Dossier

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

Kindergarteners demonstrated that bringing personal experience into problem-solving is vital for understanding data, showing that data science requires context, communication, and collaboration. Dr. Levy illustrates this through activities like food planning and mouse counting, contrasting these open-ended successes with the limitations of traditional, multiple-choice math assessment. The central message is that everyone can become a math ambassador by applying critical thinking to real-world data.

## Speakers & Context
- **Dr. Rachel Levy:** Executive Director of the North Carolina State University Data Science Academy and Professor of Mathematics.
- **Purpose of talk:** To discuss what kindergartners taught her about mathematical modeling and data science.
- **Initial experience:** Speaker’s first mathematical modeling experience involved planning food for an entire week while isolated in a roped-off section of an elementary school playground.
- **Current context:** Presented at an event hosted by the North Carolina School of Science and Mathematics.

## Theses & Positions
- **Data science definition:** Encompasses mathematical modeling, statistical modeling, and computational thinking.
- **Math shame:** A feeling that arises when something seems too scary or challenging in mathematics, leading people to avoid difficult subjects.
- **Value of context:** The ability to use information and understand its value is strongest when the data is presented within a meaningful context.
- **Open-ended problems:** Open problems allow students to *feel* like they are doing mathematics because there isn't just one right answer.
- **Communication method:** Asking students what they are thinking (via discussion) reveals much more than asking them to formally write down their thinking.
- **Role of collaboration:** Thinking about problems as a group ("we are getting smart") is more powerful than individual problem-solving.
- **Ambassadorship:** Everyone has the capacity to be a math ambassador by teaching others to look at data critically.

## Concepts & Definitions
- **Mathematical modeling:** Topic central to the talk, demonstrated across multiple life experiences.
- **Data science:** Field incorporating mathematical modeling, statistical modeling, and computational thinking.
- **Math shame:** The feeling of being intimidated or avoiding challenges in math due to past negative experiences.
- **Proportional reasoning:** The ability to understand relationships between varying quantities, demonstrated by scaling amounts (e.g., big vs. little cookies).
- **Anomaly detection:** The process of determining if a stream of data is normal or if something is wrong/weird, distinguishing between natural fluctuations and actual failure.
- **Open-ended problems:** Problems lacking a single, definitive correct answer.

## Mechanisms & Processes
- **Elementary School Food Planning:** Teams planned for a week's food, requiring them to:
    - Determine collective preferences.
    - Scour newspapers for sales/affordability based on a budget.
    - Plan cooking and fire construction.
    - Manage the physical resources in a *cooler* over one week.
- **Modeling Energy Usage for ISS:** Undergraduate teams modeled the energy consumption for the yet-to-be-built International Space Station while at NASA.
- **Food Storage Optimization:** Solving a problem requiring balancing trade-offs between:
    - Huge containers (which cause lower food quality).
    - Small containers (which retain higher quality but are much more expensive).
- **Satellite Orientation Solution:** Required integrating ideas from engineering, differential equations, and control theory to maintain internet connectivity.
- **Kindergarten Mouse Count (Modified):** Instead of the standard "3 mice to 10 mice" problem, the open question posed was: "The snake 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?"
- **Eliciting Thought via Dialogue:** Recording students' spoken explanations rather than just analyzing written work to uncover deeper thinking.

## Timeline & Sequence
- **Elementary School Period:** First math modeling experience; planning food for one week.
- **Undergraduate Period (Oberlin College):** Worked on modeling energy usage for the ISS at NASA.
- **Kindergarten Years:** Robin Stankowitz Vanderzanden’s class participated in modeling activities, including the mouse count story, birthday party planning, and cookie division.

## Named Entities
- **North Carolina State University Data Science Academy:** Speaker's current organization as Executive Director.
- **North Carolina School of Science and Mathematics:** Institution that invited the speaker.
- **Oberlin College:** Institution where the speaker was an undergraduate student.
- **NASA:** Location where the speaker worked modeling energy usage for the ISS.
- **Pomona Unified School District:** School district associated with the teacher, Robin Stankowitz Vanderzanden.
- **Bruce Pollock Johnson:** Professor at Oberlin College who brought the speaker to NASA.
- **Dr. Sylvia Hood Washington:** Colleague at NASA on the ISS energy usage modeling project.
- **Robin Stankowitz Vanderzanden:** Teacher from the Pomona Unified School District who began recording student work.
- **Pete:** Name of Robin's husband.
- **Faith:** Name of Robin's daughter, who was having a birthday.

## Numbers & Data
- **Third or fourth grade:** Approximate grade level for the speaker's first math modeling experience.
- **Three mice:** Initial number of mice mentioned in the traditional mouse count story.
- **Ten mice:** Number of mice the snake originally wanted to eat in the traditional mouse count story.
- **Five mice:** Number of mice in the jar used in Robin's modified story.
- **Six more mice:** Number of mice one student suggested for the snake's family.
- **One mouse:** Number used in the proportional reasoning example.
- **Three adults, two big kids, two little kids:** Counts used in the birthday party planning scenario.
- **Three cupcakes:** Number allotted for big kids and adults in one scenario.
- **Two each:** Number allotted for little kids in one scenario.
- **Seven cupcakes:** Number anticipated due to the recurring presence of "Auntie."

