There's No Such Thing as Not a Math Person with Rachel Thomas, P.H.D

I am so honored today to introduce you to Rachel Thomas, who is a mathematician, a data scientist, activist, I would say, and mother to a child who absolutely loves math. The greatest achievement of all. And I've benefited so much in thinking about, with Rachel and our partner about ways to support children not just in math, but in all subjects. And so just so grateful for her to be here today and share her insights and thoughts on how to help your child with math. Whether you think of yourself as a math person or not, a math person, which I believe we are about to learn, does not exist. So thank you, Rachel, and take it away.

Yeah, thank you, Manisha. Thanks so much for hosting this. So let me share my screen. All right, so helping your child with math if you're not a math person. Just briefly, a little bit of background about me. So I have a PhD in mathematics. I worked in the tech industry as a data scientist and software engineer. I've taught in a bunch of different contexts, kind of going back to when I was a teenager as a tutor. And I'll talk more about kind of some of my teaching and tutoring experience later. And then six years ago, I co founded Fast AI, which is a nonprofit research lab making AI more accessible to a broader, more diverse group of people. And we have the most popular massive open online course in the world on deep learning, which is kind of a subfield of AI. And so I've also gotten to kind of experiment with some really different formats for teaching with online and massive courses. And I've also been a university professor the last six years, first at University of San Francisco and now at Queensland University of Technology. So today I want to start with talking about some of the kind of broader obstacles to liking math to kind of better understand why so many of us may not. I think that's helpful to realize that if you or your child having problems, it's not just about you, that we are kind of in this. And I should note, I know that many of us may be from different cultures and I am kind of speaking from a Western context and kind of as a white woman who spent most of her life in the US but to talk about some of the, the trends there. And then also it's important, there are a lot of myths that I think it's helpful to counter with our, with our kids. And then I'll touch on some more practical advice of kind of what, what are some things we can do about this? And then we should, yeah, hopefully have plenty of time for Q and A and discussion. So I think Western Culture is awash in a lot of negative feelings and attitudes about math. I'll just share a few anecdotes and I feel like I have so many that I've heard kind of over the years going back and I should share. I lived in many places throughout the U.S. i grew up in Texas and then I went to undergrad in Pennsylvania. I did my PhD in North Carolina. I moved back to Pennsylvania, I moved to California. But in undergrad, the minister at my church, when he heard I was a math major, his mouth fell open and he just looked hor and he was like, but Rachel, I thought you liked people. And this kind of perception, I think of math as being antisocial or kind of the opposite of liking people. Another story is on a plane once in graduate school and the man next to me had maybe a six month old baby in his lap and he's kind of cooing to the baby and he's like, look at her, she's doing math. She's never going to use that again. Kind of talking about me in third person sitting directly next to me. And then another final, final anecdote. In San Francisco, my partner and I were touring a private school that we're considering for our daughter. And the principal talked about the, she mentioned like this math curriculum the school uses. And she's like, oh, but my brain doesn't work that way. I don't understand any of that. And so this stereotype that I'll talk about a kind of certain, the idea that certain people's brains don't work the right way to do math. And so I think these messages can be very pervasive and come from a lot of different sources. And I kind of want to dig into, dig into some of those sources. So one really, really unfortunate one, this is a study from the U.S. shows that. So in the, in the U.S. and I think this is true in many countries, 90% of elementary school teachers are women. And when women elementary school teachers have math anxiety, girl students pick up on that. And it was interesting. Boy students are less susceptible to picking that up from a woman teacher. But this is very common and many elementary education majors often require very little math. And so this anxiety can be picked up on by students. So this is, this is an issue. There are also a lot of negative stereotypes and narratives about race that can impact students and that can kind of influence how teachers treat students, particularly indigenous black and Latinx students. And so this was kind of an interesting paper on that and there was a nice write up in the Atlantic about it from a few years ago. So there are, there can be at school kind of negative, negative messages about math and also about who kind of, who's capable to do math. And so there's a kind of this pervasive myth that math is this innate ability. And Dr. Omaju Miller got her PhD in computer science education at Berkeley and studied this and she's given a TED talk that I recommend about this myth of innate ability, which kind of applies to tech and to math. And this is the view that certain people's brains are wired to do math and other people's brains, brains are not. And the evidence is all against this. Like that is it's not accurate. But the problem is when people believe that it's true and so believe that, you know, you have to have a certain type of brain to do math, it can become a self fulfilling prophecy. You know, people think I'm not good at this or I'm not capable of this. And then that can end up, end up playing out. Another set of obstacles. Kind of comes from how math is traditionally taught. So in standard schooling it's often taught in a very kind of vertical manner where each year really builds on the previous year. And so if you have one bad year, it can often be almost impossible to catch up. And so that'd be kind of like, you know, pulling the red block out from the stack. There's nothing for the green or blue block to build on. And this is very different from subjects like history. Like if you have a terrible history teacher one year year, you usually can still be fine the next year. Whereas math, it can be very hard to recover from a bad year without support. And I have, I found this in talking with people. A lot of people can kind of pinpoint the year that math went bad for them. You know, they'll say, oh, I liked math as a kid. And then, you know, I had this teacher I hated in fourth grade and it was, you know, it's never the same after that. It can also, it can be circumstances in your personal life of people that were dealing with bullying or peer pressure. Again, if it kind of threw off their math education because of this, this vertical way that it's taught, it can, it can make it very hard to recover. So there's a really, really gorgeous essay by Paul Lockhart that I recommend called A Mathematician's Lament. And Lockhart writes about a nightmare world where children are not allowed to sing songs or play instruments until they are in their 20s to spend a decade or two studying music theory and transcribing sheet music by hand before they should be allowed to sing. Because the idea is, you know, until they have kind of technically perfected all the details, they shouldn't. They shouldn't sing. And obviously, this is a terrible idea. It's great that we don't do this, but Lockhart argues this is. This is what we do with mathematics. And the subtitle is How School Cheats Us out of Our Most Fascinating and Imaginative Art Form.

