtis Brown: So there's that, I, and, and it's all the face plates and all those fun things.
• 43:49
  Curtis Brown: So those are great.
• 43:50
  Curtis Brown: 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.
• 44:02
  Curtis Brown: Texas Instruments graphing calculators.
• 44:04
  Curtis Brown: and why do they choose to use them?
• 44:06
  Curtis Brown: 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?
• 44:22
  Curtis Brown: What little thing could we help do?
• 44:24
  Curtis Brown: 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.
• 44:48
  Curtis Brown: 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?
• 45:01
  Curtis Brown: 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.
• 45:12
  Curtis Brown: 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.
• 45:18
  Curtis Brown: And, you know, the calculator part has become cool.
• 45:21
  Curtis Brown: 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
• 45:28
  Vanessa Vakharia: I sleep with her every night.
• 45:29
  Vanessa Vakharia: Yeah.
• 45:31
  Curtis Brown: 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.
• 45:47
  Curtis Brown: And that kind of gave us the opportunity to be widely adopted.
• 45:54
  Curtis Brown: Because it was widely adopted, it became sort of a, A feature, right?
• 45:58
  Curtis Brown: I mean, tis been been in movies, you've seen calculators in clips,
• 46:04
  Vanessa Vakharia: It's been in movies.
• 46:05
  Vanessa Vakharia: Like what?
• 46:06
  Vanessa Vakharia: What are you saying?
• 46:07
  Curtis Brown: yes, it made a cameo in, in a, in a Spider-Man recently.
• 46:10
  Curtis Brown: 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.
• 46:17
  Curtis Brown: It's a part of, of our growing up.
• 46:19
  Curtis Brown: And it's part of high school.
• 46:20
  Curtis Brown: It's part of learning math, right?
• 46:23
  Curtis Brown: It's a thing.
• 46:24
  Curtis Brown: But it's there because the teachers made the decision and the teachers made the decision because ti listened.
• 46:29
  Curtis Brown: So I think that's, if you want to go back to why, I think that's a major reason why.
• 46:35
  Vanessa Vakharia: Okay.
• 46:36
  Curtis Brown: Okay.
• 46:36
  Vanessa Vakharia: And Michelle.
• 46:37
  Vanessa Vakharia: Okay, we'll take both answers.
• 46:38
  Vanessa Vakharia: Um, we.
• 46:40
  Vanessa Vakharia: Okay.
• 46:40
  Vanessa Vakharia: Oh my God.
• 46:41
  Vanessa Vakharia: Can't wait to see Texas Instruments on the red carpet next year.
• 46:43
  Vanessa Vakharia: Make sure you invite me.
• 46:44
  Vanessa Vakharia: We have to wrap up.
• 46:46
  Vanessa Vakharia: You have 30 seconds to answer both of these questions.
• 46:48
  Vanessa Vakharia: They're the last questions I always ask every guest.
• 46:50
  Vanessa Vakharia: 30 seconds po.
• 46:51
  Vanessa Vakharia: Okay.
• 46:52
  Curtis Brown: I'll be
• 46:52
  Vanessa Vakharia: question number.
• 46:54
  Vanessa Vakharia: Question number one.
• 46:55
  Vanessa Vakharia: If there's one thing you could change about the way math class is taught, what would it be?
• 46:59
  Vanessa Vakharia: Go.
• 47:00
  Curtis Brown: Uh, curiosity.
• 47:03
  Curtis Brown: Engagement, I want students to be able to explore.
• 47:06
  Curtis Brown: I want students to be able to ask questions why, and I want'em to want to.
• 47:10
  Curtis Brown: so we have to do things to help students want to ask the questions why.
• 47:16
  Curtis Brown: We have to ask, we have to develop that curiosity.
• 47:19
  Curtis Brown: And where it's died, we need to have, find ways to rejuvenate it.
• 47:23
  Curtis Brown: Um, so your 45 second answer to that question.
• 47:27
  Vanessa Vakharia: That was good.
• 47:27
  Vanessa Vakharia: That's good enough.
• 47:28
  Vanessa Vakharia: Okay.
• 47:29
  Vanessa Vakharia: Final question.
• 47:30
  Vanessa Vakharia: Someone's listening to this, they're like, cool, cool.
• 47:32
  Vanessa Vakharia: I get it.
• 47:33
  Vanessa Vakharia: 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.
• 47:41
  Vanessa Vakharia: What do you say?
• 47:42
  Curtis Brown: It makes my heart hurt, first of all.
• 47:44
  Curtis Brown: I just wanna hug them.
• 47:46
  Curtis Brown: I, because everybody is a math person, we all have the ability to be math people, okay?
• 47:53
  Curtis Brown: 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.
• 48:03
  Curtis Brown: Like they haven't gotten a good experience, they haven't been exposed to the, to the fun.
• 48:08
  Curtis Brown: 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,
• 48:22
  Vanessa Vakharia: Yeah.
• 48:23
  Curtis Brown: And so it just makes me wanna hug them.
• 48:25
  Vanessa Vakharia: Okay.
• 48:25
  Vanessa Vakharia: Well they probably need a ti plushy.
• 48:29
  Vanessa Vakharia: Um, Okay.
• 48:29
  Vanessa Vakharia: Curtis.
• 48:30
  Vanessa Vakharia: Oh my god, this has been wild that we could talk forever, but we have to wrap up.
• 48:34
  Vanessa Vakharia: 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.
• 48:40
  Vanessa Vakharia: So spit it out.
• 48:43
  Curtis Brown: 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.
• 48:52
  Curtis Brown: So we talked about why do teachers use these things in their classrooms?
