## “Speaking Mathematically: Exploring How Students Align Mathematical Language with Narrative Description”

**Presented By:** **Michelle Wilkerson-Jerde, **** **Associate Professor, Tufts University, Medford, Ma

Monday, September 12, 2011 from 4:30p.m. – 5:30p.m.

**Abstract:** Mathematical and quantitative models are a powerful way to make sense of and navigate our world. But often, the ways we describe such models can seem unrelated to the events they represent. This is especially true when mathematical models are used to describe complex systems comprised of multiple, interacting entities. For example, we describe a population as “exponentially growing” even as we assume individuals’ chance of reproduction remains constant over time; or as “stable” even as members are born and die.

In this presentation, I will describe DeltaTick: a set of simulation construction tools designed to help students explore the connections between the behavior of elements in a system, and the mathematical trends those behaviors produce. DeltaTick provides a new way for students to model patterns of change that emerge from multiple, interactive causes. I will then present my ongoing analysis of “The Real World Critics”: three high school PreCalculus students who, over the course of a 40-minute session with DeltaTick, work to align their everyday understandings of population dynamics with the languages of rate and accumulation, probability, biology, and their peers. This alignment enables the group to explore what mathematical predictions they are able to make, how to test those predictions, and what kinds of phenomena can be appropriately represented using a given model.

**Bio:** Michelle Wilkerson-Jerde received her PhD from the Learning Science Program at Northwestern University. Wilkerson-Jerde’s thesis was studying and building tools to support how high students make sense of quantitative trends that reflect complex systems – systems where many interacting events and entities contribute to the same pattern. Understanding change over time in these systems can prepare students as active and informed citizens, provide them with new access point to formal mathematical topics such as calculus and differential/difference equations, and provide them a better foundation for entering the natural and social sciences. Some of Wilkerson-Jerde’s work earned Best Student Paper from the American Educational Research Association’s Special Interest Groups in Learning Sciences and Advanced Technologies for Learning. Currently Wilkerson-Jerde is an Assistant Professor in the Department of Education at Tufts University.

Michelle Wilkerson_Sm