An Integrated Research on Children's Construction of Meaningful, Symbolic, Partitioning-related Conceptions and the Teacher's Role in Fostering That Learning

Behr, 1984, Order and equivalence of rational numbers: A clinical teaching experiment, Journal for Research in Mathematics Education, 15, 323, 10.2307/748423 Behr, 1992, Rational number, ratio, and proportion, 296 Biddlecomb, 1994, Theory-based development of computer microworlds, Journal of Research in Childhood and Education, 8, 87, 10.1080/02568549409594858 Clements, 1990, How natural is fraction knowledge?, 181 Cobb, 1995, Introduction: The coordination of psychological and sociological perspectives in mathematics education, 1 Cobb, 1983, The constructivist researcher as teacher and model builder, Journal for Research in Mathematics Education, 14, 83, 10.2307/748576 Cobb, 1992, A constructivist alternative to the representational view of mind in mathematics education, Journal for Research in Mathematics Education, 23, 2, 10.2307/749161 Confrey, Jere (1990, April). Splitting, similarity, and rate of change: A new approach to multiplication and exponential functions. Paper presented at the annual meeting of the American Educational Research Association, Boston, MA. Confrey, 1998, Building mathematical structure within a conjecture driven teaching experiment on splitting, 1, 39 Cooney, 1988, An agenda for research on teaching mathematics Davis, 1993, What might a fraction mean to a child and how would a teacher know?, Journal of Mathematical Behavior, 12, 63 Davydov, 1991, The object sources of the concept of fractions, 86 Dewey, 1938, 5 Dewey, 1949 Gravemeijer, Koeno, Cobb, Paul, Bowers, Janet, & Whitenack, Joy, in press. Symbolizing, modeling, and instructional design. In: Cobb, P., E. Yackel, K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design, Mahwah, NJ: Erlbaum. Hiebert, 1988, Introduction: Capturing the themes, 1 Kamii, 1995, Equivalent fractions: Their difficulty and educational implications, Journal of mathematical behavior, 14, 365, 10.1016/0732-3123(95)90035-7 Kieren, 1976, On the mathematical, cognitive, and instructional foundations of rational numbers, 101 Kieren, 1988, Personal knowledge of rational numbers: Its intuitive and formal development., 162 Kieren, Thomas E. (1993, January). The learning of Fractions: Maturing in a fraction world. Paper presented at the meeting of the Working Group on Fraction Learning and Instruction, Athens, GA. Mack, 1990, Learning fractions with understanding: Building on informal knowledge, Journal for Research in Mathematics Education, 21, 16, 10.2307/749454 McLellan, 1908 Meira, 1995, The microevolution of mathematical representations in children's activity, Cognition and Instruction, 13, 269, 10.1207/s1532690xci1302_5 Olive, John (1993, April). Children's construction of fractional schemes in computer microworlds, Part II: Constructing multiplicative operations with fractions. Paper presented at the annual meeting of the National Council of Teachers of Mathematics. Seattle, WA. Papert, 1980 Piaget, 1971 Piaget, 1980, The psychogenesis of knowledge and its epistemological significance, 23 Piaget, 1981 Piaget, 1960 Sáenz-Ludlow, 1994, Michael's fraction schemes, Journal for Research in Mathematics Education, 25, 50, 10.2307/749292 Simon, 1995, Reconstructing mathematics pedagogy from a constructivist perspective, Journal for Research in Mathematics Education, 26, 114, 10.2307/749205 Steffe, Leslie P. (1992, July). On the nature of learning theory. Paper presented at the meeting of the International Congress of Mathematics Education (Working Group 4) Quebec, Canada. Steffe, Leslie P. (1993, April). Children's construction of iterative fraction schemes. Paper presented at the annual meeting of the National Council of Teachers of Mathematics. Seattle, Washington. Steffe, 1988 Steffe, 1989 Steffe, 1994, Interaction and children's mathematics, Journal of Research in Childhood and Education, 8, 99, 10.1080/02568549409594859 Stephens, 1990, Communication in the mathematics classroom, 228 Streefland, 1991 Tzur, Ron (1995). Interaction and children's fraction learning. Unpublished doctoral dissertation, University of Georgia, Athens. Tzur, 1999, An integrated study of children's construction of improper fractions and the teacher's role in promoting that learning, Journal for Research in Mathematics Education, 30, 390, 10.2307/749707 Varela, 1991 von Glasersfeld, 1987 von Glasersfeld, Ernst (1989). Cognition, construction of knowledge, and teaching. Synthese: A special issue of philosophy of science and education. von Glasersfeld, 1990, Environment and communication, 30 von Glasersfeld, 1991, Abstraction, re-presentation, and reflection: An interpretation of experience and Piaget's approach, 45 Yackel, 1990, The importance of social interaction in children's construction of mathematical knowledge, 12