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Synthesizing Rational Number Reasoning


Successful preparation for and passage of algebra remains a major gateway to pursuit of science, mathematics and technology related careers.  Students in many school settings continue to be likely to fail to make this transition, due largely to weakness in rational number reasoning (RNR), including multiplication and division, fractions, ratio reasoning, scaling, similarity, and the related ideas of decimal and percents.  This configuration of topics is also known as the Multiplicative Conceptual Field.  It is critical in developing algebraic and higher mathematical reasoning.

In the RNR Synthesis Project, we are identifying and synthesizing the research literature in six overlapping major rational number topics:  equipartitioning, multiplication and.   division, area and volume; ratio and rate; similarity and scaling; and fractions, decimals, and percents.  The primary aims of the project are to synthesize, rather than simply review, the research literature.  This means that we are examining the entire body of research in rational number reasoning in order to identify common significant themes and findings, introduce new distinctions to resolve differences or integrate results, discern most compelling results among controversies, and lay the groundwork for implementing robust results into practice as well as identify promising areas for new research. 

The approach in this project is to:
a) compile a bibliographic database of all the research publications;
b) evaluate and categorize each research article with respect to a number of characteristics, including type of study (empirical, theoretical, review, etc.), methodology, main results, limits to generalizability or particular studies, assessment items, and a fresh summary of each article;
c) incorporate these results into a publically accessible, searchable online database resource, and, finally,
d) create learning trajectories (cross-grade) for each of the concept areas listed above. 

In the papers that are being developed from this project, we will provide practitioners with an exhaustive online research resource base in a critical domain of mathematical reasoning and create links between research on these critical topics and instructional practice through standards, benchmarks, and assessment items.  We have already identified a number of testable hypotheses for future research.  The database resource we have developed will be released for other researchers to support their own syntheses of research literature.

PROJECT TEAM