Form.

And so the. Yeah, that there is a lot of creativity that's. That's possible within math, but that a lot of education is kind of very focused on knowing all the kind of technical details and components in a way that's. That's not appealing. And I should. Oh, I should also note about Lockhart. Lockhart was a university math professor, but he actually felt that math was kind of being taught so poorly that he went back and switched to becoming a K through 12 teacher because he really wanted to change how math was taught kind of at the younger ages. Another book that has kind of influenced my own. My own thoughts about pedagogy, and this has really kind of informed our work with FAST AI and how we approach teaching is called Making Learning Whole by education professor David Perkins. And Perkins uses an analogy with baseball, and it's a kind of similar idea. He points out that, you know, we don't. You know, kids can play baseball, and they may not be fielding, you know, a full team with every position filled and playing a full nine innings, but they can get a sense of the game. And he has this idea of kind of the whole game and getting a sense of the game, and that we really kind of rarely get that in math because we are kind of, or I should say, our education system is often overly focused on kind of these technical details that can obscure kind of the broader meaning. And I found this, even as someone that did quite well in math growing up, that I was good at learning techniques and memorizing stuff, but I often did not understand the meaning until I got to kind of university and even grad school to kind of get the deeper meaning. And this is very unfortunate that math is often taught this way. So a mathematician I admire is Piper Heron, and she completed her Ph.D. at Princeton in mathematics. And so her thesis, you can see it's on a technical topic, the redistribution of lattice shapes of rings. But she wrote her thesis in a really novel way where she tried. She used humor and sarcasm and analogies about unicycles and really tried to write it in a way that was more accessible than it would otherwise be. She also wrote very openly in the prologue of it about how alienating it was for her as a black woman in higher education in mathematics. And she wrote, my view of mathematics is that it is an absolute mess which actively pushes out the sort of people who might make it better. And this is sad, but also resonates, resonates with my experience of a lot of kind of toxicity in higher education in math. And it's, I think, important to recognize that because that does, that does permeate down, I think, and end up kind of affecting, affecting all levels of mathematics. And then it, you know, what she's describing here is also kind of how it can cultures can self perpetuate themselves, kind of by pushing out the people that could make them better. Another mathematician I admire is Cathy O', Neill, who has her PhD from Harvard. In 2016, she published the book Weapons of Math Destruction, which talked a lot about how data and algorithms are fueling inequality in a kind of a variety of areas, actually, including education, but also in the criminal justice system and employment and hiring. I mean, really looking at the social implications of big data. And she, she's written an essay, A Mathematician's Secret. We're not all Geniuses. And she says, you don't have to become a genius to become a mathematician. If you find this statement at all surprising, you're an example of what's wrong with the way our society identifies, encourages and rewards talent. And so she kind of addresses actually a few myths here. You know, this myth that you have to be a genius to be a mathematician, also the myth of the lone genius. And she talks about how a lot of work actually is really collaborative, but that's often not recognized or honored. So just in a kind of summary, some of these obstacles in traditional math education include these cultural myths about innate ability. You know, the idea that there are certain types of brains that can do math versus not, which is totally false. Myths of the lone genius. Racist and sexist stereotypes. Also adults, math anxiety or negative feelings. And this can even come from teachers, principals, kind of a variety, variety of adults. The vertical manner that math is taught in, where it can be hard without support to recover from a bad year. And then with traditional math teaching, a lack of art and creativity, kind of not showing the whole game, letting children get a sense of the game. Overly focused on memorization, overly focused on technique without meaning. And I think it's helpful to kind of see what some of these obstacles are, to realize that in many ways this is a systemic problem. And there's not necessarily going to be a silver bullet. And also to try to counter some of these myths with your kids. So what, what can we do about this? What are. Yeah, what are some things that help? I want to start by sharing a pretty transformative teaching experience I had. So I started working as a math tutor, you know, part time as a teenager and continued through undergrad and graduate school. And I had also, I had taught fresh calculus kind of as the teacher. And then much later on, kind of after working in industry for a few years, I went back and taught at an all women coding boot camp. And so this was for adult women that were changing careers. And the first half of the program was kind of much more traditional, teaching a class. And then the students would do exercises in the lab. But then for the second half, the students would build their own projects. And they had a huge amount of kind of freedom in what they chose. And they were often, you know, using libraries I had never seen before. They were all doing something different and complicated. And prior to this, I think I had always seen teaching or tutoring as kind of ideally me guiding a student towards an answer. But there was this assumption like, I need to know the answer in advance. And I didn't always, but I often did. And I always felt like I should know the answer in advance. And so helping the students with their kind of, you know, differing freeform projects that are all using different libraries was the first time where I really almost never knew the answer in advance and people would ask questions and it was like, I don't know. And really forced me to recognize that kind of the thing I had to offer was teaching my process of how I find an answer when I don't know it and what are the things I try first and what do I look at. And so this was really transformative for me and something I do try to keep in with my daughter, but of modeling. When I don't know something, this is how I try to figure it out. And also being okay going down dead ends and letting people see this. I've tried to keep that in mind, although I think the inclination is still often strong for me to feel like, oh, but I should know the answer, but it's okay to. And I think it's actually really valuable to model that not knowing. So there are many really fantastic online resources and apps that I'm going to kind of share this. I'm going to come back to this list. But first I want to address the issue of screen time, because this is something I've had many discussions with other parents about, and I know that many parents feel pretty hesitant about screen time. So I will show the list again in a moment. Yeah. So what about screen time? I really think that the idea of screen time is too broad as a category to be useful on its own because it has several axes. And so my way of thinking about it is screen time can be solo versus relational. And for relational, that can include if you are on a video call with a loved one or if you are sitting next to a parent or someone in person doing something on a screen together. It can be educational versus and perhaps I should have written non educational educational versus not. And it can be active versus passive. And within these, I would say my concern is primarily around screen time that's solo and passive and non educational. But to make this concrete, let me give some examples. So I've got a Venn diagram. So screen time that is relational but passive and recreational is. My daughter's favorite show is