## Examples & Cases
- **Elementary Playground Food Planning:** A full-scale simulation where teams planned food for a week, involving budgeting, shopping, and cooking over a roped-off area.
- **NASA ISS Modeling:** Undergraduate work tasked to model the energy usage for the International Space Station.
- **Food Storage Optimization:** Case study using variables (bumper harvest vs. small harvest, container size) to model preservation logistics.
- **Satellite Orientation:** Solving for minor angular deviations that could lead to complete internet loss.
- **Mouse Count Story (Original):** "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):** Inquiry into the needs of the snake's entire family, leading to questions about sustainability and scale.
- **Kindergarten Artwork Interpretation:** A child explaining artwork elements like "the eyes," "the chunk," and "the legs" to reveal meaning an adult might miss.
- **Kindergarten Birthday Party:** Calculating resources for two adults, two big kids, and two little kids, noting instances of proportional reasoning.
- **Kindergarten Cookie Example:** Demonstrating that a big cookie can be chopped, while multiple little cookies require many more units.
- **Aquarium Task:** An attempt at modeling with students lacking prior aquarium experience, which was labeled a "total flop."

## Tools, Tech & Products
- **Cooler:** Container used during the elementary school food planning activity.
- **Badges:** Item received by undergraduates at NASA signifying presence and participation.
- **Manipulatives:** Tools used by students, such as physical objects, to model problems.
- **Pictures:** Medium used by students to explain artwork during interpretation tasks.

## References Cited
- **National Science Foundation:** Provider of a grant used for the work with teachers from the Pomona Unified School District.

## Trade-offs & Alternatives
- **Food Storage:** The trade-off between huge containers (leading to lower food quality) and smaller containers (leading to higher quality but greater expense).
- **Toilet Paper Buying:** The decision of whether to buy too much or too little, depending on supply, budget, and preference (extra soft vs. single ply).
- **Data Elicitation:** The trade-off between formally writing down one's thinking (difficult) versus speaking/discussing it (reveals more).
- **Lesson Design Openness:** The balance needed to allow for initial problem reconstruction, diverse solving methods, and varied final answers.

## Counterarguments & Caveats
- **Playground Success:** The positive outcome in the playground was that no food was stolen, and there were few fights, suggesting success in managing limited resources.
- **Career Trajectory:** The speaker notes a pattern of self-limiting behavior, admitting she sometimes "backed away from" challenging academic tasks.
- **Math Grading:** Traditional math assessment is often binary: "either you get a check mark yay it was right or you'll get a red x on your work."

## Methodology
- **Group Planning/Simulation:** Emulated through the elementary playground food planning activity.
- **Scientific Project Modeling:** Modeling energy usage for the ISS at NASA.
- **Optimization Problem Solving:** Applied to the mixture of food storage containers needed for varying harvests.
- **Technical Application:** Using differential equations and control theory for satellite orientation calculations.
- **Qualitative Interviewing/Observation:** Crucially involving recording students' voices to capture process thinking.

## Conclusions & Recommendations
- **Actionable Advocacy:** Speaker urges joining the effort to encourage local children to engage in mathematics, statistics, and computation.
- **Pedagogical Advice:** Recommend ensuring problems are open, allow reconstruction, support varied solving methods, and value conversational communication over formal writing.
- **General Recommendation:** Advocate for sharing knowledge and perspective across different disciplines.

## Implications & Consequences
- **Math Shame Risk:** Failure to address math shame can cause individuals to feel mathematics has rejected them or that it does not belong to them.
- **Data Context:** If data is presented in a meaningful context, humans possess the ability to make sense of it and communicate that sense effectively.
- **The Future of Learning:** The speaker implies a shift is needed toward valuing the "how" (the thinking process) rather than just the definitive "what" (the right answer).

## Verbatim Moments
- *"It's cute drawing but i don't know what that is"* (Quoted when interpreting a child's artwork).
- *"I think it's the same thing with mathematics and data science"* (Comparison linking the two fields).
- *"It depends on the context"* (The principle governing many data science problems).
- *"A lot of times when she was talking to kids about food they were really curious about the leftovers"* (Observation on student focus).
- *"Another thing we learned from the kindergarteners is that they definitely bring their own experience into these mathematical modeling situations"* (Key takeaway from the children's input).
- *"If you only have one mouse and it's big snake will only need one"* (Example of proportional reasoning shown by a kindergartener).
- *"proportional reasoning is something we have trouble getting sixth graders seventh graders adults"* (Highlighting the difficulty of the concept at older levels).
- *"we are getting smart"* (The group sentiment expressed by the kindergarteners).