Math Modeling and Data Science, from Kindergarten to Industry | Rachel Levy | TEDxYouth@NCSSM
## Speaker Context - Dr. Rachel Levy: Executive Director of the North Carolina State University Data Science Academy and Professor of Mathematics. - Setting: Event where she is invited to speak. - Framing: To discuss what kindergartners taught her about mathematical modeling and data science. ## People - Bruce Pollock Johnson: Professor at Oberlin College who brought the speaker to NASA. - Dr. Sylvia Hood Washington: Person who was working on a project with the speaker group at NASA. - Robin Stankowitz Vanderzanden: Teacher from the Pomona Unified School District who started recording what she was doing with her students. - Mr. Pete: Name of Robin's husband. - Faith: Name of Robin's daughter, who was having a birthday. ## Organizations - North Carolina State University Data Science Academy: Organization where the speaker is Executive Director. - North Carolina School of Science and Mathematics: Institution that invited the speaker to talk. - NASA: Institution where the speaker worked with undergraduates. - Pomona Unified School District: School district from which Robin Stankowitz Vanderzanden is a teacher. ## Places - Playground (at elementary school): Location of the speaker's first mathematical modeling experience. - Oberlin College: Institution where the speaker was an undergraduate student. - NASA: Location where the speaker worked on modeling energy usage for the ISS. - Pomona, California: Location associated with the Pomona Unified School District. ## Tools, Tech & Products - Cooler: Item used by students during the elementary school food planning activity. - Badges: Item received by undergraduates at NASA to signify their presence. - Manipulatives: Tools used by students in the context of the mouse count story. - Pictures: Medium used by students to explain their artwork. ## Concepts & Definitions - Mathematical modeling: Topic central to the talk, discussed via various experiences. - Data science: Field encompassing mathematical modeling, statistical modeling, and computational thinking. - Math shame: Feeling experienced when something seems too scary or challenging in mathematics, leading to avoidance. - Proportional reasoning: A mathematical concept concerning relationships, demonstrated by the ability to handle varying quantities (e.g., big vs. little cookies). - Anomaly detection: The process of determining when a stream of data is normal versus when something is wrong or weird. ## Numbers & Data - Third or fourth grade: Approximate grade level for the speaker's first math modeling experience. - Three mice: Initial number of mice in the original mouse count story. - Ten mice: Number of mice the snake originally wanted to eat in the original mouse count story. - Five mice: Number of mice the snake had in the jar in Robin's modified mouse count story. - Six more mice: Number of mice one student thought the snake needed for his family. - One mouse: Number of mice used in an example demonstrating proportional reasoning. - Three adults, two big kids, two little kids: Counts used in the birthday party planning scenario. - Three cupcakes: Number of cupcakes allotted for big kids and adults in one scenario. - Two each: Number of cupcakes allotted for little kids in one scenario. - Seven cupcakes: Number of cupcakes anticipated due to Auntie always showing up. ## Claims & Theses - The speaker's first mathematical modeling experience occurred planning food for an entire week using a roped-off section of the playground. - The speaker felt empowered realizing they could make and plan all decisions for the week food scenario. - The speaker suggests that in their career, sticking with harder things would have led to different advancement. - People often struggle to formally write down what they know about data science, but telling people what they are thinking reveals more. - The answer to "how much toilet paper should I buy" depends on the context. - If you store food in huge containers, the quality of the food goes down. - If you store food in smaller containers, you can have a higher quality food. - The kind of solution thought of for the food storage problem would take too long to run even on a very powerful computer. - If you are off by just a small fraction of a degree in satellite orientation, people might lose their internet. - Kindergarteners can bring their own experiences into mathematical modeling situations. - The openness of problems allows students to feel like they are doing mathematics. - Data science includes mathematical modeling, statistical modeling, and computational thinking. - Everyone can be a math ambassador. - If data is in a meaningful context, we have the ability to make sense of it and communicate it to others. ## Mechanisms & Processes - Elementary School Food Planning: Teams figured out what everybody liked to eat, scoured newspapers for sales/affordability, planned the week's food, and planned cooking/building a fire. - Modeling Energy Usage for ISS: Undergraduate teams worked with professors and were tasked to model the energy usage for the not-yet-built International Space Station. - Solving Optimization Problem (Food Storage): Involved variables such as bumper harvest size vs. small harvest, and container size (huge vs. small). - Solving Satellite Orientation Problem: Involved using ideas from engineering, differential equations, and control theory. - Anomaly Detection: Involves determining if a data stream is normal or if something went wrong, distinguishing between natural fluctuations (like a holiday) and actual system failure. - Eliciting Thinking via Open Questions: Posing questions that don't have just one right answer, which can elicit new kinds of thinking. - Using Voice Recording: Recording students