Charlotte, NC: Information Age Publishing. (Ed.), Second handbook of research on mathematics teaching and learning (pp. Rational numbers and proportional reasoning: Toward a theoretical framework for research. Adding it up: Helping children learn mathematics. Kilpatrick, J., Swafford, J., & Findell, B. Novotná (Eds.), Proceedings of the twenty-third ICMI study: Primary mathematics study on whole numbers (pp. The model method-A tool for representing and visualizing relationships. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. Multiplication and division as models of situations. The common core state standards for mathematics. The American Mathematical Monthly, 88(4), 286–290.Ĭommon Core State Standards Initiative. Translation difficulties in learning mathematics. Journal for Research in Mathematics Education, 13(1), 16–30.Ĭlement, J., Lochhead, J., & Monk, G. Algebra word problem solutions: Thought processes underlying a common misconception. Educational Measurement: Issues and Practice, 33(1), 2–14.Ĭlement, J. Diagnosing teachers’ understandings of rational number: Building a multidimensional test within the diagnostic classification framework. For the Learning of Mathematics, 18(3), 12–19.īradshaw, L., Izsák, A., Templin, J., & Jacobson, E. Macau, China: University of Macao.īoulet, G. Novotna (Eds.), Proceedings of the twenty-third ICMI study: Primary mathematics study on whole numbers (pp. From multiplication to proportional relationships. Journal for Research in Mathematics Education, 46(1), 17–38.īeckmann, S., Izsák, A., & Ölmez, I. Two perspectives on proportional relationships: Extending complementary origins of multiplication in terms of quantities. Vancouver, Canada: PME.īeckmann, S., & Izsák, A. Allan, (Eds.), Proceedings of the joint meeting of thirty-eighth conference of the international meeting of the Psychology of mathematics education and the thirty-sixth meeting of the north American chapter of the International Group for the Psychology of mathematics education (Vol. Variable parts: A new perspective on proportional relationships and linear functions. Boston: Pearson.īeckmann, S., & Izsák, A. Mathematics for elementary teachers with activities. Solving algebra and other story problems with simple diagrams: a method demostrated in grade 4–6 texts used in singapore. Strip diagram (tape diagram, model method)īeckmann, S.Based on the data, extensions to current theories on reasoning quantitatively and with variables are proposed. The points of tension were resolved by focusing on referent units or on equality. In contrast, most arguments involving a fractional multiplier interpreted multiplication as “of.” All the points of tension that the future teachers encountered while developing their equations concerned referent units for quantities. Some arguments combined an interpretation of fractions as multiples (or iterates) of unit fractions with an interpretation of multiplication as a whole number of equal groups. The arguments also treated variables as quantities but rarely described the variables as numbers of units. The future teachers’ arguments were mathematically valid and relied on reasoning quantitatively about strip diagrams. Both equations involved a constant of proportionality that was not a whole number. One equation was for two quantities varying together and one was for a line through the origin in a coordinate plane. Findings are presented from an analysis of how six future middle-grade teachers reasoned with strip diagrams and a variable parts perspective on proportional relationships to develop and explain equations in two variables.
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