Cat: 0:00

Maybe like 25% of four year college students have moderate to high levels of math anxiety. But if you leave UCSD and drive five miles inland or something and go to a community college campus, 80% of students will probably have math anxiety.

Ashley: 0:18

In biology at UCSD, like it is definitely higher than 25% because I feel like a lot of the students that are in biology have almost like chosen life sciences, because they're kind of avoiding some of the more physical sciences and avoiding some of those classes

Cat: 0:41

Who's afraid of math?

Ashley: 0:44

everybody, everybody.

Cat: 0:45

That's my conclusion after reading a bunch of research. Way more people than I thought.

Ashley: 0:51

Well, let's just say a lot of people,

Cat: 0:53

I didn't know anything about this really. Um, despite working in education and working on education research and all this stuff about why people achieve or not and their beliefs about it, I feel like I had anxiety about learning about math, anxiety.

Ashley: 1:10

that is so meta even for this podcast,

Cat: 1:12

know, and I, I, I think it's really interesting because I went on this journey, like I started reading these papers and as, as it ever was, the more I understood this, the better I felt. And it was cool. And I hope we can get there a little bit in this episode. It's like a huge topic. Um, but I came out with, my mind changed and honestly my relationship maybe to math changed and that's a very cool thing to happen like at this time in my life.

Ashley: 1:46

this is a very big thing because I know like, you know, especially because of your educational background, like you sort of figuring out where you stand, you know, in these different fields has been kind of hard and anxiety provoking because of kind of like you not coming up through standardized tests. Like I feel like for me it's like I always got these messages as a kid. It was like you literally get the percentile that you're sitting in, right? And um, for you especially, it's like if you don't know, you never got that feedback, then you're also just like, where do I stand?

Cat: 2:17

I, I'm not sure which one of us had it worse, honestly, because is it, is it better to just not know when you're like this free floating little spirit out there and you're like, I could be anywhere on the math distribution. Who knows? Um, but uncertainty is very, very difficult to deal with. And, um, you know, that doesn't give you stability. But at the same time, like I came out of reading this research thinking, wow, it's very arbitrary how we put people on a certain distribution and what you measure and how you measure, you know, math is not one thing. It's a lot of things. So it's interesting that you remember that. I think that that's very characteristic of the stuff I was reading. A lot of people remember. Not so much the activity of solving math problems, but they remember the feeling of when they saw where they were at the end of the math test.

Ashley: 3:07

Oh, that's so interesting. I think that kind of perfectly kind of sets up what we wanted to talk about today, which is kind of like, you know, there's, there's these two things. There's, there's math ability, but then there's also math, anxiety, and like the general sort of way you feel about your math ability and the messages you're getting. So what,

Cat: 3:25

there's three themes. There's three. Three a's I think there's math ability, whatever the heck that is. Okay. There's math anxiety, and then there's math achievement. And those are all different things. So I have things to say about all of these. So I went and read all these papers. We're trying this thing in this episode. Um, and Ashley's gonna be the interlocutor for this, but I am right away gonna steer us away from the ability portion. We have some things to say about it, but, um, a big thing is it's very multidimensional. There's actually a lot that's unexplained and there's a lot of interesting stuff to learn about math anxiety. So, shall we start there?

Ashley: 4:06

Yeah. Yeah. Okay. Okay,

Cat: 4:07

Okay. Okay. Let me, let me read you a quote. Okay. From one of these papers, and it is a quote from a real person, an adult human who has math anxiety, and they say, during middle and high school, I know my attitude towards math was a hundred percent affected by my low test scores. I began to build a wall towards math, and it was, and still is sometimes tough for me to open up and soak up information. I think that. This is a really nice quote that kind of captures something very important about math anxiety. We have like this relationship to math and math anxiety refers to a really heightened feeling of like fear, tension, apprehension that a lot of people experience when they're engaging with math. So like in the moment of engaging with math and it's really pervasive. So like in the United States, um, folks estimate that maybe like 25% of four year college students have moderate to high levels of math anxiety. But if you leave UCSD and drive like five miles inland or something and go to a community college campus, 80% of students will probably have math anxiety.

Ashley: 5:19

Yeah, and I feel like this must differ so much based on like students' majors and things like that. Like in biology at UCSD, like it is definitely higher than 25% because I feel like a lot of the students that are in biology have almost like chosen life sciences, like, because they're kind of avoiding some of the more physical sciences and avoiding some of those classes, so, yeah. It's even higher than 25% in the students that I work with, just sort of anecdotally. Um, for sure. Yeah.

Cat: 5:48

interesting. Yeah.

Ashley: 5:49

And something that we actually were talking about recently in a faculty meeting was the fact that, you know, UCSD and I think like the whole uc system has been giving these like math placement exams when students join. And in the past, let's say five years, the scores on these placement exams have just like plummeted. Like students are really struggling in math right now. It is happening before college, for sure. Um, but it's just propagating through college and through their time at college, and then as a result, it's impacting all of these different things they can do in college. If you're coming in on a, you know, lower math placement, it, it impacts your whole trajectory.

