Rational Number Project: Research on Teaching and Learning in Multiplicative Structures

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This five site project is designed to accomplish the following six objectives: 1) Conduct a mathematical/psychological/instructional analysis of the content domain of multiplicative structures. This analysis will identify relationships within and between the many topics included in this domain, and will form the framework for the curriculum development, assessment, teacher education, and research components of the project. 2) Develop an objectives framework and a scope and sequence for elementary and middle school mathematics curriculum material for the domain of multiplicative structures: to consist of multiplica- tive concepts, relationships, operations, and problem situations and will include: multiplication, division, rational number concepts including fraction (part whole), ratio, decimal, operator, measurement and proportionality up to and including missing value numerical comparisons situations, qualitative reasoning and the graphical depiction and interpretation of linear functions. 3) Outline a complete assessment program to coincide with project goals. This assessment program will include a computer adaptive learner profile test and computer based simulations of clinical interviews. 4) Develop, pilot, and implement abbreviated teaching experiments designed to explore students' "logical conceptual development." Several of these mini units will also be field tested in 6-10 intact classrooms. Teachers will be interviewed. 5) Refine, redevelop and extend, rational number related materials from our previous work so as to reflect more recent project understandings. Materials will be formatted so as to be usable by middle school classroom teachers. 6) Develop and validate a model of rational belief change, which will used for both helping teachers acquire knowledge about multi- plicative structures, and for evaluating teachers' knowledge about this domain.