Today’s middle school mathematics classrooms are marked by (A) increasing cognitive diversity and (B) students’ persistent cognitive difficulties in learning algebra. Problem A stems from increased inclusion of students with special needs in mainstream classrooms, as well as the fact that students enter middle school at three different levels of reasoning that are not easily altered and that have significant implications for developing rational number knowledge and algebraic reasoning. Traditional responses to Problem A are tracked classes that contribute to opportunity gaps, i.e., inequitable access to high-quality mathematics instruction, and result in achievement gaps. Considerable attention to Problem B has led to the successful integration of algebraic reasoning into students’ developing whole number knowledge in elementary schools.
Very little attention has been paid to how students’ rational number knowledge and algebraic reasoning can be mutually supported in middle school, even though rational number knowledge is seen as critical for success in algebra. The project, directed by Amy Hackenberg at Indiana University, initiates new research and an integrated education plan to address these problems by investigating (1) how to effectively differentiate instruction for middle school students at different reasoning levels; and (2) how to foster middle school students’ algebraic reasoning and rational number knowledge in mutually supportive ways. Differentiating instruction in heterogeneous classrooms is a novel but untested response to Problem A; developing learning trajectories that connect two key domains and address three reasoning levels will be a basis for differentiated instruction and respond to Problem B. Three interdependent project phases will lead to three products: learning trajectories, instructional materials developed collaboratively with teachers, and a written assessment to evaluate students’ levels of reasoning. Educational goals of the project are to enhance the abilities of prospective and practicing teachers to teach cognitively diverse students, to improve doctoral students’ understanding of relationships between students’ learning and teachers’ practice, and to form a community of mathematics teachers committed to on-going professional learning about how to differentiate instruction.
This work is supported by the The National Science Foundation, DRL no. 1252575.