Cat: 6:29

Right. This taps into something that, which is like a big point I wanted to make in this episode right out the gate, which is math stuff is really additive. Like, one of the things that's so tricky, one of the reasons that early struggles in math are so important to understand is because it's very cumulative and there's, you know, we're not gonna get into the whole structure of math, education and curriculum. Like maybe that's a different episode, but it's so additive, you know, if you get knocked off a certain part of the track early on, it starts to determine all kinds of things that happen later. And this is something people talk about with math anxiety. We see these very cyclical kind of reinforcing loops. This might be something that, you know, people resonate with, right? Like that quote I shared, you know, I had, you know, this wall that started to build up and it kind of kept getting reinforced. So, um. You know, another little stat that I have that I think brings some color. I was reading these very, very big reviews, you know, of a lot of research for this episode. And, uh, one, one investigation looked across like 65 countries, so this is like a worldwide problem, and they estimated about 33% of 15-year-old student. So picture like the 15 year olds of the world. Like what a, a I love the age 15. I think it's really, really interesting, you know, and um, and it's an, a moment

Ashley: 7:53

I like at 15?

Cat: 7:54

yeah, think about it, right? You're, you're so sensitive, you're so interesting. You're not an adult yet, but you're learning like who you are. You're experimenting

Ashley: 8:03

deep Philly accent at

Cat: 8:06

You did? Yes. It was remarkable. We went, we went home to Ashley's home and I saw these videotapes of her and it was shocking what came out of this

Ashley: 8:16

I don't know who that person was. It wasn't me.

Cat: 8:18

It was so amazing and I, it was like a big cultural moment for us. I was like, who are, who are you?

Ashley: 8:25

Anyway, sorry, I digress.

Cat: 8:27

The, the 15 year olds of the world, like 33% of them according to this study report, feeling helpless when solving math problems. That is a big percent. Having a really negative experience about something that's like part of our human heritage, I, I found that kind of shocking. I honestly found it really sad. Another pattern. Okay, here's another anecdote that I thought was really thought provoking. There is this intergenerational transmission of math anxiety. So for instance, a 2015 paper that I read looked at high math anxiety parents who were also very engaged, parents really doing good parenting, constantly trying to help their children with their homework. And the more these high anxiety, math, anxiety parents help their kids, the more anxious the kids get about math.

Ashley: 9:21

oh this is, this sucks. Like this

Cat: 9:23

It sucks.

Ashley: 9:24

cause it's like these parents are trying, but they themselves are anxious about math and the, their kids are just learning that from them.

Cat: 9:31

absolutely. I mean, that's

Ashley: 9:32

like being transmitted.

Cat: 9:34

That's the interpretation. And you know, it's also, I think it speaks to, there's a lot of effects like this in learning science, which are like, sometimes what we think is gonna help isn't what helps. Like cramming doesn't always help quantity, it doesn't always help if you're accidentally giving somebody the wrong learning strategy. You could be sending them down this like, you know, garden path that is setting them up for future failure. And one thing that, uh, you know, some of my work is real, I've been really interested in this in my research. Some of this stuff pays off in the short term. Like if you're really math anxious, you might kind of default to really rigid strategies. Like you learned one thing about solving math and it's kind of like the thing you, you can get to work and you feel more confident about that than other things and you sort of pass that rigidity on. And it can have short-term payoffs. You see improvement, right? This is a very difficult thing in learning interventions. Like sometimes we need to see performance get worse before it can get better because we're actually teaching like more flexible strategies. So, okay. I said we weren't gonna get into curriculum, but I really fascinated by this some. Sometimes parents push back so hard about math education changes and one thing is they're like, this is harder. It's worse. My kid's understanding less, but over, over time, like the new way of teaching might actually be teaching more flexibility. I think that's like something we miss sometimes.

Ashley: 10:58

You have a really unique educational trajectory and maybe you think about math ability and like your own sort of like math anxiety a little bit differently than, than many other people do because you have these kind of different inputs or like lack of inputs as you were, as you were younger. What does this all mean to you? How does this fit in with your schema of like your own ability and achievement?

Cat: 11:20

You know, so there's so many difficult parts of my upbringing, of course, and I've shared some of those. There are parts that I feel grateful for in a really interesting way. I feel free.

Ashley: 11:35

Hmm.

Cat: 11:35

feel like this separation. And this feeling of, I had no idea where I was relative to other people. And my, my brain and my mind did not get trained constantly to compare myself to other people. I, I think I was always sort of aware of the fact that people were really different and like, curious about that just because I felt very different, you know? Um, but I do think that there's an element of I didn't take tests and that left me with this freedom to imagine that I could be anybody. And I loved that. And like, I got into these math classes so late and it was so, it was almost like so weird. People didn't have a narrative for me. So, you know, I took. I tested out of every math requirement in college via standardized tests. And um, I also went to a liberal arts school that was kind of like, we don't care if you do many math. And they had like basically a math class for non-math people, which was a geometry class. And the geometry class was just logic puzzles. And the logic puzzles were just word problems. And I love a freaking word problem. Okay. Like my whole life was just reading books and I was like, oh, is math words, I don't know, is math shapes? I could do shape math? You know, and I think that I almost had this like coming in laterally, coming in like sneaky into math, just, you know, with completely different identities in my mind than most learners. And then I got into grad school and then I took statistics and I was like, oh, statistics is totally logic. You know, that's like, you have this number of people and how do you know, and this thing's happened and how do you set up the experiment? And I felt very confident with it actually. Um, but then the things that I remember really being so frightened of was like the math portion of the SAT and this kind of like. I do think there are huge gaps in my math vocabulary because I was raised without like a solid algebra, you know, curriculum, or I was trying to teach myself out of books, and the books were kind of out of date. And I did the Saxon math thing that every homeschooler does, and it's very rote math learning, and it's like those rigid strategies. So I was kind of like, eh, whatever this is, I'm not good at this. Yeah. But then I weirdly ended up in a math heavy career, but I, for a long time I was like, this isn't the same kind of math, you know? And yeah.

