Rational Numbers: An Integration of Research
Thomas P. Carpenter, Elizabeth Fennema, Thomas A. Romberg
Lawrence Erlbaum Associates, 1993 - Education - 372 pages
Until recently there had been relatively little integration of programs of research on teaching, learning, curriculum, and assessment. However, in the last few years it has become increasingly apparent that a more unified program of research is needed to acquire an understanding of teaching and learning in schools that will inform curriculum development and assessment. The chapters in this volume represent a first step toward an integration of research paradigms in one clearly specified mathematical domain.
Integrating a number of different research perspectives is a complex task, and ways must be found to reduce the complexity without sacrificing the integration. The research discussed in this volume is tied together because it deals with a common content strand. During the last ten years specific content domains have served as focal points for research on the development of mathematical concepts in children. The areas of addition and subtraction, algebra, rational numbers, and geometry are notable examples. Whether a similar organizational structure will prevail for programs of research that integrate the study of teaching, learning, curriculum, and assessment is an open question. The perspectives presented in this volume illustrate the potential for adopting this perspective.
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Toward A Unified Discipline of Scientific Inquiry
Toward a Semantic Analysis
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algorithm analysis applied assessment Behr Eds Carpenter chapter classroom cognitive complexity composite unit concept of rational concepts and operations construct cookies Council of Teachers covariation curriculum decimal domain duplicator/partition-reducer example Fennema formal Grouws Hiebert Hillsdale informal knowledge instruction intensive quantity interpretation intuitive Kieren Lawrence Erlbaum Associates Leinhardt Lesh Mack manipulative Mathematics Education mathematics-of-quantity measure measure spaces metacognitive middle grades multiplicative notation number line operand part-whole partition-reducer partitioning pieces pizza problem situation problem solving procedural knowledge prospective teachers protoquantitative quantity question quotient quotient field ratio and proportion rational number concepts reasoning recursive recursive theory relationships representational contexts represented Research in Mathematics research on teaching Reunitize schema semantic shrinker singleton units solution specific strategies Streefland stretcher/shrinker structure subconstructs suggested symbolic representations symbols and procedures Table Teachers of Mathematics teaching and learning thinking understanding of rational unit fractions whole number