Overview and Project Timeline

Overview and Project Timeline

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. 

In Phase I (Years 1-2, fall 2013-spring 2015) Amy, as a teacher-researcher, taught diverse groups of 6-9 middle school students in a series of three design experiments after school. We also began two major strands of analysis (see Analysis in Progress).

In Phase II (Year 3, 2015-2016 academic year) research team members formed a study group with 15 middle school mathematics teachers to explore differentiating instruction in their classrooms. These teachers came from across the state of Indiana—from Evansville, Bloomington, Ellettsville, Indianapolis, and Hammond. We kicked off the group with a 3-day workshop in July 2015, held monthly meetings during the academic year, and completed the year with a 1-day workshop in June 2016 (see Teacher Study Group).

Phase III years 4-7 (fall 2016-spring 2020) constitute the third phase of the IDR2eAM project. The purposes of the project in these three years are to study:

  • How to differentiate instruction for middle school students;
  • How teachers learn to differentiate instruction;
  • How differentiating instruction impacts students and teachers affectively;
  • How students’ rational number knowledge and algebraic reasoning are related.

During Phase III Amy, the classroom teacher, and research team members are co-conducting design experiments with whole classrooms of middle school students. Amy has co-taught two different units with classroom teachers from the Teacher Study Group in which we planned together to differentiate instruction. This way of doing research is about using teaching as a method of investigation into teaching and learning. Using teaching as a method of investigation requires developing conjectures about students’ ways of thinking and classroom instruction and making tests of those conjectures in the process of teaching. So, each of these design experiments required gathering initial data about students via written assessments and interviews, as well as follow-up assessments and interviews.

From summer 2017 onward we have been analyzing data from Phase III (see Analysis in Progress).