Ashley: 14:19

So it's like, for you, the fear and the anxiety came from maybe not knowing where you stood a little bit

Cat: 14:27

Yeah.

Ashley: 14:28

and like a little bit of, you know, like you said, like teaching yourself through these resources, which you didn't know if they were reliable and like kind of some, some uncertainty around that. So I, I think like something I'm like now grappling with is like. Is it better for students to know where they stand or not? Because in your case, you didn't really know where you stood and that was hard. But also when students take standardized tests and then we tell them, oh, you're in this percentile, then they like very statistically speaking, know where they stand in this certain assessment. And that can also be, you know, anxiety provoking. But is it more about the messages and how we frame that standing? You know, as you said, this sort of interpretation cycle, is that the important thing?

Cat: 15:17

I think it's a good place to start, you know, and I, I do think that there's something about being so different that you sort of just are outside of the usual pathways of oppression. You're so like far outside the power structure, you're just like, oh, well I'm just gonna be, I'm so weird. No one even has the box to put me in. That would be the bad box if they could grapple with how different I am. But they can't, so they're like, we don't even know, you know, you're like this asteroid that's like, came onto our planet. You're, you know, my classmates used to call me an alien and it was like I didn't know what to be scared of. And that was a superpower. I was not scared of kids who took calculus. I wasn't scared of like, and I didn't have that sense of status.

Ashley: 16:07

Hmm.

Cat: 16:08

And I think that's actually really true about me. Like in one of my early tech jobs, um, uh, my boss told me, and it was not a compliment, you know, told me you talk to everyone the same way. They're a, they're a director. You know, they're, you really, it doesn't matter what title people have. And I was like, yeah,'cause I'm talking about the evidence and the facts in the world. And I was like, thank you very much. And she was like, that's not how we want you to be.

Ashley: 16:35

Yeah. Yeah. I mean, these systems are in place to, um, sometimes even unintentionally oppress people who have the knowledge and the insight capital I,

Cat: 16:51

I think we're very, we're very comfortable with there being a status and, you know, the idea that we could have a, not a status, not a meritocracy, not a hierarchy, but truly radically pursue this idea that we need to serve everyone. You know, even if they come in with a completely different background than we expect. You know, it's a very, it's like the challenge of our time, I feel.

Ashley: 17:15

Mm. So like I know sort of anecdotally, I've like talked to some parents who are just like, I don't know the math that my kids are doing. Like, I can't even help my middle school kid. And then as a result, they are anxious about it. And rather than, you know, maybe like directly problem solving or accepting the difficulty of it, they're kind of conveying this anxiety and like really, like we're talking about kinda like mindsets, like we're talking about mindsets towards how we accomplish this kind of work. And I think that those are transmissible, like we know this with like fixed and growth mindset kind of work too, is like, and I, there's some work in education that's like, okay, if you're a professor and you have a really fixed mindset and that's very clear to your students, like one students will recognize this, and two, it will be transmitted to students and they will start adopting the same kind of mindset.

Cat: 18:09

Yes. Yeah. Yeah. So, okay. Something I wanna tie this to is teachers' beliefs. Okay.'cause I did read about this and you talked about, um, you know, college level, but something that's really, really critical in math. Um, you want to guess, like what, what like level of school do you think is like, super critical for math?

Ashley: 18:31

Hmm. Oh, that's interesting. I mean, I feel like some of this stuff gets formed in like el, like as early as elementary school, I would imagine.

Cat: 18:40

it's right out the gate. It's elementary school teachers, so, so elementary school is like a really interesting time in life. It's a super important developmental period, obviously, and it's like this beginning place, you know? So I said math was really additive. Okay, I want to read you another quote. And this is from a teacher with math anxiety. Okay? So this is from one of these studies I read. So the teacher says, one day I was teaching a concept and literally cried in front of my kids because I didn't get it either. When I expressed my disdain towards mathematics and my students witnessed my meltdown, they immediately shut down and I lost them during math lessons for weeks afterward. I know that seeing their teacher get frustrated with the math left a long lasting, if not lifelong impression on them.

Ashley: 19:30

oh God.

Cat: 19:32

I thought that was another sad is that not so poignant, like, you know, how hard being a teacher is

Ashley: 19:39

mm.

Cat: 19:40

and I could just imagine the moment of overwhelm. Elementary school teachers are really overwhelmed when it comes to teaching math. A lot of them have math anxiety. They haven't been trained super well. You know, themselves. They report this high level of math anxiety and we, we think this is a really big factor in a lot of people developing it themselves.