Bluey, about an animated family of dogs. It's a really, it's a really sweet show. I really like it. And we watch it together as a family in the evening. And I do, I think recreation is important, but that's something that we do together. Something that's educational and relational would be sitting with a parent watching an educational video together and discussing it. Active and relational would be. Yeah. Skyping with the grandparents. We've, we've always lived kind of far away from sides of our family and so kind of from a young age my daughter's used to. Yeah. Having video calls with relatives and that, that's like a meaningful, a meaningful part of our relationships. The kind of the sweet spot. Or I shouldn't say the sweet spot. I think these all have their purposes and uses, but kind of combining all three, relational, educational and active, that could be sitting with a parent doing an educational game together on the tablet. My, my partner and our daughter have often they'll like work through an app together and they'll even alternate like taking turns answering questions. So it's kind of like a back and forth. My partner answers a question, our daughter answers one. I also see things of my daughter playing Minecraft with a friend and they're on a video call and so they are also kind of chatting and hanging out as they play. And then I mentioned kind of the category that we really try to avoid and we have, we have used it in desperation before, but is having a child watching a movie on their own. That's, I would say, like the one that we don't build into our daily lives and kind of really see as like a last resort. But I have found that many, many conversations about screen time, I think it really collapsed because people are kind of just talking about one category or kind of talking about it as one monolith. And often that monolith is, I think, based on kind of the worst. The worst incarnation of it, of a child on their own doing something quite passive. I should note no judgment. I realized that particularly with the pandemic, there have definitely been desperate times. But this is a framework of how I see these different categories. I just want to note on this slide, I am going to mention disordered eating, and I'll probably talk about this for two minutes. There's also, I think, a related question of if something's really desirable to children is really restrictive, kind of a good way to reduce or control their desire around that. And there's a whole body of research kind of coming from the area of food and eating showing that that's not the case. And so you have studies such as this one, which talks about restricting access to palatable foods. And here, palatable foods means kind of sugary, fatty foods, showing that this actually focuses children's attention on the restricted foods, increasing their desire to obtain and consume. And so that this is kind of this backfire effect, I think, of creating a forbidden fruit. There's other research showing that kind of over being overly restrictive or restrained around food can even be a predictor of binge eating. And so I think this is important to keep in mind of kind of in thinking about desirable things for kids, of the idea of being overly restrictive, backfiring. All right, so to return to my list of online resources and apps for, for kids, I do want to note a key, I think is really sitting with your child and working on them together at least the first few times. I think it's way, way less effective to kind of just, you know, give your child the app. Oh, Manisha has her hand up or no, you're clapping. Okay, Manisha's clapping. Yeah, that it is really, yeah. Really important to sit with your child. Also a way of making it relational and kind of really helping them to get in the flow with it. And also, if you have not checked out educational apps in the last five to 10 years, there have just been, I think, major, major advances in terms of programs that are incredibly visual and incredibly well thought through that are really fantastic. And I do. I want to share about another transformative education experience, and that's with my own daughter and so this was with the pandemic. We. Yeah, so the pandemic totally upended our plans, which I think is true for most people. And prior to it, our daughter had attended an in person Montessori preschool that she was kind of at all day. And then we ended up having her at home with us for 12 months. And so we had not been planning to homeschool but we ended up trying modulo with Manisha. And my daughter participated, participated in what was called Kids Club. And she was with a group of, I think it's just about four or five kids, it was quite small, with a tutor. And what they did for math is they would spend an hour a day and the children would just play a math game, each on their own device. And they were all, you know, connected on a video call. They could screen share if they wanted to ask for help or chat about it, but they could all totally go at their own pace. And this was really, really amazing to see. Like I don't think I had seen an educational program that was so centered on kind of, this is mastery based learning to let children go at their own pace. And it was really fantastic. And I think this is another limitation of traditional schooling is that I think often many of the kids are bored because the subject's going too slowly and many of the other kids are bored and lost because it's going too quick. And this can even vary from topic to topic. Whereas this approach of each kid getting to work at their own pace was really, really powerful. And I think that most of the kids that did this ended up actually incredib advanced and covering a lot of material. And we actually didn't even have any educational goals for our daughter at this time. She was in this weird limbo where her, where her birthday is. She had just missed the cutoff to start primary school. And so she was five years old and really she was ready for what in the US we call kindergarten and Australia is called prep. But she had missed the cutoff. So we didn't even have like this is something she has to learn. But she actually ended up kind of several years ahead. Just through this, she was having fun playing a game for an hour a day with a group of, you know, a few children that she became friends with and a tutor. And so that was, that was pretty powerful. And I should note Beast Academy does have a book, book version that's paper. And we recently have also been trying right start math which is a, involves a lot of manipulables, so kind of things that children can do with their hands. And that is also kind of a not screen based approach. So again, just. Yeah. A reminder to try to counter the myths on. Yeah. Myths of innate ability, myths about having to be a genius or myths about a kind of alone or solitary genius. In summary. Yeah, I think it's helpful to recognize the cultural and structural factors we're facing and some of the challenges with how math is traditionally taught to counter the myth of innate ability to be okay. Modeling, not knowing in the process of trying to figure it out. And that it's I think fine for your child to see you go down dead ends trying to figure something out because that is, that is a lot of life and a lot of solving hard problems is trying stuff that doesn't work at first. Adaptive computer based learning I think is. Yeah, there have just been so many kind of improvements in this and really kind of engaging tools that can be supportive. Really sitting and working with your child and making it relational. Also say an outside tutor can be helpful to change the dynamic sometimes. I know. So I've gotten to this with my, with my daughter and practicing the piano. If my partner or I suggest it, you know, she really doesn't want to do it. That recently we've tried kind of having her do it on a video call and if somebody else suggested it's like, oh sure, I love playing the piano and you can kind of sometimes change up the dynamic. Yeah. So that's, that's some advice I have. And I see that there are comments in the chat. Actually haven't been checking because I can't, I can't read the chat while I, while I talk. But yeah, let's head into Q and A and I will, I will catch up on the chat as well.

