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 have published a paper about this theory.
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 three other papers in progress, two that are under review at journals and one that is in progress.
PHASE III
In summer 2017 we began retrospective analysis of the first experiment from Phase III. We have explored the video data for important moments (Brown, 1992) and have already presented from this data at research conferences and conferences for teachers; created a video case for prospective secondary teachers, and published an article for teachers in the new NCTM journal, Mathematics Teacher: Learning and Teaching PK-12.
In the first whole classroom experiment, we worked with eighth grade students and classroom teacher on a unit based on Say It With Symbols from the Connected Mathematics Project (CMP3).
In the second whole classroom experiment, we worked with the seventh grade students and the classroom teacher on a unit based on Comparing and Scaling from CMP3.
We are currently at work on two avenues of analysis from this data; The first avenue is about clearly understanding the ways of thinking (fractions knowledge, multiplicative concepts) of six focus students from each experiment. A research team is coding interview data to make retrospective assessments. We plan to develop at least two papers about this analysis.
The second avenue is focused on taking paper presentations and developing them into 1-2 manuscripts about tiering instruction in both experiments. Our most recent research conference proposal was at PME-NA in November 2019, focused on the second experiment.