Ashley: 20:00

yeah. So this strikes me as like sort of a core. Issue here, which is that we need people to teach math, who they themselves believe they can do math. And that's really hard when those people came up through the same system with the same math anxieties, right? It's like this like terrible cycle. So like, yeah, what, what do we do with that? That's really, really tough.

Cat: 20:23

And you know, it's not like these teachers are, I mean, I, I think elementary school teachers are heroes, honestly. As someone who's worked with a lot of teachers, you know, I mean, just watch like Abbott Elementary or something like, you know, there's, they're dealing with these such situations of constraint. So none of this is like to critique teachers in my mind. Um,

Ashley: 20:44

They're not getting the support they need to, you know, develop professionally in these ways. Like there's no way.

Cat: 20:50

but I'm, I'm really interested in like, the networks of beliefs that we hold and how that impacts us. You know, this is one of the things I've been studying with software developers and, and, um, it's interesting with teachers, like, with teachers with higher math anxiety, they do stuff like, um, they, you know, emphasize rote learning. You know, they're kind of more afraid to let kids experiment in the classroom. I. They're afraid to do conceptual activities. You know, they worry about, they worry about those, probably those moments, like the quote, they don't wanna be shown up, they don't wanna look too vulnerable. So they start to lean on, you know, kind of like safe activities. And again, I wanna make that point again, that sometimes we do these things that are like the short term, it's keeping us safe in the moment. But what that, what that creates is a systematically less rich classroom learning experience and less modeling failure, you know, in front of students. Um, they also present lessons in a really dogmatic manner. They probably don't even know they're doing that, right? But there's some interesting stuff that's like, you could take the same curricula, you know, one, one is delivered by an anxious teacher and one's not. The teacher's gonna teach differently, right? So this is a challenge in education interventions.

Ashley: 22:07

yeah, totally. And you know, like, this really actually speaks to me personally because, you know, I've. I've taught some classes at, you know, uc, San Diego, that are very much in my wheelhouse. They're neuroscience, you know, like I feel very, very comfortable. But then like in more recent years, especially because I care so much about students, like having computational skillsets and kind of growing beyond the lab and being able to do things like beyond what we can like physically do in the lab space. Like I've been teaching more like data science and things like that, and that is outside of my wheelhouse. I never took a class in data science. Like I'm self-taught in a lot of these things and I know that when I get in front of the class and I talk about stuff, I'm just a little bit uncertain about like I haven't fully like, you know, unit tested the thing in my head, like, you know, then I. I know I sound different, like at least I sound different in my head. And I don't know if this like comes out to students, right? But like there's a little more hesitation, there's a little bit more anxiety like in the way I'm presenting it. And so like, I can relate to this, you know? And it's really hard because, and I, and I think you're totally right, it's like what I see myself doing is I leave less space for experimentation and I'm like, this is how it is. This is how it is, this is how it works. Okay, we'll move on to the next thing, right? Because I'm like, I'm not quite ready to, to deal with like the question about, well, why is it this way? And I'm like, well, I'm 90% sure I have an answer about that, but I may not. Right? So just, yeah, from the instructor point of view, like I, I can see how this happens, how this plays out in someone's mind. It's like a little bit protective in a way. You're like protecting, you know, your place in front of the classroom as the instructor, as the teacher, um. Yeah, it's very real. But, but that space for problem solving, that space for failure, that conveying of a mindset towards growth is like just as important as the content itself.

Cat: 24:02

mm. Yeah. I love that. Thank you for sharing. Yeah, I didn't, I didn't have a lot of, you know, experiences in a classroom with math because I had the fun life of never having math classes, you know? And so for me there was kind of this like, just, just bizarre. Like, I don't even know if I know what math is, you know? And I think a lot of people end up in that place too. Like, um, maybe they've, they sort of remember, you know, another interesting part of this, um, I'm jumping around a little bit, but there's something researchers call, um, motivated for getting. And if you are in a stressful, and try to think about for a second, think about like a really stressful event in your life and maybe what's your memory of it? Like, you know, is it, is it kind of warped? Is it kinda weird? Is it a little bit like something's missing? You know, the way we,

Ashley: 24:55

memories sort

Cat: 24:55

yeah. Right. That's one, one form. I'm not sure, you know, I'm not a memory expert, but. Um, we, as we encode different information differently when we're stressed. Right. And this happens on, you know, the neuroscience levels. You know, we're in a different physiological state. And so one thing that people talk about with math anxiety is, you know, students who are, are having a fundamentally different experience in the moment of engaging with math. They're not able to encode memories in the same way. And they, we have these mechanisms that come on board to kind of protect us to like suppress distressing experiences. Um, and this is motivated for getting, so then it creates this thing where you, you don't really deeply encode the math strategy because you were so stressed in the moment, and then later you can't retrieve it. You know, so you don't have the same like, bank of strategies to draw on. And you're like, why is everybody so much better than me? You know, we're all going through the same stuff, but you didn't really go through the same stuff. And this is like a point I wanna make. Is that like, when you're psychology is different, you're like living in a different world.

Ashley: 26:03

hmm.

Cat: 26:04

When you're having a different psych, you know, when you're having like threat, you know, when you're having something bad happen to you, when you're treated differently by your teacher, you're living in a different experience than other students.

