Mechanisms of change in the development of mathematical reasoning

Advances in Child Development and Behavior

Volumn 33, Issue , 2005, Pages 79-123

  Alibali, Martha W ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CHILD; CHILD DEVELOPMENT; COGNITION; CONCEPT FORMATION; GESTURE; HUMAN; MATHEMATICS; PROBLEM SOLVING; SPEECH; VERBAL BEHAVIOR;

CHILD; CHILD DEVELOPMENT; COGNITION; CONCEPT FORMATION; GESTURES; HUMANS; MATHEMATICS; PROBLEM SOLVING; SPEECH; VERBAL BEHAVIOR;

EID: 26944487342     PISSN: 00652407     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0065-2407(05)80005-9     Document Type: Article

References (82)

1. Aleven V.A.W.M.M., and Koedinger K.R. An effective metacognitive strategy: Learning by doing and explaining with a computer-based Cognitive Tutor. Cognitive Science 26 (2002) 147-179
2. Alibali M.W. How children change their minds: Strategy change can be gradual or abrupt. Developmental Psychology 35 (1999) 127-145
3. Alibali M.W., Bassok M., Solomon K.O., Syc S.E., and Goldin-Meadow S. Illuminating mental representations through speech and gesture. Psychological Science 10 (1999) 327-333
4. Alibali M.W., and DiRusso A.A. The function of gesture in learning to count: More than keeping track. Cognitive Development 14 (1999) 37-56
5. Alibali M.W., and Goldin-Meadow S. Transitions in learning: What the hands reveal about a child's state of mind. Cognitive Psychology 25 (1993) 468-523
6. Alibali M.W., and Kita S. On the role of gesture in thinking and speaking: Prohibiting gesture alters children's explanations of conservation tasks. Manuscript submitted for publication (2005)
7. Actes du colloque [Proceedings of the meeting of]ORAGE. Alibali M.W., Kita S., Bigelow L.J., Wolfman C.M., and Klein S.M. Gestures play a role in thinking for speaking. In: Cavé C., Guaïtella I., and Santi S. (Eds). Oralité et gestualité: Interactions et comportements multimodaux dans la communication (Orality and gestuality: Multimodal interaction and behavior in communication) (2001), L'Harmattan, Paris, France 407-410
8. Alibali, M. W., & McNeil, N. M. (in preparation). Changes in problem representation as a mechanism of knowledge change.
9. Alibali M.W., McNeil N.M., and Perrott M.A. What makes children change their minds? Changes in problem encoding lead to changes in strategy selection. In: Gernsbacher M.A., and Derry S. (Eds). Proceedings of the 20th Annual Conference of the Cognitive Science Society (1998), Erlbaum, Mahwah, NJ 36-41
10. Alibali M.W., Ockuly K.M., and Fischer A.D. Sources and consequences of changes in problem representation. Paper presented at the Annual Meeting of the Jean Piaget Society. Vancouver, British Columbia (2005)
11. Alibali M.W., Spencer R.C., and Kita S. Spontaneous gestures influence strategy choice in problem solving. Paper presented at the Biennial Meeting of the Society for Research in Child Development. Atlanta, Georgia (2005)
12. Atkinson R.K., Renkl A., and Merrill M.M. Transitioning from studying examples to solving problems: Effects of self-explanation prompts and fading worked-out steps. Journal of Educational Psychology 95 (2003) 774-783
13. Baroody A.J. The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In: Baroody A.J., and Dowker A. (Eds). The development of arithmetic concepts and skills (2003), Erlbaum, Mahwah, NJ 1-33
14. Bielaczyc K., Pirolli P., and Brown A.L. Training in self-explanation and self-regulation strategies: Investigating the effects of knowledge acquisition activities on problem solving. Cognition and Instruction 13 (1995) 221-252
15. Bisanz J., and LeFevre J. Strategic and nonstrategic processing in the development of mathematical cognition. In: Bjorklund D.F. (Ed). Children's strategies: Contemporary views of cognitive development (1990), Erlbaum, Hillsdale, NJ 213-244
16. Blöte A.W., Van der Burg E., and Klein A.S. Students' flexibility in solving two-digit addition and subtraction problems: Instruction effects. Journal of Educational Psychology 93 (2001) 627-638
17. Briars D., and Siegler R.S. A featural analysis of preschoolers' counting knowledge. Developmental Psychology 20 (1984) 607-618
18. Byrnes J.P., and Wasik B.A. Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology 27 (1991) 777-786
19. Canobi K., Reeve R.A., and Pattison P.E. Patterns of knowledge in children's addition. Developmental Psychology 39 (2003) 521-534
20. Carpenter T.P. Conceptual knowledge as a foundation for procedural knowledge: Implications from research on the initial learning of arithmetic. In: Hiebert J. (Ed). Conceptual and procedural knowledge: The case of mathematics (1986), Erlbaum, Hillsdale, NJ 113-132
