An empirically-based trajectory for fostering abstraction of equivalent-fraction concepts: A study of the Learning Through Activity research program

The Journal of Mathematical Behavior - Tập 52 - Trang 134-150 - 2018
Melike Kara1, Martin A. Simon1, Nicora Placa1
1New York University, Dept. of Teaching & Learning, 239 Greene St, #420, New York, NY 10003 USA

Tài liệu tham khảo

Askey, 2014 Biddlecomb, 2000 Bright, 1988, Identifying fractions on number lines, Journal for Research in Mathematics Education, 19, 215, 10.2307/749066 Brousseau, 2014 Confrey, 2012, Equivalence and comparison of fractions Empson, 1999, Equal sharing and shared meaning: The development of fraction concepts in a first-grade classroom, Cognition and Instruction, 17, 283, 10.1207/S1532690XCI1703_3 2012 2012 Hackenberg, 2009, Students’ whole number multiplicative concepts: A critical constructive resource for fraction composition schemes, Journal of Mathematical Behavior, 28, 1, 10.1016/j.jmathb.2009.04.004 Hargrove, 2012, Investigating equivalent fractions with relationship rods Heinz, 2000, Moving students through steps of mathematical knowing: An account of the practice of an elementary mathematics teacher in transition, The Journal of Mathematical Behavior, 19, 83, 10.1016/S0732-3123(00)00037-7 Hunting, 1984, Understanding equivalent fractions, Journal of Science and Mathematics Education in Southeast Asia, 7, 26 Kamii, C. (1994, April). Equivalent fractions: An explanation of their difficulty and educational implications. Paper presented at the National Council of Teachers of Mathematics Research Pre-session jointly sponsored with the AERA SIG/RME, Indianapolis, IN. Kamii, 1995, Equivalent fractions: Their difficulty and educational implications, Journal of Mathematical Behavior, 14, 365, 10.1016/0732-3123(95)90035-7 Kaput Center for Research and Innovation in STEM Education, 2015 Lamon, 2012 Larson, 1980, Locating proper fractions on number lines: Effect of length and equivalence, School Science and Mathematics, 80, 423, 10.1111/j.1949-8594.1980.tb09687.x 2017 National Assessment of Educational Progress, 2009 National Governors Association Center for Best Practices, 2010 Olive, 1999, From fractions to rational numbers of arithmetic: A reorganization hypothesis, Mathematical Thinking and Learning, 1, 279, 10.1207/s15327833mtl0104_2 Piaget, 1977, The role of action in the development of thinking Piaget, 1980 Piaget, 2001 Simon, 1995, Reconstructing mathematics pedagogy from a constructivist perspective, Journal for Research in Mathematics Education, 26, 114, 10.2307/749205 Simon, 2006, Key developmental understandings in mathematics: A direction for investigating and establishing learning goals, Mathematical Thinking and Learning, 8, 359, 10.1207/s15327833mtl0804_1 Simon, 2017, Explicating mathematical concept and mathematical conception as theoretical constructs, Educational Studies in Mathematics, 94, 117, 10.1007/s10649-016-9728-1 Simon, M. A. (this issue). An emerging methodology for studying mathematics concept learning and instructional design. Simon, M. A., Kara, M., Placa, N., & Avitzur, A. (this issue). Towards an integrated theory of mathematics conceptual learning and instructional design: The Learning Through Activity theoretical framework. Simon, 2016, Categorizing and promoting reversibility of mathematical concepts, Educational Studies in Mathematics, 93, 137, 10.1007/s10649-016-9697-4 Stafylidou, 2004, The development of students’ understanding of the numerical value of fractions, Learning and Instruction, 14, 503, 10.1016/j.learninstruc.2004.06.015 Steffe, 2003, Fractional commensurate, composition, and adding schemes: Learning trajectories of Jason and Laura: Grade 5, The Journal of Mathematical Behavior, 22, 237, 10.1016/S0732-3123(03)00022-1 Steffe, 2010 Steffe, 2000, Teaching experiment methodology: Underlying principles and essential elements, 267 1991, Vol. 8 Streefland, 1993, The design of a mathematics course a theoretical reflection, 109 van Galen, 2008 Wong, 2007, 824