Ashley: 26:13

Yeah. Totally. And I think, I think it's interesting'cause it's like, I would've thought initially that you're like, okay, if I have this, like really, um, you know, little t traumatic experience, like when I'm a kid, like, you know, we talk about those being like things we remember really strongly. But I think the stuff we remember. Is how it felt and maybe where we were and who was there, and sort of the social, social, like emotional factors, you know, in that memory. We don't remember the math problem we were doing or like

Cat: 26:45

you, don't remember like the, the joy of math. Think about what you get cut, what's cut out out of this picture. You don't remember, like insight, Eureka, you're, you're blocked from all of that because like, what's the tiger? You know, the tiger coming at you through the jungle that you have to suddenly fight is like, you know, your teacher not liking you. You're like, kids are just so tapped into that because it's like such a core part of our cognition. So everything that we're kind of talking about here, I wanna give a name to it because there's like three models that people use to talk about where math anxiety comes from. And like in true podcast fashion. I have one that I like that I wanna talk about last, that I think is the best one. But there's another one I really like and it's that I wanna name, it's called the disruption account. So in the disruption account of math, anxiety, math, anxiety essentially steals cognitive resources from us and it, this causes poor math performance. So, you know, it's a really, really kind of breaks your brain a little bit to realize you use your same mind and brain for everything.

Ashley: 27:57

including dealing with anxieties.

Cat: 28:00

Totally. So some, here's, here's an interesting anecdote, so you might think to yourself, alright, you know, let's say working memory is really important for solving math problems. We kind of think it is because you need to like be able to pull stuff into your mind. You have this working memory. So you might think, okay, you know, maybe kids with high working memories, they're less likely to have math anxiety. You know, they're gonna be good at math. Everything's great. Actually there's this really cool kind of paradoxical effect out there. Kids with really strong high working memories can be sabotaged. Even more are like, look more susceptible to math, anxiety. And a reason that we think explains this is because anxiety, essentially co-ops your functions like working memory.

Ashley: 28:47

So I

Cat: 28:48

So I think this is kind of neat just because it helps us, like expand our minds and stop thinking like, is the cause that people don't have the resources to solve math or not, but actually like there's a resource that we need and it's, it's both good for math and uniquely susceptible to being taken over by anxiety.

Ashley: 29:06

When I think about working memory, like the way we kind of describe it in terms of the brain is like, it's like your, your brain's kind of keeping an idea alive a little bit. And the idea is you kind of like keep it alive by reverberations through these like circuits in your frontal cortex and you're kind of just like reliving the thing you just saw and it kind of gets like, you know, almost like juggled around, you know, for a little bit. And people actually call it like the juggler and like, you know, if you think about, and I know like for me, um, you know, if I am almost like ruminating over something a little bit, like I just had a social interaction, it's kind of still bouncing around in my brain a little bit. Like I've got this like anxious ruminations thing just happened, like. I, I wonder, you know, that that is kind of like a form of working memory, like reliving this thing that just happened. So when I think about people that are anxious and I think about what working memory is, it kind of makes sense to me that those things would go hand in hand, which is that if you're an anxious person, like you almost maybe have an overactive working memory, like you're still tossing this thing around, that you should have just popped into your short-term memory and ultimately in your long-term memory, like it should have been gone by now, but you're still thinking about it. You're

Cat: 30:13

You know, and

Ashley: 30:14

ruminating. Yeah.

Cat: 30:16

Yeah. I think this speaks to some of the experience of, of gifted students. Sometimes you're so good at something, you double down on that strategy and it actually makes some things really hard for you. And it's, it's like things can be both good and bad. You know what, like our minds are amazing and terrible, and like, we're trying to solve so many things in the world. And that's just something I, I hope people listening can come away from this episode just feeling a little bit like, it's not really like, am I good or am I bad? You know, your mind is trying to survive in this complex world. Um, here's some evidence that I really wanted to get your opinion on, babe. That I think is like very neuroscience. And I, I really want to know like, is this good neuroscience? Okay. About this, it kind of speaks to this, um, disruption account. So there's this fun study that I read from 2014 and they used a transcranial direct current stimulation, okay? And so they applied this to the dorsal lateral prefrontal cortex. Um, and they looked at both people with high math anxiety and people without math anxiety and had them do things like solve a simple arithmetic problem. So, a reason to do this is to kind of test this, like stealing cognitive resources idea, because I think the idea that, um, TDCS can, you know, kind of prevent that stress thing from happening, or I don't know how you would describe it, kind of prevent that rumination maybe, um, in this moment you can kind of, you know, freak the brain out a little bit in this specific area and keep that from happening. And so they got this very different result. The people with high math anxiety solve the math problems better, essentially improve their reaction time in their math decision making. The people who didn't have the math anxiety, um, this, this stimulation made them worse. So what do you, what do you think? Is this good evidence or is this like, kind of weird neuroscience like psychology,

Ashley: 32:12

I mean, I think this is fun. No, no, I think this is fun. I mean, like, you know, these kinds of like techniques, you know, are really interesting because. They're doing something to disrupt a, a particular area of the brain. And so this one is disrupting a part of the frontal cortex. And so, yeah. Um. And it is kind of like the one thing we can do in humans to disrupt, like to ethically disrupt activity. So we're kind of like limited in this way with what we can do with humans, but it does do this. Um, I kind of feel like, like thinking about this in this kind of theory that like maybe people are almost like relying too much on their working memory is really interesting because when I think about stuff like, you know, I was like down the street the other day, um, throwing free throws like for basketball and just trying to like get into a flow state with it, right? And we know that like with, you know, really trained motor movements like that, it's actually kind of worse to think about it too much, right? You

Cat: 33:13

You use the wrong part of your brain.

