CURRICULUM IMPLICATIONS OF RESEARCH ON THE LEARNING, TEACHING AND ASSESSING OF RATIONAL NUMBER CONCEPTS
Thomas R. Post University of Minnesota
Kathleen A. Cramer University of Wisconsin, River Falls
Merlyn Behr Louisiana State University
Richard Lesh Educational Testing Service, Princeton, N.J.
Guershon Harel Purdue University
Recent advances in our views of the domain of rational number concepts in conjunction with changes in our perceptions of children's understanding of rational number and proportionality have altered conceptions of how these topics should be addressed in the school curriculum. New content, different emphases, increased instructional time recognizing the centrality of this domain, modified instructional techniques and assessment practices, and rethought approaches to teacher pre- and in-service development in mathematics all will serve to substantially alter our in-school approaches to the teaching and learning of rational number concepts. This chapter initiates a discussion of several of these new directions.
The charge to the authors represented in this book was to relate each chapter as far as possible to the multiple research perspectives or strands: content analysis, student thinking, teacher thinking, classroom instruction, assessment, and curricular implications. In one sense, this chapter on curricular implications may be the easiest chapter to write, because by its very nature the discipline of mathematics education is an applied science. Each researcher/participant ultimately has the same overall goal or objective -- that of improving the quality of mathematics instruction and learning on behalf of children. From this perspective, it should be possible to identify relevant implications from most of the literature published in the area. On the other hand, this may be the most difficult of the chapters to develop because the vast majority of published pieces do not concern themselves overtly with curricular implications, and the sheer enormity of published material precludes any definitive compilation of implications for the classroom.