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Adding + It Up: Helping Children Learn Mathematics
Lamon, S.J. (1993). Ratio and proportion: Connecting content and children’s thinking. Journal for Research in Mathematics Education,24, 41–61.
Lamon, S.J. (1994). Ratio and proportion: Cognitive foundations in unitizing and norming. In G.Harel & J.Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 89–120). Albany: State University of New York Press.
Lamon, S.J. (1995). Ratio and proportion: Elementary didactical phenomenology. In J. T.Sowder & B.P Schappell (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 167–198). Albany: State University of New York Press.
Langrall, C.W., & Swafford, J.O. (2000). Three balloons for two dollars: Developing proportional reasoning. Mathematics Teaching in the Middle School,6, 254–261.
Lappan, G., & Bouck, M.K. (1998). Developing algorithms for adding and subtracting fractions. In L.J.Morrow & M.J.Kenney (Eds.), The teaching and learning of algorithms in school mathematics (1998 Yearbook of the National Council of Teachers of Mathematics, pp. 183–197). Reston, VA: NCTM.
Lappan, G., Fey, J.Fitzgerald, W., Friel, S., & Phillips E. (1996). Bits and pieces 2: Using rational numbers. Palo Alto, CA: Dale Seymour.
Lesh, R., Post, T.R., & Behr, M. (1988). Proportional reasoning. In J.Hiebert & M.Behr (Eds.), Number concepts and operations in the middle grades (pp. 93–118). Reston, VA: National Council of Teachers of Mathematics.
Liebeck, P. (1990). Scores and forfeits: An intuitive model for integer arithmetic. Educational Studies in Mathematics,21, 221–239.
Mack, N.K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education,21, 16–32.
Mack, N.K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education,26, 422–441.
Moreno, R., & Mayer, R.E. (1999). Multimedia-supported metaphors for meaning making in mathematics. Cognition and Instruction,17, 215–248.
Morris, A.L. (in press). A teaching experiment: Introducing fourth graders to fractions from the viewpoint of measuring quantities using Davydov’s mathematics curriculum. Focus on Learning Problems in Mathematics.
Moss, J., & Case, R. (1999). Developing children’s understanding of the rational numbers: A new model and an experimental curriculum. Journal for Research in Mathematics Education,30, 122–147.
Mukhopadhyay, S., Resnick, L.B., & Schauble, L. (1990). Social sense-making in mathematics; Children’s ideas of negative numbers. Pittsburgh: University of Pittsburgh, Learning Research and Development Center. (ERIC Document Reproduction Service No. ED 342 632 ).
Peck, D.M., & Jencks, S.M. (1981). Conceptual issues in the teaching and learning of fractions. Journal for Research in Mathematics Education,12, 339–348.
Post, T., Behr, M., & Lesh, R. (1988). Proportionality and the development of pre-algebra understanding. In A.F.Coxford & A.P.Schulte (Eds.), The ideas of algebra, K-12 (1988 Yearbook of the National Council of Teachers of Mathematics, pp. 78–90). Reston, VA: NCTM.
Post, T.P., Wachsmuth, I., Lesh, R., & Behr, M.J. (1985). Order and equivalence of rational numbers: A cognitive analysis. Journal for Research in Mathematics Education,16, 18–36.