Ashley: 33:15

Yeah, you're actually kind of like, if you think about it too much, and like people might know this when they think about their golf swing or any number of things, it's like, if you think about it too much, it's actually kind of bad. It's like it gets in the way. Um, and there's not actually really, I, I'm like researching this for my book. It's very separately from this conversation. But, um, there's some really interesting research about this and I almost feel like this is kind of a similar thing, which is like maybe working memory and these circuits that are like kind of anxiety provoking in themselves. It's actually not the optimal way to solve a math problem, but people with anxiety are overusing them as they're trying to solve these math problems.

Cat: 33:49

Yes, the res, some of the research would totally agree with you, which is, well, I, again, I wanna hold back from saying is it right or is it wrong? You know, I'm a social constructivist and I think what works is right, like, and

Ashley: 34:03

that's the second, no, third time you've said that in 24 hours, I think.

Cat: 34:07

I am trying really hard, I'm trying really hard to tell the world that I'm a social constructivist. But anyway, yes. When you look at this stuff, like I said earlier. Essentially relying on one single strategy, even if you're really good at that strategy, opens you up to possible failure when, when that leg is knocked out from under you. And it's kinda like, you know how people with asthma can have really great lung CAPA volume because they've overcompensated for the things that are happening, you know, in the rest of their respiratory system. You can overcompensate for other things you struggle with, which makes you very good at some particular part of it. And this is the complexity of even saying what is good and bad with people's performance because, you know, that's impressive and cool and maybe necessary, but then, you know, we want to give people access to the full diverse range of the things that they could do, you

Ashley: 35:06

Totally. Yeah, totally. And I wanna, I want to give like a more specific example of what I mean by this. Like sort of moving things to like more permanent memory, because I think this is kind of interesting. So like, you know, you can walk down the street regardless of how anxious you are, right? Like your brain knows how to walk,

Cat: 35:25

Well, not if you're so anxious that you're having a full out

Ashley: 35:29

If full on panic attack, maybe not right? Then we have some other physiological things going on. But like, you know, you can go for a walk even if you're in a like really intense state of anxiety, right? But like when you were an infant learning how to walk, that might not have been the case actually. Right? Like these things would get in the way because when you were learning how to walk. Right. Like these systems are, um, vulnerable to some of these other inputs like the sort of state that you're in. But what we do through development is we move some of these things and it's like gross oversimplification, but we move some of these things out of these vulnerable circuits into, you know, kind of deeper circuits in the brain that can operate without input. You know, they're like literally just oscillating as we move through our day, just like breathing, um, these sorts of things. So anyway, yeah, I think, I think it's really interesting'cause it's like we think about working memory as being a good thing and as you're pointing out like there's no correct strategy here. Right? But we think about it as being a good thing for learning and for being flexible and thinking about different strategies. But actually it's a strategy that is like maybe more vulnerable to, uh, anxious states or any other kind of like state change. Yeah.

Cat: 36:41

yeah. And I, I think you're bringing up too, like how interesting it is to pay attention to developmental periods. Which is something that, you know, you can be interested in as a neuroscientist. Like what's the brain doing? And, and I've been interested in it just from a sociocognitive point of view. Like, what do we, and, and even like throughout the lifespan, you know, it's, it's not just those 15 year olds we were talking about, right? It's like you join a new team that's an entry point. You're forming a new identity or something. I do wanna get through. So I, I wanna get through the other models for math anxiety. So if there's like math, anxiety experts listening, you never know. I want, you know, you all to know that I did my freaking homework. Um, so it

Ashley: 37:23

really excited when she has homework because she hasn't had much homework in her life, so, you know, she really did it. She really wants you to know.

Cat: 37:29

I'm always looking for that. A, because I have uncertainty about where I am in the freaking distribution.

Ashley: 37:35

Damn, damn. It always

Cat: 37:37

Okay. So it would be remiss of me not to mention that there is another far less sexy model called the reduced competency account. It kind of is what it says on the tin. It's like math anxiety is the outcome of having poor math ability in the first place. You freaking loser. Um, I don't like this model very much. Um, I think that probably there's some more nuance to it than the way I just described it, but it's a bit of an old school, like you underperform then you get anxious about it because again, you're a freaking loser. Yeah.

Ashley: 38:11

Yeah. And I guess built into this is some idea that there are some innate things that some people have that make them better at math or something.

Cat: 38:20

Well it's, it's maybe kind of agnostic to that. It's like whatever happens happens to make you bad at math and then that creates anxiety. Um, it's, I, you know, these kinds of like really one-way relationships are old school in psychology. I. Like, almost all the modern theories are much more like bi-directional, dialectical relationships that inform each other, you know? And I, I think the modern reduced competency people probably would acknowledge that, would say, you know, like you, you do get locked into this loop and then your, you know, your anxious experience creates worse achievement. But, you know, it is important to say, there's a lot of research where people have said basically, you know, the low achievement causes the anxiety.

