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# Recent Presentations

# Article from March 2014

 

 

 

 

 

 

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 is intended to yield a theory of differentiating instruction for cognitive purposes with middle school students. We will be revising this paper in summer 2017 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, and we submitted two papers to journals in May 2016 and July 2016; we have revised and resubmitted one of these papers in April 2017 and we are working on revision of the other.

PHASE III

In summer 2017 we are beginning 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. Because the unit we worked on with the eighth grade students and classroom teacher was Say It With Symbols from the Connected Mathematics Project, we plan to write a paper about students' meanings of equivalence in conjunction with a paper about how differentiation proceeded.