Analysis in Progress

PHASE I

We have two major strands of analysis of Phase I data underway.

The first strand of analysis is about how differentiating instruction functioned in the design experiments. A sub-group of the research team has been coding design episode data and supporting documents using ATLAS.ti software. We presented a paper from this analysis at the Research Conference of the National Council of Teachers of Mathematics in April 2016. This analysis has yielded a theory of differentiating instruction for cognitive purposes with middle school students. We are revising this paper in summer 2018 to submit to a journal.

The second strand of analysis is about how students’ rational number knowledge and algebraic reasoning are related. A sub-group of the research team has been developing portraits of each of the 22 students who participated in the design experiments in Years 1 and 2. This analysis requires close viewing of video of students in targeted episodes, elaborating transcripts, and writing summaries, memos, and syntheses. This analysis is yielding findings about how students learn to reason reciprocally and inversely with algebraic unknowns, about how students construct algebraic unknowns, and about students' meanings of multiplication and division when working with unknowns. We have conducted numerous presentations about this work; we have published one paper from this work in December 2017; and we have two other papers in progress, one to be submitted in summer 2018.

PHASE III

In summer 2017 we began retrospective analysis of the first experiment from Phase III. We are currently exploring the video data for important moments (Brown, 1992) to develop conference paper proposals and manuscripts.

In the first whole classroom experiment, the unit we worked on with the eighth grade students and classroom teacher was Say It With Symbols from the Connected Mathematics Project (CMP3). So, we plan to write a paper about students' meanings of equivalence.

In the second whole classroom experiment, the unit we worked on with the seventh grade students and classroom teacher was adapted from Comparing and Scaling from CMP3. So, we plan to write a paper about students' ratio reasoning at different levels.

In addition, our main focus from Phase III is a paper about tiering instruction, a technique we used in both experiments. We have submitted two proposals to present with the classroom teachers at the NCTM Annual Conference in 2019.