talking about their math thinking, as opposed to just looking at written work. ## Timeline & Events - Elementary School Period: Speaker's first math modeling experience involving planning food for a week in a roped-off playground area (timeframe was one week). - Undergraduate Period (Oberlin College): Working on modeling energy usage for the ISS at NASA. - Kindergarten Years: Robin's class engaged in modeling activities like the mouse count story, birthday party planning, and cookie division. ## Examples & Cases - Elementary Playground Food Planning: Planning all food, buying supplies, budgeting, and planning cooking for a week while isolated in a roped-off area. - NASA ISS Modeling: Working on a project to model the energy usage for the International Space Station with professors like Bruce Pollock Johnson and Dr. Sylvia Hood Washington. - Food Storage Optimization: Determining the mixture of food storage containers needed to handle variable harvests while balancing quality degradation vs. container cost. - Satellite Orientation: Solving a problem requiring input from engineering, differential equations, and control theory to maintain internet connectivity. - Anomaly Detection Data Stream: Analyzing data to determine if unusual traffic patterns are due to a natural event (holiday) or a system breakdown. - Mouse Count Story (Original): Using the narrative of a snake eating mice, originally posed as "the snake has three mice but the snake really wants to eat ten mice how many more mice does the snake eat." - Mouse Count Story (Modified): Robin posed the question: "the snake was very hungry and he had five mice in the jar but he really wanted more so how many more mice should snake get in so that he won't be hungry anymore." - Student Artwork Interpretation: Kid showing artwork and explaining parts like eyes, chunk, and legs to help the adult see things they might not have seen. - Kindergarten Birthday Party Task: Calculating the number of cupcakes needed for two adults, two big kids, and two little kids, noting instances of proportional reasoning. - Kindergarten Cookie Example: Relating fractions by stating that if you have a big cookie you can chop it, but if you have little cookies you're going to need a lot of them. - Aquarium Task: Attempting a modeling task with students who had little prior experience with aquariums, which was described as a "total flop." ## Trade-offs & Alternatives - Food Storage Containers: Trade-off between huge containers (lower quality food) and small containers (higher quality food, but much more expensive). - Toilet Paper Buying Decision: Trade-off between buying too much or too little. - Data Interpretation: Trade-off between asking people to formally write down their thinking versus just asking them what they are thinking. - Lesson Openness: Trade-off between needing openness at the start (reconstructing the problem) vs. the middle (different solving ways) vs. the end (different answers). ## Counterarguments & Caveats - The speaker notes that the positive outcomes of the elementary playground experience were that no one stole the food ahead of time, and there weren't too many fights. - Regarding academic difficulty, the speaker acknowledges that sometimes they backed away from challenging things or performed less well than desired, leading to a pattern of playing it safe. - The speaker notes that the initial structure of math education only offers binary results: "either you get a check mark yay it was right or you'll get a red x on your work." - The aquarium task was stated to be a "total flop" because students didn't have a lot of experience with aquariums. ## Methodology - Group Planning/Simulation: Used for the elementary playground activity. - Scientific Project/Modeling: Used at NASA to model energy usage for the ISS. - Optimization Problem Solving: Applied to food storage container mixture. - Technical Application: Used differential equations and control theory for satellite orientation. - Qualitative Interviewing/Observation: Recording students' voices to understand their thought processes in math problems. ## References Cited - National Science Foundation: Provider of a grant used for the work with teachers from the Pomona Unified School District. ## Conclusions & Recommendations - The speaker advises joining in going out into the world encouraging our littlest people to do mathematics to do statistics to learn computation. - The speaker recommends encouraging people to bring their own understanding to bear in a situation. - The speaker encourages talking to other people to get other perspectives. ## Implications & Consequences - Failing to address "math shame" can lead people to feel like math has rejected them or that math doesn't belong to them. - The ability to use information and understand its value in context, even if not formally written down, is crucial. - If one only looks at the data, one misses the chance to see the deeper thinking process demonstrated by children. ## Open Questions - The speaker implies that many people are carrying "math shame" that needs addressing. - The speaker suggests that the capacity to understand data's value exists, but formalizing it is difficult. ## Verbatim Moments - "it's cute drawing but i don't know what that is" - "I think it's the same thing with mathematics and data science" - "it depends on the context" - "A lot of times when she was talking to kids about food they were really curious about the leftovers" - "another thing we learned from the kindergarteners is that they definitely bring their own experience into these mathematical modeling situations" - "if you only have one mouse and it's big snake will only need one" - "proportional reasoning is something we have trouble getting sixth graders seventh graders adults" - "we are getting smart"