• 48:57
  Curtis Brown: Why is this here?
• 48:59
  Curtis Brown: This is another piece of the puzzle.
• 49:00
  Curtis Brown: Um, and that is the idea of focus.
• 49:04
  Curtis Brown: Have lots of tools that are out here.
• 49:06
  Curtis Brown: That exist in the world today, right?
• 49:08
  Curtis Brown: Like you mentioned the internet earlier this morning about like being a tool, and then it's the appropriate usage of that tool.
• 49:15
  Curtis Brown: Like think about for a minute, all of the things that are out there on the internet, like there's a ton, right?
• 49:21
  Curtis Brown: 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.
• 49:31
  Curtis Brown: Like there's a keypad that's designed, it's all keys that are math tools and keys, right?
• 49:37
  Curtis Brown: Like, think about for a minute the focus that that gives you.
• 49:42
  Curtis Brown: When I'm using this thing, I'm using it for doing math.
• 49:45
  Curtis Brown: I'm using it for exploring mathematics.
• 49:48
  Curtis Brown: I'm not using it, and then switching to another tab really quick when my teacher isn't looking and then switching back.
• 49:54
  Curtis Brown: Like, I can't do that.
• 49:55
  Curtis Brown: This is a purpose-built device.
• 49:57
  Curtis Brown: It's my thinking space about mathematics.
• 50:00
  Curtis Brown: 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?
• 50:09
  Curtis Brown: And that's another reason why teachers love and that's another reason why the longevity is there.
• 50:17
  Curtis Brown: Does that make
• 50:17
  Vanessa Vakharia: Well, well, it makes so much sense.
• 50:19
  Vanessa Vakharia: I'm actually kind of like, oh my God.
• 50:22
  Vanessa Vakharia: Like this is like the answer to the argument of people being like, well, we have phones in our pockets.
• 50:27
  Vanessa Vakharia: It's like, yeah, you do, but
• 50:30
  Curtis Brown: Like, oh my gosh, we got all these other tools that we could have access to.
• 50:34
  Curtis Brown: They're out here.
• 50:35
  Curtis Brown: Everything's all over the place.
• 50:36
  Curtis Brown: Why?
• 50:36
  Curtis Brown: Why do we need this thing?
• 50:38
  Curtis Brown: And the answer to that question is I need this thing because it's my thinking space, it's my focus space.
• 50:44
  Curtis Brown: It doesn't have access to all those other things that could be distractions, right?
• 50:49
  Curtis Brown: I'm not getting notifications on my graph calculator.
• 50:53
  Curtis Brown: I'm not getting that Facebook, right?
• 50:55
  Curtis Brown: I'm not getting that friend invite just now.
• 50:57
  Curtis Brown: Oh my gosh, 10,000 people love my post, I don't get that little post.
• 51:02
  Curtis Brown: I don't get that on my graphing calculator.
• 51:04
  Curtis Brown: It doesn't come up and cover my parabola.
• 51:09
  Vanessa Vakharia: Yeah.
• 51:12
  Vanessa Vakharia: Oh my God.
• 51:13
  Vanessa Vakharia: 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.
• 51:25
  Curtis Brown: No, exactly.
• 51:27
  Curtis Brown: We can't do that.
• 51:28
  Curtis Brown: We choose not to do that.
• 51:31
  Vanessa Vakharia: Perfect.
• 51:32
  Vanessa Vakharia: And now we're gonna say goodbye and there's a little someone special who would like to say bye to you today, Curtis.
• 51:39
  Curtis Brown: Ah, bye-bye.
• 51:40
  Curtis Brown: Calculator buddy.
• 51:42
  Vanessa Vakharia: Oh yeah.
• 51:42
  Vanessa Vakharia: Sorry guys.
• 51:43
  Vanessa Vakharia: This is my calculator plushie, who I've named Calcie.
• 51:46
  Vanessa Vakharia: I was given her at NCTM two years ago, and
• 51:51
  Curtis Brown: Hold
• 51:51
  Vanessa Vakharia: Sorry.
• 51:51
  Vanessa Vakharia: You're gonna take it back.
• 51:52
  Vanessa Vakharia: Michelle gave me one actually.
• 51:55
  Curtis Brown: No, I don't have one.
• 51:58
  Curtis Brown: I didn't get
• 51:59
  Vanessa Vakharia: Oh.
• 51:59
  Curtis Brown: What?
• 52:00
  Curtis Brown: Michelle?
• 52:02
  Curtis Brown: For real.
• 52:03
  Vanessa Vakharia: And that concludes our interview today.
• 52:05
  Curtis Brown: Even.
• 52:06
  Vanessa Vakharia: Goodbye.
• 52:08
  Vanessa Vakharia: Shut it down.
• 52:08
  Vanessa Vakharia: Shut it down.
• 52:11
  Vanessa Vakharia: Whew.
• 52:12
  Vanessa Vakharia: Okay.
• 52:12
  Vanessa Vakharia: 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.
• 52:19
  Vanessa Vakharia: 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.
• 52:27
  Vanessa Vakharia: 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.
• 52:41
  Vanessa Vakharia: 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.
• 52:49
  Vanessa Vakharia: You can also DM me on Instagram at the Math Guru or email me at vanessa@themathguru.ca.
• 52:55
  Vanessa Vakharia: 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.
• 53:03
  Vanessa Vakharia: Maybe you've doubled down on something you already thought.
• 53:05
  Vanessa Vakharia: So get in touch and I will see you not next week, but the week after that.
• 53:09
  Vanessa Vakharia: And until then, I'm sending you all the peace, love, and pi