Ashley: 39:01

Yeah, and I'm thinking back to that first quote we read earlier, which kind of describes this reduced competency framework, which is like, you know, this person is saying, um, my attitude towards math was affected by my low test scores. But you know, we, we ourselves like, may not even be aware of the fact that there is also this feedback where your anxiety is impacting your test scores.

Cat: 39:27

Yeah. And I, you know, there's a lot of. There's, there's a lot of times we look at individuals and we, our minds really prefer to make individual explanations. This is called the fundamental attribution error. And, and it's quite widespread and it operates in a lot of complex ways, but we make attribution errors a lot. So I'm very wary. Um, you may have heard around town that I'm a social constructivist, and so I'm very, I'm very wary of a starting place that's like an isolated individual, and I, you know, individuals are always in environments, so I. The third theory that I really love for where does math anxiety come from is this thing called the interpretation account of math anxiety. And it's a synthesis theory. It, it's the main one that's pushed by the review that I'm gonna link in our show notes that I read for this. But basically, this account of math anxiety says we need to pay attention to these like cycles of appraisal that are happening. Math anxiety gets cemented by how students interpret their previous math experiences and how they interpret that math achievement moment. So like the bad test score, you know, could be this initiating event, but why does that initiate math anxiety for some people and not others? The answer is kind of found in this appraisal cycle. So. This maps onto this really big thing in psychology that we call call appraisal theory. And essentially, this probably makes sense to you if you just think about your life. You know, we are always interpreting and making meaning out of the things that are happening to us. And then those, those are kind of like our theories. You know? Like what, cause what causes me to get this low math score? Is it the fact that I'm just suck at math and I'll never get better at it? You know, that's a theory, right? And that theory could be something we, we more or less believe in. It could be something that really gets cemented. I really like this account. I think that one thing that I really like about this model is it ties much more nicely into the way we talk about other forms of anxiety. I kind of noticed as I was reading these studies we're very clinical about math. We're very like, what's the cognition, you know, of math? And, and, and we're kind of like. I, I almost feel like averse to talking about the fact that there is a huge emotional part of this and a huge psychological part of this. And, you know, I think it makes sense to integrate like a clinical perspective from anxiety to math anxiety, but it was it very similar to how I feel like people reacted when I started studying code review anxiety and all these like older software engineers were just like, well, I know how to tell people to get over code review anxiety, get better at coding. And we were like, Hmm, doesn't match anxiety theory actually, because we see people who are very good at coding still feel really anxious. So the differences in these anxious rumination and all this other stuff and, and also like maybe we could care regardless of how good people are at the faint.

Ashley: 42:35

Yeah. I mean, do you think, like, so, so when you're like a little kid in school, right? You start taking these standardized tests and it's treated almost like this scientific fact about who you are. We can place you on this distribution of scores. You know, it's like, it, it has this air of being very objective, right? Very, like we're measuring a fundamental thing about who you are. Like, is that contributing to this treatment of math ability, you know, as like very like, I don't know, not, not appreciating all of these other factors.

Cat: 43:12

I would think almost definitely. There's, you know, I have a section of my notes here that's like, what helps, so what are interventions, what helps? And there's a whole area that you and I are pretty familiar with, right?'cause we're, we're curious about doing these ourselves. And, um, this is the area that you might describe as like narrative and mindset interventions. So this is like trying to help students get distance from the experience and trying to help them think about new and different theories for how abilities operate. And that shows success here. Um, so like for one thing you might think about, okay, well I want your, I want this student to think if I fail, this is a cue for me to escalate my effort instead of running away, instead of doing everything I can to not take math again, instead of like kind of self sorting myself off the track. You know, if, if we can get more students to like, put in a little bit more effort, like the benefit, economic benefit to their life might be huge, right? You'll, you'll get more students coming to you in college ready to become scientists or something because of these early beliefs. So people do intervene on those early beliefs, you know, and it does really, really seem to help. It. It is also the case that helping improve people's math skills help helps. you know, very directly saying, look, some people have been really underserved in their education, or they haven't done this memory formation, or they haven't learned these strategies. What can we do to catch them up? Actually, that skill building builds self-efficacy and I talked about earlier, like math flexibility. So I think that there's this whole thing which is like, if you can get to a place where you see this as an activity and a dynamic thing and a thing that maybe you, you actually have the capacity to do, you know, but, but no one ever introduced you to it and there could be many strategies and maybe you're good at a different kind of math. You know, for me, reading this literature, I was struck over and over again asking myself, do I even know what math is?

Ashley: 45:20

Like, like in terms of like, you're like, what kind of math are they actually talking about here?

Cat: 45:24

Right? Like it's really. Interesting to ask yourself. You know, I don't know. I, I was ask, I like to ask myself rhetorical questions'cause I'm always like trying to reform my identity, but as a, but, um, you know, am I a calculus person? Am I a geometry person? Like, I really think these little questions of like kind of interrogating what do, what do I think goes into this, you know, and, and, um, it's very complex. Different things go into these like different areas of math and I think that's something that we, math is just this monolith in our minds. And I love, love, love, love, like applied statistics. I love the logic problems of it. I don't love doing basic arithmetic.