21. Chi M.T.H. Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In: R. G. (Ed). Advances in instructional psychology Vol. 5 (2000), Erlbaum, Mahwah, NJ 161-237
22. Chi M.T.H., Bassok M., Lewis R., Reimann P., and Glaser R. Self-explanations: How students study and use examples in learning to solve problems. Cognitive Science 13 (1989) 145-182
23. Chi M.T.H., de Leeuw N., Chiu M.H., and LaVancher C. Eliciting self-explanations improves understanding. Cognitive Science 18 (1994) 439-477
24. Chi M.T.H., Feltovich P.J., and Glaser R. Categorization and representation of physics problems by experts and novices. Cognitive Science 5 (1981) 121-152
25. Chi M.T.H., and VanLehn K. The content of physics self-explanations. Journal of the Learning Sciences 1 (1991) 69-106
26. Church R.B., and Goldin-Meadow S. The mismatch between gesture and speech as an index of transitional knowledge. Cognition 23 (1986) 43-71
27. Crowder E.M., and Newman D. Telling what they know: The role of gesture and language in children's science explanations. Pragmatics and Cognition 1 (1993) 341-376
28. Curry L.A. The effects of self-explanations of correct and incorrect solutions on algebra problem solving performance. In: Forbus K., Gentner D., and Regier T. (Eds). Proceedings of the 26th Annual Meeting of the Cognitive Science Society (2004), Erlbaum, Mahwah, NJ
29. de Ruiter J.-P. Gesture and speech production. Doctoral dissertation, Katholieke Universiteit Nijmegen, Nijmegen, The Netherlands (1998)
30. Didierjean A., and Cauzinille-Marmeche E. Eliciting self-explanations improves problem solving: What processes are involved?. Cahiers de Psychologie Cognitive/Current Psychology of Cognition 16 (1997) 325-351
31. Dweck C.S., and Elliot E.S. Achievement motivation. In: Mussen P.H., and Hetherington E.M. (Eds). Handbook of child psychology: Vol. IV. Social and personality development (1983), Wiley, New York 643-691
32. Dweck C.S., and Leggett E.L. A social-cognitive approach to motivation and personality. Psychological Review 95 (1988) 256-273
33. Elliot E.S., and Dweck C.S. Goals: An approach to motivation and achievement. Journal of Personality and Social Psychology 54 (1988) 5-12
34. Fuson K.C. Conceptual structures for multiunit numbers: Implications for learning and teaching multidigit addition, subtraction, and place value. Cognition and Instruction 7 (1990) 343-403
35. Fuson K.C., and Briars D. Using a base-ten blocks learning/teaching approach for first- and second-grade place-value and multidigit addition and subtraction. Journal for Research in Mathematics Education 21 (1990) 180-206
36. Garber P., Alibali M.W., and Goldin-Meadow S. Knowledge conveyed in gesture is not tied to the hands. Child Development 69 (1998) 75-84
37. Gelman R., and Meck E. Preschoolers' counting: Principles before skill. Cognition 13 (1983) 343-359
38. Goldin-Meadow S., Alibali M.W., and Church R.B. Transitions in concept acquisition: Using the hand to read the mind. Psychological Review 100 (1993) 279-297
39. Goldin-Meadow S., Nusbaum H., Kelly S.D., and Wagner S.M. Explaining math: Gesturing lightens the load. Psychological Science 12 (2001) 516-522
40. Goldin-Meadow S., and Singer M.A. From children's hands to adults' ears: Gesture's role in the learning process. Developmental Psychology 39 (2002) 509-520
41. Graham J.A., and Argyle M. A cross-cultural study of the communication of extra-verbal meaning by gestures. International Journal of Psychology 10 (1975) 57-67
42. Hadar U., and Krauss R.M. Iconic gestures: The grammatical categories of lexical affiliates. Journal of Neurolinguistics 12 (1999) 1-12
43. Hiebert J., and LeFevre P. Conceptual and procedural knowledge in mathematics: An introductory analysis. In: Hiebert J. (Ed). Conceptual and procedural knowledge: The case of mathematics (1986), Erlbaum, Hillsdale, NJ 1-27
44. Hiebert J., and Wearne D. Cognitive changes during conceptually based instruction on decimal fractions. Journal of Educational Psychology 81 (1989) 507-513
45. Hiebert J., and Wearne D. Instruction, understanding and skill in multidigit addition and subtraction. Cognition and Instruction 14 (1996) 251-283
46. Hostetter A.B., and Alibali M.W. On the tip of the mind: Gesture as a key to conceptualization. In: Forbus K., Gentner D., and Regier T. (Eds). Proceedings of the 26th Annual Meeting of the Cognitive Science Society (2004), Erlbaum, Mahwah, NJ
47. Kendon A. Do gestures communicate? A review. Research on Language and Social Interaction 27 (1994) 175-200
48. Kieran C. Concepts associated with the equality symbol. Educational Studies in Mathematics 12 (1981) 317-326
49. Kita S. How representational gestures help speaking. In: McNeill D. (Ed). Language and gesture (2000), Cambridge University Press, Cambridge, UK 162-185
