Today’s middle school mathematics classrooms are marked by (A) increasing diversity and (B) students’ persistent difficulties in learning algebra. 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 IDReAM Project investigates (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 different reasoning levels will be a basis for differentiated instruction and respond to Problem B.