Wonderful. Thank you so much, Rachel. This was absolutely fantastic. I think. Should we stop screen sharing so we can see?

Oh, yes. Yeah, let me stop sharing. There you go.

Yeah. And thanks again to everyone who came out today and I. Such a rich and wonderful presentation and so fun thinking back on these last two years of checking out different apps and seeing what works and what doesn't. And I really want to highlight one of the big points you made, which is around modeling. A lot of the questions we got were, you know, how do I help my child with multiplication and things like that. And I think that, you know, kind of starting from this place where first of all understanding that we all have our own anxiety about math, you know, and if you're coming from a place where you feel anxious about math, Math, your abilities in math Yourself, your child is going to pick up on that whether you articulate it or not. So actually sitting down and learning with your child and acknowledging areas that you have difficulty and saying, like, okay, well, how do we learn multiplication tables? This is kind of complicated. And like any other problem in your life, saying, well, should we Google some good techniques for learning multiplication together? And I think if your child can see, watch as you struggle and show grit in learning something that's hard for you, that will also inspire them as well. So, yeah, so I think most of the comments were complimentary, Rachel. And we will send the resources that Rachel suggested to everybody after the workshop. And so, yeah, if you have a question, feel free to put it in the chat or raise your hand. I think we have a great question here from Madeline. Would you recommend these for older math phobic adults, older teens? What else do you recommend?

And I should also, yes, say that kind of having a younger child I'm still learning about and exploring options for older children. It's actually really, I defer this to you, Manisha. I mean, I will say my, my partner is actually doing a kind of a deep dive on various math curriculums right now and is going to write something about this that, I mean, something we are seeing also is that there's no one math curriculum or one math app that does everything well. There is kind of. They all have different strengths and weaknesses. And so there is also an element, I think, of kind of tailoring of kind of what in particular you're studying and then what are the strengths of. You know, some are, I think, great at being visual or great at having manipulables where you're kind of able to engage in this more tactile way. But that it's, I don't know that there's anything that does everything. In fact, there's not anything that does everything well.

Yeah. So in the beginning of the pandemic, I did dozens of consultations with parents around their children. I think there are definitely different tools that work better for different kids. And when you have have a teen who over the years has developed really low confidence in their ability to do math, which I think primarily comes from trying to catch up with other kids in your class, Everyone is supposed to learn at the same rate, but in fact, people learn at different rates. And then you miss an important concept and you fall behind, you start thinking you're terrible at math or maybe you're brilliant at math, but you're a terrible test taker. All these different kinds of problems. So it wasn't on Rachel's list, but one of the tools I like to start teens at with this just prodigy game. I think it can help a student to kind of build back concepts that they've missed. And what's nice is they're kind of these big, you know, you can win battles and get points. And so I found with kind of 12 or 13 year old crew it was just a foundation that helped them start feeling like they were actually good at math and they could catch up at their own rate. And then on modulo we actually built a curriculum planner where you can answer a couple questions about your child's learning style and, and get tools recommended to you. And I found that's pretty consistently good across the board. So sometimes you can use that as well. And I recommend playing around a little bit and going from there. Hope that's helpful. Yeah, go ahead Rachel. Sorry.

