A micro-developmental approach to studying young children's problem solving behavior in addition

Alibali, 1999, How children change their minds: Strategy change can be gradual or abrupt, Developmental Psychology, 35, 127, 10.1037/0012-1649.35.1.127 Ashcraft, 1982, The development of mental arithmetic, Developmental Review, 2, 213, 10.1016/0273-2297(82)90012-0 Baroody, 1985, Mastery of basic number combinations: Internalization of relationships or facts, Journal for Research in Mathematics Education, 16, 83, 10.2307/748366 Baroody, 1987, The development of counting strategies for single digit addition, Journal for Research in Mathematics Education, 18, 141, 10.2307/749248 Baroody, 2003 Bjorklund, 2000 Bjorklund, 1990, Children's strategies: Their definition and origins, 309 Bjorklund, 2004, Young chidlren's arithmetic strategies in social context: How parents contribute to children's strategy development while playing games, International Journal of Behavioral Development, 28, 347, 10.1080/01650250444000027 Bjorklund, 2001, Children's use of multiple and variable addition strategies in a game context, Developmental Science, 4, 184, 10.1111/1467-7687.00164 Brown, 2008, Progression in numeracy ages 5–11: Results from the Leverhulme longitudinal study, 85 Carpenter, 1984, The acquisition of addition and subtraction concepts in grades one through three, Journal for Research in Mathematics Education, 15, 179, 10.2307/748348 Crowley, 1997, Strategy discovery as a competitive negotiation between metacognitive and associative mechanisms, Developmental Review, 17, 462, 10.1006/drev.1997.0442 Davis, 1992, Understanding understanding, Journal of Mathematical Behavior, 11, 225 DfES (Department for Education and Skills), 2006 Dixon, 2002, The prehistory of discovery: Precursors of representational change in solving gear system problems, Developmental Psychology, 38, 918, 10.1037/0012-1649.38.6.918 Dixon, 2005, From regularities to concepts: The development of children's understanding of mathematical relation, Cognitive Development, 20, 65, 10.1016/j.cogdev.2004.12.001 Dowker, 2005 Dowker, 1996, Estimation strategies in four groups, Mathematical Cognition, 2, 113, 10.1080/135467996387499 Fayol, 1994, From declarative and procedural knowledge to the management of declarative and procedural knowledge, European Journal of Psychology of Education, 9, 179, 10.1007/BF03172778 Fuson, 1982, An analysis of the counting-on solution procedure in addition, 67 Garton, 2004 Ginsburg, 1983, The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques, For the Learning of Mathematics, 1, 4 Goldin, 1998, Representational systems, learning and problem solving in mathematics, Journal of Mathematical Behavior, 17, 137, 10.1016/S0364-0213(99)80056-1 Goldin-Meadow, 1994, Do you have to be right to redescribe?, Behavioral and Brain Sciences, 17, 718, 10.1017/S0140525X00036748 Granott, 2002, Microdevelopment: A process-oriented perspective for studying development and learning, 1 Groen, 1972, A chronometric analysis of simple addition, Psychological Review, 79, 329, 10.1037/h0032950 Hatano, 1988, Social and motivational bases for mathematical understanding, 55 Jordan, 2009, Individual differences in trajectories of arithmetical development in typically achieving 5- to 7-year-olds, Journal of Experimental Child Psychology, 103, 455, 10.1016/j.jecp.2009.01.011 Karmiloff-Smith, 1984, Children's problem solving, Vol. 3, 39 Karmiloff-Smith, 1985, Language and cognitive processes from a developmental perspective, Language and Cognitive Processes, 1, 61, 10.1080/01690968508402071 Karmiloff-Smith, 1990, Constraints on representational change: Evidence from children's drawing, Cognition, 34, 57, 10.1016/0010-0277(90)90031-E Karmiloff-Smith, 1991, What every cognitive psychologist should know about the mind of the child, 277 Karmiloff-Smith, 1992 Karmiloff-Smith, 1993, What's special about the development of the human mind/brain?, Mind & Language, 8, 569, 10.1111/j.1468-0017.1993.tb00305.x Karmiloff-Smith, 1994, Précis of beyond modularity: A developmental perspective on cognitive science, Behavioral and Brain Sciences, 17, 696, 10.1017/S0140525X00036621 Kuhn, 1995, Microgenetic study of change: What has it told us, Psychological Science, 3, 133, 10.1111/j.1467-9280.1995.tb00322.x LeFevre, 1996, Multiple routes to solution of single-digit multiplication problems, Journal of Experimental Psychology: General, 125, 284, 10.1037/0096-3445.125.3.284 McNeil, 2005, Why won’t you change your mind? Knowledge of operational patterns hinders learning and performance on equations, Child Development, 76, 883, 10.1111/j.1467-8624.2005.00884.x Opfer, 2008, Representational change and magnitude estimation: Why young children can make more accurate salary comparisons than adults, Cognition, 108, 843, 10.1016/j.cognition.2008.05.003 Piaget, 1970 Piaget, 1971 Pine, 2004, More gestures than answers: Children learning about balance, Developmental Psychology, 40, 1059, 10.1037/0012-1649.40.6.1059 Pine, 1999, What children do and what children know: Looking beyond success using Karmiloff-Smith's RR framework, New Ideas in Psychology, 17, 17, 10.1016/S0732-118X(98)00014-2 Pine, 2000, The effect of explaining another's actions on children's implicit theories of balance, Cognition and Instruction, 18, 35, 10.1207/S1532690XCI1801_02 Pressley, 2006, Cognitive strategies, Vol. 2, 511 Siegler, 1987, The perils of averaging data over strategies: An example from children's addition, Journal of Experimental Psychology: General, 116, 250, 10.1037/0096-3445.116.3.250 Siegler, 1996 Siegler, 2000, The rebirth of children's learning, Child Development, 71, 26, 10.1111/1467-8624.00115 Siegler, 2006, Microgenetic analyses of learning, Vol. 2, 464 Siegler, 1989 Siegler, 1991, The microgenetic method: A direct means for studying cognitive development, American Psychologist, 46, 606, 10.1037/0003-066X.46.6.606 Siegler, 1984, Strategy choices in addition and subtraction: How do children know what to do?, 229 Siegler, 1998, Conscious and unconscious strategy discoveries: A microgenetic analysis, Journal of Experimental Psychology: General, 127, 377, 10.1037/0096-3445.127.4.377 Spensley, 1999, The development of cognitive flexibility: Evidence from children's drawings, Human Development, 42, 300, 10.1159/000022639 Star, 2008, Flexibility in problem solving: The case of equation solving, Learning and Instruction, 18, 564, 10.1016/j.learninstruc.2007.09.018