Proportions Playground: A Dynamic World to Support Teachers' Proportional Reasoning

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Proportions are a critical topic in mathematics that is simultaneously complicated and over-simplified in typical instruction. Current research undertaken by the research team suggests that the over-simplification is related to limitations in teachers' understandings of proportional relationships. Presenting proportions in a dynamic environment offers teachers the opportunity to create key developmental understandings related to this area of mathematics. This project focuses on the creation of the initial functionality for a dynamic microworld, Proportions Playground, designed to support teachers in developing a coherent understanding of proportional reasoning. Proportions Playground is conceptualized as a tool for supporting the development of coherent understandings by allowing teachers to interact in concrete ways with otherwise abstract ideas and by allowing teachers easy access to dynamic objects and other representations. It is meant to address the significant limitations for reasoning about the relationships between measurable aspects of two objects as well as in manipulating those relationships. Building from work currently underway, Proportions Playground will explore key areas in which there are opportunities for engaging teachers in the development of a coherent and robust understanding of proportional reasoning that extends beyond the typical "3 given, 1 unknown" proportion problem. This approach attempts to engage teachers in an array of dynamic, visually-rich sets of tasks designed to challenge teachers' preconceptions of proportions and to strengthen their connections between proportions and related areas of mathematics. This project is funded by the Discovery Research PreK-12 (DRK-12) and EHR Core Research (ECR) Programs. the DRK-12 program supports research and development on STEM education innovations and approaches to teaching, learning, and assessment. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field.The Proportions Playground project seeks to both develop a unique pilot software application for the iPad and explore how it supports teachers in developing a coherent, robust definition of proportions. The software will be designed to support either numeric manipulation (e.g., graphing software) or geometric constructions (e.g., dynamic geometry software). Specifically, for this project the mathematics of interest will include the relationships between similarity and proportion and the nature of covariation. The research will focus on how teachers are developing a robust and coherent understanding of proportions and how the dynamic environment promotes such understandings. Working with six teacher advisors, the project will develop three task sets. Using teaching experiments and individual interviews, results will be used to refine the task sets. The revised task sets will be piloted with 40 teachers. Data will be collected on participants' thinking and any changes seen in the knowledge resources they are using. The researchers will be looking for factors that seem to impact teachers' thinking as well as evidence to support or deny the assertion that the Proportions Playground activities engage teachers in (a) different ways of reasoning about proportions and (b) support them in drawing from a wide array of resources so that coherence may be developed were the teachers to have a prolonged engagement with the tools. The project will rely on Epistemic Network Analysis to identify the connections between knowledge resources.