Research on Student Understanding of Fundamental Algebraic Concepts

This project is focused on unpacking which core concepts are fundamental to understanding algebra. In particular, we are interested in mapping out how students currently think, as well as what types of thinking are most critical to longterm understanding of and success in algebra. Our focus is on conceptual understanding rather than procedural fluency, although we also explore how these two different types of knowledge interrelate. Much of this work is focused on students' structure sense, and on their understanding of substitution equivalence. Much of this work is generalizable to any mathematical domain that uses formal mathematical symbolism, and is not just restricted to algebra. At present, we are in the process of developing a database of concept inventory questions that test core conceptual knowledge in algebra. This work is currently focused on college students, especially those placed into developmental mathematics classes, but the research is also strongly related to work that has been conducted with K-12 students as well. The eventual aim of this research is to generate a rigorously-tested curriculum which focuses on core mathematical concepts at the center of all mathematical work, and in this way to provide an alternate pathway for students who place into developmental mathematics classes to pursue STEM fields in college.