I would say so I see a question from Julie. It's one thing to encourage development into healthy math mindsets at a young age, but how would you approach a student who already is kind of set in these negative math beliefs beliefs say in high school or middle school, especially while trying to avoid sounding like you're just lecturing. Yeah. And I think, I think that can be a tricky balance. I do think as students get older they also can hear some about the, you know, hear more about the kind of the origins of these beliefs. And I think it's helpful to hear the research on kind of how, how pervasive these myths are and that they're, that they're not true. Something else I actually almost had a slide on this is I know there's been research say for, from like UC Berkeley where they overhauled their engineering curriculum to include a lot more kind of problems related to social good around like cleaning water or kind of more applications that had kind of like clear social benefits and found that this really increased the number of women majoring in engineering. So I know sometimes the kind of the particular application or being able to connect it to something that the teen cares about could potentially be helpful. Do you have anything to add Manisha or.

Yeah, I mean I think always as a tutor my first step is building confidence in the students ability to do it. So even if you can help them kind of score really well on one quiz and then you know, afterwards. But I, but I always say coming. I always start with number one, acknowledging feedback. Math is really frustrating. I felt that too. In this context. In this context, in this context I think that we can find some good tools to help you Improve at math. Are you open to trying? And then as the student sees that they are succeeding, then they start building confidence and it kind of spins out from there. But I think that always, always in communicating with young children or teens, starting with where they're feeling right now, not jumping to, oh no, you're good enough math. Oh no, you can do it. But this is frustrating. I felt this way too. Here are some things I think that can help. Are you open to trying?

Yeah, no, I definitely agree with that. I guess another thing I thought of also is I feel like, to not push on things that they hate. Like, I definitely, you know, like, if we see my daughter doesn't like something, we don't force it because we don't want her to feel more negatively. But really kind of trying to find is there something else that should be more amenable to and showing like I think, yeah, acknowledging like, hey, you really don't like this, this particular thing. So. Next question from Madeline. Any tools you would recommend for folks with learning disabilities who have trouble with notations? Yes, I think if, yeah, if you're having trouble with kind of the math notation, I am still maybe early in this, but I think potentially something like right start could be helpful with. It's just a lot of kind of physical objects that you move. And so I think that could be helpful that it's kind of less. Seems less notation based so far or even I think Matific was pretty good at having a lot of kind of visual like you're seeing. Seeing the areas or the shapes. So I would, yeah, I think recommend towards kind of physical objects and also visual things that are less, less centered on kind of just written notation. I see a question about what are your thoughts about standardized testing for high school students? Sat, psat, act? What does the latest research on this say? Which I'm not sure if you want. If you want to clarify Jitendra more more specifically, I think standardized tests are still required many places so they can, you know, they're necessary. I know some colleges are doing away with them now. You know, I do think it's, you know, it's been unfortunate and harmful that so much of our education or sorry, I shouldn't say are, but I know US Education system has really, you know, focused on teaching towards tests to various tests and that's, that's been pretty harmful. But at the same time, these tests can act as, you know, gatekeepers for opportunities and so can. Can be necessary. But feel free to clarify if you wanted. If that's not the question, you are asking? Jessica asks and yeah. Hello, Jessica. It's good to see you again. Are there any good resources for high school age children? I know my child is very much into art, but is feeling doubtful about her math ability despite being quite good at it. That's a good question. Something that springs to mind, I think for someone good at art. And you're probably already doing this, I mean, I would definitely recommend some of the kind of artistic computer programming options. I think with JavaScript you can do some really kind of visually appealing, fun things that I think would have, would be appealing to an artist as well as kind of looking at kind of various AI artistic generation tools that I think could hit from the art angle and kind of also have a pathway into further math. Let me pause and ask Manisha if she has additional recommendations on that.

Yeah, it's interesting. I mean, this question and the last question about learning disabilities. I think I like to think about like the term neurodivergent. What I found as a classroom teacher is that there are so many different learning styles and there's this particular type of kid that is really good at learning the way school teaches. And that's maybe about 10% of the children and the rest are, you know, labeled, you know, are neurodivergent. And so it's not like there's one type of normal and then there's the neurodivergent. Actually there's so many different ways. And so I think that's why it's really important to explore the resources that work for you. I think one of the reasons I am a good tutor is because I was really terrible at test taking myself and especially on math exams. And so when I tutored, I was trying to teach the kids as if this is a game, you know, like in this world there are people who think in certain ways and this is one way of thinking. And here's how you can learn this game of thinking. And then in terms of, you know, just this question about art, you know, I mean, there's so much interesting overlap between art and math, obviously and you look at some of the great painters. But I would say that, you know, for, you know, explore different tools and I would say, I would think that the area to really hone in on is the doubtful, doubtful about her math ability. And we talk a lot about this idea of, you know, in our culture, we're very much praising kids like, you did great. You're not doing well. Instead of bringing the focus to like, wow, I really admire how you pushed past, through that difficulty, you know, and actually talent really being about. What do you do when you confront an obstacle as opposed to the result at the end? So I would say, you know, really kind of like focusing on that area. Why is she doubtful about her math ability? And how is that impacting her? In other words, ways. Not sure if that helps answer the question.

