Students’ whole number multiplicative concepts: A critical constructive resource for fraction composition schemes
Tài liệu tham khảo
Armstrong, 1995, Multiplication and division of fractions: The search for meaning, 85
Ball, 2000, Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics, 81
Ball, 2001, Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge
Behr, 1992, Rational number, ratio, and proportion, 296
Behr, 1993, Rational numbers: Toward a semantic analysis–emphasis on the operator construct, 13
Behr, 1984, Order and equivalence of rational numbers: A clinical teaching experiment, Journal for Research in Mathematics Education, 15, 323, 10.2307/748423
Biddlecomb, 1994, Theory-based development of computer microworlds, Journal of Research in Early Childhood Education, 8, 87, 10.1080/02568549409594858
Biddlecomb, 2002, Numerical knowledge as enabling and constraining fraction knowledge: An example of the reorganization hypothesis, Journal of Mathematical Behavior, 21, 167, 10.1016/S0732-3123(02)00117-7
Biddlecomb, B., Olive, J. (2000). JavaBars [Computer software]. Retrieved June 4, 2002 from http://jwilson.coe.uga.edu/olive/welcome.html.
Carpenter, 1999
Clement, 2000, Analysis of clinical interviews: Foundations and model viability, 547
Cobb, 2008, Experimenting to support and understand learning processes, 68
Confrey, 2000, Transformative teaching experiments through conjecture-driven research design, 231
Davis, 1993, What might a fraction mean to a child and how would a teacher know?, Journal of Mathematical Behavior, 12, 63
Empson, 2006, Fractions as the coordination of multiplicatively related quantities: A cross-sectional study of children's thinking, Educational Studies in Mathematics, 63, 1, 10.1007/s10649-005-9000-6
Fosnot, 2001
Greer, 1992, Multiplication and division as models of situations, 276
Hackenberg, A. J. (2005). Construction of algebraic reasoning and mathematical caring relations. Unpublished doctoral dissertation, University of Georgia.
Hackenberg, 2007, Units coordination and the construction of improper fractions: A revision of the splitting hypothesis, Journal of Mathematical Behavior, 26, 27, 10.1016/j.jmathb.2007.03.002
Hackenberg, A. J. (submitted for publication). Students’ reversible multiplicative reasoning with fractions. Cognition and Instruction.
Hunting, 1996, Engaging whole-number knowledge for rational-number learning using a computer-based tool, Journal for Research in Mathematics Education, 27, 354, 10.2307/749369
Izsak, 2008, Mathematical knowledge for teaching fraction multiplication, Cognition and Instruction, 26, 95, 10.1080/07370000701798529
Izsak, 2008, Teaching and learning fraction addition on number lines, Journal for Research in Mathematics Education, 39, 33
Kamii, 2000
Kieren, 1980, The rational number construct: Its elements and mechanisms, 125
Kieren, 1995, Creating spaces for learning fractions, 31
Lappan, 2006
Mack, 1995, Confounding whole-number and fraction concepts when building on informal knowledge, Journal for Research in Mathematics Education, 26, 422, 10.2307/749431
Mack, 2001, Building on informal knowledge through instruction in a complex content domain: Partitioning, units, and understanding multiplication of fractions, Journal for Research in Mathematics Education, 32, 267, 10.2307/749828
Olive, 1999, From fractions to rational numbers of arithmetic: A reorganization hypothesis, Mathematical Thinking and Learning, 1, 279, 10.1207/s15327833mtl0104_2
Olive, 2002, The construction of an iterative fractional scheme: The case of Joe, Journal of Mathematical Behavior, 20, 413, 10.1016/S0732-3123(02)00086-X
Steffe, 1991, The constructivist teaching experiment: Illustrations and implications, 177
Steffe, 1992, Schemes of action and operation involving composite units, Learning and Individual Differences, 4, 259, 10.1016/1041-6080(92)90005-Y
Steffe, 1994, Children's multiplying schemes, 3
Steffe, 2002, A new hypothesis concerning children's fractional knowledge, Journal of Mathematical Behavior, 20, 267, 10.1016/S0732-3123(02)00075-5
Steffe, 2003, Fractional commensurate, composition, and adding schemes: Learning trajectories of Jason and Laura: Grade 5, Journal of Mathematical Behavior, 22, 237, 10.1016/S0732-3123(03)00022-1
Steffe, 2004, On the construction of learning trajectories of children: The case of commensurate fractions, Mathematical Thinking and Learning, 6, 129, 10.1207/s15327833mtl0602_4
Steffe, 1988
Steffe, 2000, Teaching experiment methodology: Underlying principles and essential elements, 267
Steffe, 1994, Interaction and children's mathematics, vol. 4, 8
1983
Streefland, 1991
Thompson, 2003, Fractions and multiplicative reasoning, 95
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
Tzur, 2004, Teachers’ and students’ joint production of a reversible fraction conception, Journal of Mathematical Behavior, 23, 93, 10.1016/j.jmathb.2003.12.006
Vergnaud, 1988, Multiplicative structures, 141
von Glasersfeld, 1995, vol. 6