Transcript

Math Modeling and Data Science, from Kindergarten to Industry | Rachel Levy | TEDxYouth@NCSSM

[Music] hi i'm dr rachel levy i'm executive director of the north carolina state university data science academy and professor of mathematics thanks to the north carolina school of science and mathematics for inviting me here today to talk to you about what kindergartners taught me about mathematical modeling and data science my first mathematical modeling experience that i remember is from elementary school my teacher told us that we were going to have to spend an entire week on part of the playground that was roped off we weren't going to be able to talk to kids in any of the other classes and we were going to have to plan our food for the entire week so i remember breaking into teams figuring out what everybody liked to eat scouring the newspapers for what we were going to buy what was on sale what we could afford with our budget and planning it all out for the week what could we fit in our cooler what were we going to be able to cook on the fire if we could figure out how to build one and how are we going to make it for the whole week to feed all of us as a young person i was probably in third or fourth grade it felt really empowering to realize that we could make all these decisions do all this planning and plan for the week and it went really well at the end of the week our teacher said she was pretty surprised that no one stole the food ahead of time i know that she said that we did fine with the cooking and you know there weren't too many fights over over much during the week even though we were all isolated on the island so this this was an extremely memorable experience for me and i really think it laid the groundwork for things that i would do in the future the next time i remember doing math modeling i was a senior undergraduate at oberlin college and i was really really fortunate that one of my professors bruce pollock johnson brought us to nasa to work with dr sylvia hood washington on a project to try to model the energy usage for the not even yet built uh international space station this was so exciting we got to put our badges on we felt really important because we were going to nasa and they even told us at the end of the project that some of the ideas that we had come up with as a group were new to them and that they might try to implement them so this was incredibly wonderful for us as undergraduates and it really made me think hmm you know do do would i want to do this for my career but at the same time i was really holding on to some math shame what do i mean by math shame a couple of times in high school and college i had had experiences where something seemed too scary and too challenging and i had backed away from it or maybe i just hadn't done as well as i wanted to and then i decided i was going to try to do things that were less challenging so that i could be more successful and in some ways i think my academic life rewarded me for playing it safe but i can also see a lot of times in my career that if i had stuck it out and tried to do the harder things i would have really advanced in a different kind of way and i i think i really needed some different kinds of support and encouragement in order to feel confident uh to to take on challenges even uh if i was feeling in the moment like i couldn't do it or like i was a failure if i tell someone i'm a mathematician they'll tell me about times that they felt like they couldn't do mathematics or oh i thought i was good at mathematics until this happened so why are so many people carrying math shame when you when you do math in school what happens either you get a check mark yay it was right or you'll get a red x on your work that says you didn't do so well and i think those red marks in some ways act like little cuts that never heal and i i see a lot of people walking through life experiencing these feelings that math has has rejected them has told them they're not good enough and help and made them feel like math doesn't belong to them when you see kids artwork a lot of times when you look at a kid's artwork you'll think hmm i don't know what that is it's cute drawing but i don't know what that is that kid says it's an elephant and you're like i i don't see it you might say oh tell me about your elephant or show me and the kid will show you oh these are the eyes this is the chunk this is the legs and a lot of times when a kid explains their artwork to you they can help you see things that you might not as an adult have seen yourself i think it's the same thing with mathematics and data science a lot of times people have the capacity especially when they're familiar with the situation to use information and understand how that information is going to be valuable to them how they can interpret it how they can use it in that context but if you just ask them to formally write it down sometimes people are going to have a really hard time doing that and instead if you just ask them what they're thinking they're able to tell you a lot more it may turn out that you are actually doing data science in your life in a way that you might not recognize for example you might ask a question like how much toilet paper should i buy next time i go to the grocery store well the answer is it depends and that is true with most data science and mathematical modeling questions as well it depends on the context if you're trying to solve the problem for me of why i'm going to buy toilet paper and how much toilet paper i should buy you might ask me who i'm buying it for or does it matter what kind i buy does it have to be extra soft or can it be single ply you might ask how much budget do i have to buy a toilet paper how much room do i have to store it if i buy a lot of it will it can i buy it in bulk and get it at a better price and if so is that what i want to do um and then maybe you might want to know what's worse for me to buy too much or too little at harvey mudd college as a professor of mathematics i got to solve a lot of industrial problems with students for many different companies so i'll just tell you about three that we solved that you might find a little bit interesting and give you some sense of the variety of things you can solve with data science what mixture of food storage containers should a company buy so that it can be able to handle the food that's coming in whether it's a big big bumper harvest or just a small harvest that year when you have a variety of things coming in it turns out that if you store things in huge containers the quality of the food goes down and if you store things in smaller containers you can have a higher quality food but smaller containers are much much more expensive than big containers so this was an optimization problem a lot of times in calculus students study optimization when we started trying to solve this problem there were so many variables it turned out that the kind of solution we were thinking about would take way too long to run even on a very powerful computer so we had to really simplify the problem and go back to the client and say hey can we solve a simpler problem for you and try to find something that's feasible so that you could recalculate this as your harvest is coming in a second problem we worked on is satellite orientations and it turns out that if you are off by just a small fraction of a degree people might lose their internet so we in this problem we used ideas from engineering we used ideas from differential equations from control theory and it was a really fun problem to solve and again the company said oh you know you brought us an idea we hadn't thought about before we're going to take that back and see if we can make that work a third problem was anomaly detection once you have data coming in a big question is when is this stream of data normal and when has something gone really bad or weird so that you need to wake someone up and make them fix it or find somebody who can figure out what the problem is sometimes a stream of data is weird because something really weird actually happened maybe there was a holiday and all of a sudden there was a lot more traffic or a lot less traffic that isn't something someone needs to fix it's just a feature of the fact that it was a different kind of day but then other times it may be that something broke down and the traffic isn't coming through because something actually went wrong in the system after working