The aim of this project is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.
About Me (Bio):
My research focuses on middle-school and secondary mathematics education. I am interested in studying students' reasoning, particularly as it relates to mathematical generalization, justification and proof, and the development of algebraic thinking. My completed research projects include the study of middle school students' generalizations and proofs during units on linear and quadratic functions, an investigation of the classroom features supporting high-school students' generalizations about slope, and studies of girls' performance and participation in mathematics. My research has been supported by multiple collaborative NSF-funded projects, including a) Coordinating Social and Individual Aspects of Generalizing Activity: A Multi-Tiered "Focusing Phenomena" Study (NSF-RoLE), which examined the ways in which classroom environments influenced students' mathematical generalizations, and b) New Trends in Gender and Mathematics Performance, which supported the examination of existing literature and current state assessment data to study girls' and boys' performance on mathematics items. One of my current NSF-supported projects through REESE, Inductive and Deductive Reasoning in and out of Mathematics (IDIOM), studies students' ways of reasoning both inductively and deductively about problems in mathematics and the natural world. By exploring the similarities and differences in how students reason in mathematical and non-mathematical contexts, I and my colleagues (Dr. Eric Knuth and Dr. Charles Kalish at U.W. Madison) hope to develop a deeper understanding of the ways in which students use evidence to make decisions, provide justifications, and ultimately move towards deductive proofs. My newest project, Supporting Students' Proof Practices through Quantitative Reasoning in Algebra (NSF-DRK12), examines the ways in which reasoning with quantities supports students' developing proof competencies in algebra. Throughout the course of the project I will scale up these results to support teachers' abilities to promote their students' proof understanding in the classroom.