Rational Numbers

Thomas P. Carpenter, Elizabeth Fennema, Thomas A. Romberg

• Contents: Part I:Overview.T.P. Carpenter, E. Fennema, T.A. Romberg, Toward A Unified Discipline of Scientific Inquiry. Part II:Content Analyses of Rational Numbers.M.J. Behr, G. Harel, T. Post, R. Lesh, Rational Numbers: Toward a Semantic Analysis -- Emphasis on the Operator Construct. T.E. Kieren, Rational and Fractional Numbers: From Quotient Fields to Recursive Understanding. Part III:Students' Thinking.N.K. Mack, Learning Rational Numbers With Understanding: The Case of Informal Knowledge. L.B. Resnick, J.A. Singer, Protoquantitative Origins of Ratio Reasoning. S.J. Lamon, Ratio and Proportion: Children's Cognitive and Metacognitive Processes. Part IV:Teachers and Teaching.D.L. Ball, Halves, Pieces, and Twoths: Constructing and Using Representational Contexts in Teaching Fractions. C.A. Brown, A Critical Analysis of Teaching Rational Number. J.A. Hiebert, Benefits and Costs of Research That Links Teaching and Learning Mathematics. J.T. Sowder, N. Bezuk, L.K. Sowder, Using Principles From Cognitive Psychology to Guide Rational Number Instruction for Prospective Teachers. Part V:Assessment.S.P. Marshall, Assessment of Rational Number Understanding: A Schema-Based Approach. Part VI:Curriculum and Instruction.L. Streefland, Fractions: A Realistic Approach. T.R. Post, K.A. Cramer, M. Behr, R. Lesh, G. Harel, Curriculum Implications of Research on the Learning, Teaching, and Assessing of Rational Number Concepts.

"...the chosen references exemplify the points well....[the volume] draws on relevant studies but stays focused on the goal of identifying and integrating issues...goes beyond the content, learning, and instruction focus found in earlier works....Mathematics educators...would certainly find this volume relevant. It would also interest researchers engaged in the careful study of teaching and learning within instructional settings....It is precisely in smoothing some of the sharp edges separating rational number issues in teaching, learning, assessment, and content that Rational Numbers: An Integration of Research makes its contribution."—Contemporay Psychology