Ashley: 46:06

Mm.

Cat: 46:06

Well, maybe some people do and that comes really quickly to them, and they have like a flow state when they're adding numbers or something. The fact that I do or don't have, that feels to me like it says almost nothing about what I can contribute in the world. It just says like, maybe I should bring a calculator with me to a restaurant. You know, like,

Ashley: 46:24

But back to the sort of interpretation theory, like some people would interpret that, you know, lack of a passion for adding numbers as being like, oh, well I'm not a math person'cause I don't get into a flow state when I'm like, you know, calculating derivatives or whatever. Like, and maybe. Maybe we need to be really careful about how we frame people's interpretations and like coach them through interpreting stuff, like standardized test scores or, you know, at, at my level, like when students fail an exam, like what does that conversation with the professor look like? Do they even get to have a conversation with the professor about what happened and how they can work differently, you know, in order to do better and that sort of thing. Yeah. Yeah. And I think the applied point is really important too. Like, and I see this in a lot of my students, is like, they, we learn math really abstractly most of the time. It's not applied to data and numbers from the real world. And then it just becomes this kind of thing floating out there and, and none of us wanna do things that are floating out there without any grounding in reality. I mean, it's like really helpful to have that grounding and be like, these are statistics that are useful for understanding the world.

Cat: 47:37

Well, actually I think some people struggle on the other side. Some people prefer the really abstract and then struggle with the, you know, that's an interest. So like, but the point is I think the larger point is really good, which is just like, how stupid to let this stuff block us. You know? If it's just differences, you know, and the same, you know, we want to think about how many people can. Succeed in our world. We want this pluralistic, you know, collection of humanity to succeed. And I, I really left reading all this literature thinking math anxiety is a huge problem. We're not talking about it. It's really common. It's weird that we're not talking about it. It's here. It's not an, an, an, an anomaly. It's like so common that you might just expect a lot of people around you to have it. And we have these people showing up at every level of our society. And I think the answer is not to just say, well, you, oh, well, you know, because there are very malleable parts of this. And I think that our, our mindsets are a great malleable piece of this. You know, to go back to those elementary school teachers, you know, like there was this interesting research that showed that people's stereotypes, like first and second grade teachers, their stereotype endorsement went along with math anxiety. So like, the more that you thought. Boys are probably good at math and girls are good at reading those kinds of stereotypes. The more likely you also were to just have math anxiety in general. So, you know, I'm really interested in like our networks of beliefs and how we kind of get stuck in these like tragic patterns that limit us. You know, and I think this is one of them, you know, that we really fall into this trap thinking ability beliefs. Um, you think, you know, thinking that ability is fixed and yeah. Intervening on that seems really productive. You know, this was such a fun episode for me to prep for and do like, I feel like I, I found a place in the math universe. I was reading this big lit review that was about the cognitive factors, you know, not the psychological stuff, which I feel really like I have a lot of expertise in, but actually the cognitive factors. And I, I feel like when I opened up this paper, I was a little scared that I was gonna like, read about something that I felt like I wasn't good at, and then, and then have my fear confirmed that maybe I'm not a math person. Like it was still in me. Right? And, and that's not what happened. Like, I read this lit review and I was like, Hmm, all right. You know, I think I have some of these cognitive factors pretty dialed in, and then I can remem, you know, and then I think other, other ones maybe I don't have, and, and, you know, maybe I'm somewhere pretty average on the spectrum or the distribution. It all just became not loaded anymore. It just became like, oh, well some, you know, some people have brown hair and, and what do we, what do we do with that? You know? And I think. Un unloading that and taking all of the like, judgment out of it, you know, and, and really saying, I, I want all people to succeed. And there were so many pieces of this early math ability stuff that just felt like, you know, if you have a slightly harder problem, uh, time learning vocabulary, and then you're a little slower following a word problem about math in your elementary school classroom, that is not what should determine the fact that you could be a scientist later. It's just a thing that happened to you and we know how to make it better, and it, it doesn't say anything about your worth, you know? And, and also I think there are just domain specific skills and domain general skills, and we're pulling on all of them in every moment of problem solving. And this like hunt for some mystical single ability. It's really letting us down all the time. Like, you know, one of the things that I saw in this research was even in this deep lit review where they tried to model these cognitive factors and they ended up estimating across all this research. They were like, we can maybe account for like 29% of the longitudinal variance in arithmetic kind of outcomes for students. You know, that's like impressive, you know, 30. But like that leaves,

Ashley: 52:01

on. Yeah.

Cat: 52:01

it's a lot more going on. And that area that like 70%, 71% is just like, here be dragons.

Ashley: 52:12

Yeah. So there's this power in, you know, realizing like, one, we can separate the, the, the, the really terrible feelings from this like, and sort of look at it straight in the face and be like, what is going on here? Like, what determines to some degree or like what helps math ability, I guess, like separate from. How we feel about it. Like, it seems like you're, you're saying like disentangling the feelings about it is, is a powerful thing that we can do. And secondly, to acknowledge that like, you know, even in this perfect world where we've measured a lot of different things, like there is just the nature of like human ability being really multifaceted and like us problem solving in like so many different ways. And it's not as if math ability is one thing. It's really, really not