Sorry, I thought of one more thing while you're talking about that, and that was the areas of combinatorics and permutations. So there's kind of these whole fields of math that involve different problems of, I don't know, like, how many ways are there to divide these donuts up amongst a group or coloring problems of kind of where, like the borders of different colors. I'm not explaining this well, but there's this area of math that has a very, very different flavor from algebra and calculus. And this is another kind of gripe I have with traditional math teaching is that so often this goes under. It's called discrete math, and it's typically taught in college and required of computer science majors. But I feel like most other people don't get to see it. But it's math with a very, very different flavor from the algebra sequence. And it makes me kind of sad. I think a lot of students in high school, you know, kind of go through the algebra sequence and maybe kind of start calculus, and they're kind of, I think, just getting one flavor of math and not seeing that there are these other flavors. And so I would, yeah, I think, also recommend looking into discrete math or combinatorics because it is kind of a different flavor. And that could be helpful also for. And to me, I don't know, it seems a bit more artsy. But I think for someone that, you know, if the algebra calculus sequence is not really kind of resonating with their interest.

I think I should also just mention, I mean, there's huge debate about the way that math is taught in school and what math is taught in school. And, you know, very, you know, knowledgeable people would say that the whole curriculum is totally ridiculous and useless. So I think it's worthwhile to be open about that with your child and say, okay, well, then, you know, if this is silly to be learning, why are we learning it? Well, okay, there are some benefits. Benefits to doing well in school and such, how you can advance in life. And there's benefits to learning the way that other people, you know, so really, you know, get specific about why they're learning it and figure it out, Help them figure it out, help you figure it out for yourself. Because unfortunately, being a child, a lot of time means just doing what people tell you without any real reason why. And a lot of people don't take the time to really understand it themselves or explain it to kids. And I find, you know, when I really, really get specific, you know, know, with children, they really resonate with it. You know, even if it's, you know, for example, a six year old, you know, I don't want to learn, you know, how to draw well, you know, if you don't develop your fine motor skills, here are the consequences. Do you know what fine motor skills are? Oh, like, do you understand this is an age where it's important to learn them. And you know, you can talk to a 6 year old about that just as, you know, you can have a real conversation about stuff with the teen and let them decide if they want to opt in or not. You know, it is important to respect them in that way.

Yeah, and I definitely agree with that. Kind of distinguishing the what are the things that you're doing? Kind of like the SAT question earlier where, you know, aspects of this are just about this ritual that's needed to access certain opportunities versus things that you find more intrinsic value in. And definitely had conversations with my daughter also about kind of like related, like what are things we do just because they're kind of social conventions that kind of are generally accepted in society but we personally don't think are very meaningful versus things that are really kind of about our family's values. See next question. So there are questions about U cubed and Moems and Math Kangaroo. And I have to admit, so U cubed has been on my list to check out, but I have not yet. And then I'm actually not familiar with, with Math Kangaroo or Moems, so I cannot speak to these. I don't know if you have views on these. Manisha.

I have not used UQ ed myself, but I know the team who created it and they're awesome and they're really passionate about bringing data science into class. There's a whole class about learning to love math that parents can take. So I think it's a really interesting and wonderful approach. And I'm not familiar with moms or Math Kangaroo, but I think if your kid is into contests, contests can be fun. If your kid gets stressed out by them, then don't do them. So that's how I feel about that.

Madeline asks, when someone's facing a math problem and starts to panic or freeze, are there questions you recommend asking by a tutor or for people to ask themselves to move closer to answers. What do you personally do? I think, I think a lot of Manisha's advice earlier about the importance of kind of confidence building and trying to find some areas where you can build confidence through wins sounds helpful as well as I think probably talking about tactics of just how to deal with panic and anxiety. Do you have more to say on this, Manisha?

I have so much to say on this, but I think first of all, really recognizing the feelings like that, noting being the first part of it, not trying to jump to confidence before you say, I see.

Yeah, yeah.

And make sure you understand. They may say, like, no, I'm not scared, I'm excited. Right. You don't know. Right. And then, yeah, I mean, it could be a bigger problem. But I think it's really about really kind of getting in touch with what they're feeling. I think I hear a lot of times people say, oh, my child is such a perfectionist. And I think I don't quite agree with that term. I think there's something deep beneath that that needs to be noted, which is like, what's going on with the perfectionism? And really is. I think it really does often come back to like, are you praising hard work or are you praising character? That they can't change. They can't change if they're smart or I don't want to say dumb, but they can't change, you know, their iq, but they can change. But something they have power over is how hard they work. And, you know, I think, yeah, just really, you know, just really all the time coming back to acknowledging other feeling. And, you know, you can even go further and say, like, where do you feel this in your body? Is it, you know, what is it kind of a buzzy feeling or is it jumpy feeling? And, you know, talking about that physical sensation of the panic there's great. My mom used to play Mozart when I did math. A nice snack can be setting up the environment away and then relating to it. You know, if there are things that you feel scared about in your life and how you overcome that.

Yeah, no, that's great.

Yeah.

And I definitely, definitely second and agree with the. Yeah. Acknowledging and understanding the kind of the underlying. The underlying feeling.

And we have.

Yeah, we've done. My daughter actually loves this for kind of negative feelings to go through. Like, we ask her, like, what color is the feeling and how does it sound and to really. And this is maybe like a kind of younger age. But yeah, she really kind of enjoys that sort of Kind of descriptive of coming up with that sort of description.

