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Mathematics for Young Children

The following sources are recommended by a professor whose research specialty is elementary mathematics.


Six Superlative Sources

· Copley, J.V. (Ed.) (1999). Mathematics in the early years. National Council of Teachers of Mathematics.

· Nelson, G.D. (Ed.) (1999). Dialogue on early childhood science, mathematics, and technology education. American Association for the Advancement of Science.

· Kamii, C.K., and Housman, L.B. (1999). Young children reinvent arithmetic: Implications of Piaget's theory (2nd ed.). Teaching College Press.

· Clements, D.H. (1989). Computers in elementary mathematics education. Prentice Hall.

· Clements, D.H. (1999). Playing math with young children. Curriculum Administrator, 35(4), 25-28.

· Clements, D.H. (1999, October). The geometric world of young children. Early Childhood Today, 34-43.

Other Excellent Sources

· Stigler, J.W., and Perry, M. (1988). Mathematics learning in Japanese, Chinese, and American classrooms. In G.B. Saxe and M. Gearhart (Eds.), Children's mathematics (pp. 27-54). Jossey-Bass.

· Stigler, J.W. (1988, October). The use of verbal explanation in Japanese and American Classrooms. The Arithmetic Teacher, 27-29.

· Pursuing excellence, A study of U.S. eighth-grade mathematics and science teaching, learning, curriculum, and achievement in international context: Initial findings from the Third International Mathematics and Science Study. (1996, November). National Center for Education Statistics.

· National Research Council. (1989). Everybody counts: A report to the nation on the future of mathematics education. National Academy Press.

· National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics.

· National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.

· Price, Jack. (1996, March). Helping parents understand change. NCTM News Bulletin, 3.

· Baroody, Arthur. (1987). Children's mathematical thinking (3-49). Teachers College Press.

· Wheatley, G.W. (1990). Spatial sense and mathematics learning. Arithmetic Teacher, 37(6), 10-11.

· Kamii, Constance. (2000). Young children reinvent arithmetic (3-51). Teachers College Press.

· Finn, Chester. (1986, November). Research in brief: How the experts teach math. U.S. Department of Education, Office of Educational Research and Improvement.

· Brownell, William. (1987, April, originally 1956, October). Meaning and skill: Maintaining the balance. The Arithmetic Teacher, 18-25.

· Clements, D.H., and Battista, M.T. (1990). Constructivist learning and teaching. Arithmetic Teacher, 38(1), 34-35.

· Kamii, C., and Lewis, B.A. (1990). Constructivism and first-grade arithmetic. Arithmetic Teacher, 38(1), 36-37.

· von Glaserfeld, E. (1987). Learning as a constructive activity. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (3-17). Lawrence Erlbaum.

· Davis, R.B. (1991). Giving pupils tools for thinking. Arithmetic Teacher, 38(5), 23-25.

· Kamii, C.K., and Lewis, B. (1993). The harmful effects of algorithms in primary arithmetic. Teaching K-8, 23(4), 36-38.

· Macmillan, A. (1990). Constructivism in a kindergarten mathematics class. Mathematics Education Research Journal, 2(2), 12-27.

· Steffe, L.P., and Olive, J. (1991, May). The problem of fractions in the elementary school. Arithmetic Teacher, 22-24.

· Davis, R.B., and Maher, C.A. (1990). What do we do when we "do mathematics"? In R.B. Davis, C.A. Maher, and N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (pp. 65-78), Journal for Research in Mathematics Education Monograph Number 4. National Council of Teachers of Mathematics.

· Clements, D.H. (1997). (Mis?)Constructing constructivism. Teaching Children Mathematics, 4(4), 198-200.

· Price, Jack. (1995). Taking a look at teaching from two examples. NCTM News Bulletin, May/June 1995, 3.

· Cobb, P. (1988). The tension between theories of learning and instruction in mathematics education. Educational Psychologist, 23, 87-103.

· Confrey, J. (1990). What constructivism implies for teaching. In R.B. Davis, C.A. Maher, and N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (107-122), Journal for Research in Mathematics Education Monograph Number 4. National Council of Teachers of Mathematics.

· Maher, C.A., and Davis, R.B. (1990). Building representations of children's meanings. In R.B. Davis, C.A. Maher, and N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (79-90), Journal for Research in Mathematics Education Monograph Number 4. National Council of Teachers of Mathematics.

· Cobb, P., et al. (1988, September). Research into practice: Creating a problem-solving atmosphere. Arithmetic Teacher, pp. 46-47.

· Wood, T., and Yackel, E. (1990). The development of collaborative dialogue within small group interactions. In L.P. Steffe and T. Wood (Eds.), Transforming children's mathematics education (244-252). Lawrence Erlbaum.

· Burns, M. (1985, February). The role of questioning. Arithmetic Teacher, 14-16.

