Developing a framework and the construction of an understanding of place value

Referencias

Confrey, J. (1991). Learning to listen: A student's understanding of powers of ten. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 111-138). Dordrecht: Kluwer Academic Publishers. Fennema, E., & Franke, M. (1992). Teachers' knowledge and its impact. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Simon & Schuster. Fuson, K. (1990). Conceptual structures for multiunit numbers: Implications for learning and teaching multidigit addition, subtraction, and place value. Cognition and Instruction, 7, 343-403. Grossman, A. S. (1983). Decimal notation: An important research finding. Arithmetic Teacher, 30(9), 32-33. Hart, K. (1989). Place value: Subtraction. In D. Johnson (Ed.), Children's mathematical frameworks 8-13: A study of classroom teaching (pp. 8-45). Windsor, England: NFER-NELSON. Hiebert, J. (1985). Children's knowledge of common and decimal fractions. Education and Urban Society, 17, 427-437. Irwin, K. (2001). Using everyday knowledge of decimals to enhance understanding. Journal for Research in Mathematics Education, 32, 399-420. Kamii, C. (1985). Young children reinvent arithmetic: Implications of Piaget's theory. New York: Teachers College Press. Kamii, C. (1986). Place value: An explanation of its difficulty and educational implications for the primary grades. Journal of Research in Childhood Education, 1, 75-86. Khoury, H. A., & Zazkis, R. (1994). On fractions and non-standard representations: Pre-service teachers' concepts. Educational Studies in Mathematics, 27, 191-204. McClain, K. (2003). Supporting preservice teacher' understanding of place value and multidigit arithmetic. Mathematical Thinking and Learning, 5, 281-306. Nesher, P., & Peled, I. (1986). Shifts in reasoning: The case of extending number concepts. Educational Studies in Mathematics, 17, 67-79. Putnam, R. T., Heaton, R. M., Prawat, R. S., & Remillard, J. (1992). Teaching mathematics for understanding: Discussing case studies of four fifth-grade teachers. Elementary School Journal, 93, 213-228. Putt, I. J. (1995). Preservice teachers ordering of decimal numbers: When more is smaller and less Is larger! Focus on Learning Problems in Mathematics, 17(3), 1-15. Resnick, L., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education, 20, 8-27. Sackur-Grisvald, C., & Leonard, F. (1985). Intermediate cognitive organizations in the process of learning a mathematical concept: The order of positive decimal numbers. Cognition and Instruction, 2, 157-174. Sierpinska. (1994). Understanding in mathematics. London: Falmer Press. Stacey, K., Helme, S., Steinle, V., Baturo, A., Irwin, K., & Bana, J. (2001). Preservice teachers' knowledge of difficulties in decimal numeration. Journal of Mathematics Teacher Education,, 4(3), 205-225. Stacey, K., & Steinle, V. (1998). Refining the classification of students' interpretations of decimal notation. Hiroshima Journal of Mathematics Education, 6(49-69). Steffe, L. (1988). Children's construction of number sequences and multiplying schemes. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (Vol. 2, pp. 119-140). Reston, VA: Lawrence Erlbaum Associates. Steffe, L. (1990). On the knowledge of mathematics teachers. In R. B. Davis, C. Maher & N. Noddings (Eds.), Journal for Mathematics Education Monograph 4: Constructivist views on the teaching and learning of mathematics (pp. 167-184). Reston, VA: NCTM. Steffe, L. (1994). Children's multiplying schemes. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 3-39). Albany, NY: State University of New York Press. Steffe, L., Cobb, P., & von Glasersfeld, E. (1988). Construction of arithmetical meanings and strategies. New York: Springer-Verlag. Steffe, L., & D'Ambrosio, B. (1995). Toward a working model of constructivist teaching: A reaction to Simon. Journal for Research in Mathematics Education, 26, 146-159. Thanheiser, E. (2009). Preservice elementary school teachers' conceptions of multidigit whole numbers. Journal for Research in Mathematics Education, 40, 251-281. Thipkong, S., & Davis, E. J. (1991). Preservice elementary teachers' misconceptions in interpreting and applying decimals. School Science and Mathematics, 91(3), 93-99. Whitehead, J. (1989). Creating a living educational theory from questions of the kind,'How do I improve my practice?'. Cambridge Journal of Education, 19(1), 41-52. Widjaja, W., Stacey, K., & Steinle, V. (2008). Misconceptions about density of decimals: Insights from Indonesian pre-service teachers. Journal of Science and Mathematics Education in Southeast Asia. Zazkis, R., & Khoury, H. A. (1993). Place value and rational number representations: Problem solving in the unfamiliar domain of non-decimals. Focus on Learning Problems in Mathematics, 15(1), 38-51