Just one quick thing too. The words lazy. I think some parents perceive their child as lazy. And I think actually laziness can be a manifestation of some really deep fear. So fear can, you know, nervousness and fear on math can take different forms. Not always a panic attack, per se.

Jessica has made a recommendation for manga books about linear algebra and regression analysis, which sound really fantastic. So I will, I will check those out because, yeah, I love, whenever you can kind of have a different, in a more kind of visual or fun format presenting material and then Jitendra, et cetera can qualify his question. So do you want to do that now out loud?

Sure, Let me just turn on my camera. Hi, thank you so much for this talk. Rachel, big fan of your work with FAST AI. Thank you so much.

Thank you.

So my question is actually my daughter is a sophomore in high school school. So bear with me until I quickly give her backstory. Way back in fourth grade, she started to feel a lot of peer pressure. She grew up very close to two very good friends who were breezing through their math, whereas she always had to struggle. Now slowly through middle school, we, we always did exactly what I loved. What Manisha said, acknowledge first. So we used to acknowledge her feelings and her emotions and her struggle with it. But we always encouraged her. And then she, she started gaining some confidence in middle school. She on her own started to develop more and more skills and we helped her accordingly. In middle school, she was able to jump one more level in the math curriculum. And then by the time she came to high school, she had jumped two levels. And then now she's in the highest possible level in math. Now we didn't want her to do that. We wanted all of it to come intrinsically on her own motivation. And she, we wanted her to do it because she wanted to do it, not to prove anything to anybody. And now in the high school, she is going through the pre calculus honors. But the key argument we still keep having is she struggles with, with every concept, every chapter, and she has managed to still do well in her testing grades. The point is, her point is that if I struggle, it means I don't get it. That means I'm not good enough for math still. And our point is, doesn't mean anything like that. People have different styles of learning and therefore your style is slightly different. But struggle does not, is not an indication that you don't get it as well as anybody else does. And then a small supporting part of this argument was David Epstein's book on titled Range, in which he is talking about this particular aspect where some students struggle through math and they actually take a longer time, they take a different route, but they get the concepts in a much more deeper way. So I felt that the standardized testing seems to impose a sort of a time limit and that seems to, you know, mess up her understanding and therefore she runs into panic. So let me pause here and see if you have any thoughts or reactions.

Yeah, no, I agree that the standardized testing. Yeah. So what you're saying, like I, yeah, I agree with you that yeah, even. Yeah, it's really unfortunate that people often associate being good with something with the idea of being good with it effortlessly. That those kind of concepts end up coupled even though they shouldn't be. And that kind of being good at something, even if you have to work hard or I mean that can be even more meaningful that you're working hard. And as you said, you may be learning it more deeply. It can also be really hard to compare what's really going on with other people. I experienced this in school of people that I sometimes thought were doing well effortlessly and that turning out to not necessarily be the case. So you don't always kind of know what's going on inside with someone else. But yeah, I do think standardized testing poses the set of issues and I've definitely known people that do very well in their schoolwork and then yeah, not as well on standardized testing and that it becomes this, I think definitely like ongoing source of anxiety. And I don't have a great strategy or solution kind of beyond what we've already discussed in terms of acknowledging and trying to address that anxiety. Yeah, I don't know if you have something more specific, Manisha, but I do think it's a real problem because I feel like there are people who they're kind of efforts end up not being recognized by the system because they, you know, can't perform in this kind of very narrowly contrived format. Which I think is. Is unfortunate. Although, I mean I think it is. Is good that more, more universities are moving away from, from relying so heavily on, on the sats.

Jitendra, what. What do you think the fear is coming from? Is it a fear of self worth or what do you think is underlying the fear?

Beautiful question. We feel that over the years, the way my wife and I have worked with her is we feel she's gently but slowly but surely picking up that level of self worth and confidence. But I think the entire mechanism where the teachers are under pressure to Finish certain portions and they have to finish certain topics. And therefore there is a certain degree of rush in the classrooms. And then you got to finish off some homework, a huge amount of assignments and stuff. I think that is what is putting some amount of pressure on the students in general. Some of them just breeze through it, some of them take a little longer. That's all. I'm. Inwardly, I'm confident that this is going to work out.

Do you think, I mean, in terms of this test itself, what do you think that means to your daughter to do poorly on the test or not do as well she hoped. What does that signify to her? What would be like the statement that comes to her mind?

Lovely question again. For her, it is a question. It feels like self worth. And we try to tell her it has nothing to do with her as a person or her abilities. It has to do with the testing criteria, the way the mechanism, the test is brain.