· McCullough, D., and Findley, E. (1983, March). How to ask effective questions. Arithmetic Teacher, 30(7), 8-9.

· Baroody, A.J. (1996). An investigative approach to the mathematics instruction of children classified as learning disabled. In D.K. Reid, W.P. Hresko, and H.L. Swanson (Eds.), Cognitive approaches to learning disabilities (547-615). Pro-Ed.

· Silver, Edward A., and Smith, Margaret S. (1990, April). Teaching mathematics and thinking. Arithmetic Teacher, 34-37.

· Grouws, Douglas A., and Good, Thomas L. (1989, April). Issues in problem solving. Arithmetic Teacher, 34-35.

· Lampert, Magdalene. (1989, March). Arithmetic as problem solving. Arithmetic Teacher, 34-36.

· Callahan, Leroy G. (1985, October). One point of view: Pressing problems in primary mathematics programs: Time, texts, and tests, Arithmetic Teacher, 33, 2.

· Romberg, T.A., and Wilson, L. (1992). Alignment of tests with the standards. Arithmetic Teacher, 40(1), 18-22.

· Estrich, Susan. (1995, September 21). A novel school plan: Back to basics. USA Today, 15A.

· Clements, D.H. (1989). Consensus, more or less. Review of Steffe and Cobb (1988), Construction of arithmetical meanings and strategies, and of Fuson (1988), Children's counting and concepts of number. Journal for Research in Mathematics Education, 20, 111-119.

· Fuson, Karen C. (1988). Children's counting and concepts of number (5-7, 46-49, 66-67, 403-417). Springer-Verlag.

· Fuson, Karen C. (1990). Issues in place-value and multidigit addition and subtraction learning and teaching. Journal for Research in Mathematics Education, 21, 273-280.

· Baroody, Arthur J. (1990). How and when should place-value concepts be taught? Journal for Research in Mathematics Education, 21, 281-286.

· Carpenter, T.P., Fennema, E., Peterson, P.L., Chiang, C.P., and Loef, M. (1989). Using knowledge of children's mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26, 499-531.

· Loef, M., Carey, D.A., Carpenter, T.P., and Fennema, E. (1988, November). Integrating assessment and instruction. Arithmetic Teacher, 53-55.

· Kamii, C., and Joseph, L. (1988, February). Teaching place value and double-column addition. Arithmetic Teacher, 48-52.

· Killion, K., and Steffe, L.P. (1989, September). Children's multiplication. Arithmetic Teacher, 34-35.

· Kamii, C., and Dominick, A. (1997). To teach or not to teach algorithms. Journal of Mathematical Behavior, 16, 51-61.

· Hembree, R. (1986, September). Research gives calculators a green light, Arithmetic Teacher, 18-21.

· Burrill, G. (1997, November). Computation, calculators, and the "basics." NCTM News Bulletin, 3.

· Wheatley, G.W. (1990). Calculators and constructivism. Arithmetic Teacher, 38(2), 22-23.

· Clements, D.H. (1985, Winter). Beyond "1, 2, 3...": Computers and mathematical thinking. Beginnings, 12-16.

· Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas (vi-vii, 19-23, 55-78). Basic Books.

· Clements, D.H. (1988). Early experiences with mathematics. Logo Exchange, 7(1), 30-32

· Clements, D.H., and Sarama, J. (1996). Turtle math: Redesigning Logo for elementary mathematics. Learning and Leading with Technology, 23(7), 10-15.

· Clements, D.H., and McMillen, S. (1996). Rethinking "concrete" manipulatives. Teaching Children Mathematics, 2(5), 270-279.

· Clements, D.H., and Sarama, J. (1997). Computers support algebraic thinking. Teaching Children Mathematics, 3(6), 320-325.

· Battista, M.T., and Clements, D.H. (1988, November). A case for a Logo-based elementary school geometry curriculum. Arithmetic Teacher, 36, 11-17.

· Battista, M.T., and Clements, D.H. (1990). Constructing geometric concepts in Logo. Arithmetic Teacher, 38(3), 15-17.

· Burger, W.F. (1988, November). An active approach to geometry. Arithmetic Teacher, 36, 2.

· Battista, M.T., and Clements, D.H. (1998). Finding the number of cubes in rectangular cube buildings. Teaching Children Mathematics, 4, 258-264.

· Battista, M.T., Clements, D.H., Arnoff, J., Battista, K., and Borrow, C.V.A. (1998). Students' spatial structuring of 2D arrays of squares. Journal for Research in Mathematics Education, 29, 503-532.

· Clements, D.H. (1999). Teaching length measurement: Research challenges. School Science and Mathematics, 99(1), 5-11.

· Clements, D.H., Battista, M.T., and Sarama, J. (1998). Students' development of geometric and measurement ideas. In R. Lehrer and D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (201-225). Lawrence Erlbaum Associates.

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