with undergraduates for a while on these kinds of real problems and remembering back to the power of my own experience as an undergraduate at nasa and also my experience on the island as an elementary school student i kept wondering is this kind of learning something that we could be doing more of with kids in elementary school i was very lucky to be able to work with some great collaborators with a grant from the national science foundation and some teachers from pomona unified school district in pomona california to look at how teachers could interact with their students and do mathematical modeling and some data science one of the teachers robin stankowitz vanderzanden decided to keep studying her class she started recording what she was doing with her students in her class so what i'm going to share with you next are some of the lessons that robin's kindergarten class taught us about how much our youngest learners can do in data science in mathematical and statistical modeling and thinking that that really uh relates to the kinds of problems we solve in the workplace robin took a story called mouse count which is a story that many teachers use in order to do mathematical kinds of problems in mouse count there's a snake and snake is very hungry and wants to eat some mice and in the way most teachers use this story is they say okay the snake has three mice but the snake really wants to eat ten mice how many more mice does the snake eat and the students count up from three they may use manipulatives and figure out three plus what is ten in the end i must tell you that the mice get away so so no mice were harmed in this story what robin did that was a little different is she had learned in our um in our studying of mathematical modeling that sometimes if you ask more open questions where there isn't just one right answer like three plus seven is ten where all the students are supposed to get the answer seven sometimes you can elicit new kinds of thinking in your students that you might not even realize they were capable of so what did her kindergarteners teach us robin posed the question that snake was very hungry and he had five mice in the jar um but he really wanted more so how many more mice should snake get in so that he won't be hungry anymore the first thing we learned is that kindergarteners rarely eat alone so even though robin was trying to ask questions about snake eating these mice the kids kept saying well what about snake's family we need to talk about snake in his family snake needs to eat to feed his family and so no matter how many times she posed the question the answers she would get were about snake and his family and we and so we saw the ways in which these young students were bringing their own experiences and ideas into their math problems and felt empowered to do that so you see here a student writes the mice are small his family is helping the family is big they are and you see here one two three four five six this student thought that the snake needed six more mice in order to feed himself and his family another lesson we learned is that while that snake needed six mice to feed his family sometimes one is enough so in this problem you see um a student has drawn a snake on the left and one mouse on the right and one thing we did in order to understand what these students were thinking is that in addition to looking at what they wrote we recorded their voices remember i said that sometimes people if you try to ask them to write down their thinking in mathematics it's very hard even in a context they know well to write it down in a formal way but if you just have them talk about it often they can explain their thinking in a way that will surprise you so this student said if you only have one mouse and it's big snake will only need one this is pretty incredible actually for an elementary school and a kindergarten student to say because this is an example of proportional reasoning proportional reasoning is something we have trouble getting sixth graders seventh graders adults we this is something we really have trouble sometimes getting people to think about and this came up in more than one problem later when kids were talking about cookies later they said the same thing if you have a big cookie you can chop it they were already talking about fractions and you only need one but if you have little cookies you're going to need a lot of them another task robin worked on with her students had to do with mr pete which is the name of her husband and her daughter faith who was having a birthday she said that at this birthday party there would be two adults two big kids and two little kids and cupcakes were regular size with chocolate frosting how many cupcakes should there be for the party they had some information two adults two big kids and two little kids but they could think about how many cupcakes there should be for this party again you'll see instances of proportional reasoning so here you see the big kids get three each the adults get three each and the little kids get two each a lot of times when she was talking to kids about food they were really curious about the leftovers they wanted to know uh how hungry are you they want to know do you like the food and they always wanted to know if there were leftovers that they could share with somebody that was hungry that didn't have enough another thing we learned from the kindergarteners is that they definitely bring their own experience into these mathematical modeling situations one kid said oh you better have seven cupcakes because auntie shows up always to the party whether you invited her or not so for these students food was really providing a meaningful context something everyone had experienced and could relate to uh she did try a task with an aquarium and the students didn't have a lot of experience of what an aquarium was it was a total flop so it is important that with with mathematical modeling that people are able to bring their own experience to the situation i hope you see that the openness of these problems where the students had some openness in the beginning where they could reconstruct the problem as they needed openness in the middle because they had different ways of solving the problem with manipulatives with symbols with their words withdrawing with pictures and open at the end because they came up with different answers from each other allowed them to feel like they were doing mathematics they were doing thinking they were using the data the information they were given they were thinking about the constraints and then they were also being creative about solutions if they needed to exceed the constraints that were given recording their voices in addition to looking at their written work was really crucial for them to communicate their understanding and then at the end the kids said instead of a lot of math classes where you think of it as an individual sport these kids said we are getting smart and i loved that they were saying we're getting smart that they really saw this even though they each had their individual solutions they talked about them so much as a group and and did some problem solving together that they really feel like this is an activity where we're getting smart these days i think a lot about data science which to me includes mathematical modeling statistical modeling computational thinking communication domain knowledge data science cuts across business across all different disciplines and really in everyone's work uh practically in any field i think everyone can be a math ambassador and go out and talk about the power of mathematics how important it is with all of the data in today's everyday world that people be able to go look at data critically be able to interpret it bring tools to bear mathematical statistical computational visualization physicalization interpretation i think that everyone has this opportunity to improve over time their ability to look at data but even our youngest learners show that if it's in a context that is meaningful to a person we have this ability to make sense of what we think and to communicate it to others i hope you'll join me in going out into the world encouraging our littlest people to do mathematics to do statistics to learn computation uh to think about data to to bring their own understanding to bear in a situation and also to talk to other people to get other perspectives thank you very much for listening and i appreciate your time