So I think, yeah, so I think that's. That's the first problem, you know, is that you're telling her that's not true. Right? It's not true. It has to do with your self worth, you know, And I think you'll get further with her if instead of saying it's not true, say, just try to be curious. Okay, so if you don't do well on this test, like, what does that mean? What's the statement? Okay, I am, I am worse than my peers. Okay, well, if that's true, what does that mean? I'm going to get a terrible job. Okay. What happens if you get a terrible job? I'm not going to be happy. You know, kind of really, really explore curiosity. There's a wonderful spiritual teacher, we can't really go too in depth called Byron. Katie. She has a whole line of questioning, you know, is that true? Is that true? But you really have to approach it with genuine curiosity, not with this ulterior motive to make her feel better about. And I say this as someone who's like afraid to take a COVID test because then I might find out I actually have Covid, you know, So I, I am incredibly scared of anything that puts a label on me, you know, and it just, it doesn't work to say, you know, because on a certain extent it does impact her life how she does on this test, and it does impact the kind of people she's going to be around. So it's not to tell her. It doesn't matter. It doesn't reflect what she knows is not true. It does reflect how good she is at taking tests and that's the whole thing. So I. And just another kind of practical thing. My mom is actually a pre med advisor and she has students listen to this thing called binaural Beats when they're practicing for the mcat. It's a sound thing that they listen to sounds at different tones. And she's had a really enormous success with that. Her students who have a lot of anxiety around the mcat. So sound can be healing as well. Well, but I can send you some more resources about that as well.

Thank you so much.

Yes, I see a question from Madeline. If you were to use AI to help people learn. Matt, Math what are some most predictive factors to consider and what should be the things you optimize for? Yeah, I mean that's kind of getting it. I think why I wouldn't necessarily want to be using AI in this way of just. I mean I think, I think there are some great programs that you know, I think adaptive learning and it may not be AI, but it's using some sort of algorithm to kind of up the. If you're getting things seem too easy for you to up the difficulty level. I think it's hard with, I mean with math kind of a goal, primary goal is I want people to enjoy it and I want them to also understand it. And so I don't think it can be kind of boiled down to.

A.

I don't know that it can even be boiled down to kind of a slate of metrics. And then I, I mean there's also this element I think with. With math programs about. Yeah. The importance of kind of asking questions that are interesting. And I think this is an issue with some math education. It's just a lot of the questions are really kind of boring or repetitive and kind of how to make things make things interesting. And it's. And it's also tough because as we've talked about kind of like every child is different and also everybody's at different place. But that even just kind of finding I think interesting questions that are kind of at the right level and meeting someone where they are can be. Can be quite difficult. I shared a link in the chat to some of the research that I mentioned around Berkeley's engineering program. And this is by kind of one of the researchers that worked on that. Sorry, that's separate question. But there had been a follow up question about the kind of social good engineering applications. Yeah. Any further questions? Yes, the recording will be made available will be publicly shared.

Rachel, I have a question. What was your most Fun thing to learn about math as a teenager. What did you find really exciting or fun? It might not be taught in school.

Oh.

I don't know.

It's actually. I had a. I had a really fun geometry teacher. I was very lucky in high school, but he would do stuff like he used it and this was just like at a public high school in Texas, like fishing reels to make a. Make a parabola to kind of illustrate about points being equidistant or I can remember him, like, drawing on the ceiling that he. I don't know, that was, I guess, a kind of a fun math experience. And he had to do a lot of visual things. Like we had to create our own tessellation and I made one of octopi that I was really proud of. So that was, I don't know, a fun, kind of fun math experience for me.

Yes. Madeline has a great one too, I think. Wrap up the call. What is the most beautiful idea in math to you?

The most beautiful idea? It's not. It's not maybe a single idea, but I really. I think linear algebra is so, so eloquent. Oh, actually, sorry, I just remembered this. A resource for teenagers and older kids would be three Blue One Brown. Brown does incredibly, just beautiful videos and he had to, you know, write his own graphics software library to create the visualizations he wanted. Actually, I'll throw a link in there. Three Blue One Brown does. Yeah, just really, really fantastic. And I think for anyone that likes art would enjoy these videos. And so, yeah, I definitely recommend those for teens and older children.

Yeah.

So I think as a field, though, I found, yeah, linear algebra, so, so beautiful. And three Blue one Brown does a great, great series on linear algebra and really showing about how it's kind of transforming. Transforming vector spaces, but you can think of it as kind of transforming these shapes. And he illustrates that in a really, really beautiful visual way.

Wonderful. Well, thank you so much for today, Rachel. And just to reiterate, this is our kickoff event for the new tutoring company we've started. Tutora is really focused in a lot of the ideas we've talked about around reinforcing grit and helping students build confidence around math and really supporting that intrinsic desire to learn and the intrinsic talent that every student brings. And we also do a lot of interesting things in online learning and terms of incorporating educational apps with the support of a tutor. Then we also run Modulo, and Modulo is a tool to help parents participate more in their child's education. We have a curriculum planner on the site where you can explore different resources to support your child with math and other subjects. And then, of course, we have masteryhour.org, which is our nonprofit that provides online, unlimited free math tutoring to any child who needs it with really wonderful, generous college student volunteers. And I'll just put the resources in the chat. And especially for Tutora, 100% of profits are going to support Mastery Hour. And we're just getting started. So we would really appreciate your referrals to schools, school counselors who might know students who would benefit from tutorial. And I am happy to talk to any family who needs extra support. I'm going to send you all links to the recording and the resources after the talk. And thank you so much for putting an hour aside in your Saturday or Sunday, if you're in Australia, to day. And once again, thank you so much to Rachel. I think this is one of the best presentations we've ever hosted. It was so wonderful listening to you. Yes.

Thank you for organizing and thank you. Thank you for everyone who came and thanks for all the great questions. Yeah, this was really fun.

Wonderful. All right, well, have a fantastic afternoon, everyone, and thank you so much again, Rachel. We'll give you a virtual round of applause.

Thank you. Thank you.