50. Lavergne J., and Kimura D. Hand movement asymmetry during speech: No effect of speaking topic. Neuropsychologia 25 (1987) 689-693
51. Licht B.G., and Dweck C.S. Determinants of academic achievement: The interaction of children's achievement orientations with skill area. Developmental Psychology 20 (1984) 628-636
52. Ma L. Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States (1999), Erlbaum, Mahwah, NJ
53. McClelland J.L. A connectionist perspective on knowledge and development. In: Simon T.J., and Halford G.S. (Eds). Developing cognitive competence: New approaches to process modeling (1995), Erlbaum, Hillsdale, NJ 157-204
54. McNeil N.M., and Alibali M.W. Learning mathematics from procedural instruction: Externally imposed goals influence what is learned. Journal of Educational Psychology 92 (2000) 734-744
55. McNeil N.M., and Alibali M.W. You'll see what you mean: Students encode equations based on their knowledge of arithmetic. Cognitive Science 28 (2004) 451-466
56. McNeil, N. M., & Alibali, M. W. (in press-a). Knowledge change as a function of mathematics experience: All contexts are not created equal. Journal of Cognition and Development.
57. McNeil, N. M., & Alibali, M. W. (in press-b). Why won't you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development.
58. Mwangi W., and Sweller J. Learning to solve compare word problems: The effect of example format and generating self-explanations. Cognition and Instruction 16 (1998) 173-199
59. Neuman Y., Leibowitz L., and Schwarz B. Patterns of verbal mediation during problem solving: A sequential analysis of self-explanation. Journal of Experimental Education 68 (2000) 197-213
60. Neuman Y., and Schwarz B. Is self-explanation while solving problems helpful? The case of analogical problem solving. British Journal of Educational Psychology 68 (1998) 15-24
61. Perry M. Learning and transfer: Instructional conditions and conceptual change. Cognitive Development 6 (1991) 449-468
62. Perry M., Church R.B., and Goldin-Meadow S. Transitional knowledge in the acquisition of concepts. Cognitive Development 3 (1988) 359-400
63. Pine K.J., and Messer D.J. The effect of explaining another's actions on children's implicit theories of balance. Cognition and Instruction 18 (2000) 35-51
64. Pirolli P., and Recker M. Learning strategies and transfer in the domain of programming. Cognition and Instruction 12 (1994) 235-275
65. Renkl A. Learning from worked-out examples: A study in individual differences. Cognitive Science 21 (1997) 1-29
66. Renkl A., Stark R., Gruber H., and Mandl H. Learning from worked-out examples: The effects of example variability and elicited self-explanations. Contemporary Educational Psychology 23 (1998) 90-108
67. Rimè B., Shiaratura L., Hupet M., and Ghysselinckx A. Effects of relative immobilization on the speaker's nonverbal behavior and on the dialogue imagery level. Motivation and Emotion 8 (1984) 311-325
68. Rittle-Johnson B. Promoting flexible problem solving: The effects of direct instruction and self-explaining. In: Forbus K., Gentner D., and Regier T. (Eds). Proceedings of the 26th Annual Meeting of the Cognitive Science Society (2004), Erlbaum, Mahwah, NJ
69. Rittle-Johnson B., and Alibali M.W. Conceptual and procedural knowledge of mathematics: Does one lead to the other?. Journal of Educational Psychology 91 (1999) 175-189
70. Rittle-Johnson B., Siegler R.S., and Alibali M.W. Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology 93 (2001) 346-362
71. Schwartz D., and Black J.B. Shuttling between depictive models and abstract rules: Induction and fallback. Cognitive Science 20 (1996) 457-497
72. Shrager J., and Siegler R.S. SCADS: A model of children's strategy choices and strategy discoveries. Psychological Science 9 (1998) 405-410
73. Siegler R.S. Three aspects of cognitive development. Cognitive Psychology 8 (1976) 481-520
74. Siegler R.S. How does change occur? A microgenetic study of number conservation. Cognitive Psychology 28 (1995) 225-273
75. Siegler R.S. Microgenetic studies of self-explanation. In: Grannott N., and Parziale J. (Eds). Microdevelopment: Transition processes in development and learning (2002), Cambridge University Press, Cambridge, UK 31-58
76. Siegler R.S., and Crowley K. Constraints on learning in nonprivileged domains. Cognitive Psychology 27 (1994) 194-226
77. Siegler R.S., and Shipley C. Variation, selection, and cognitive change. In: Simon T., and Halford G. (Eds). Developing cognitive competence: New approaches to process modeling (1995), Erlbaum, Hillsdale, NJ 31-76
78. Valenzeno L., Alibali M.W., and Klatzky R.L. Teachers' gestures facilitate students' learning: A lesson in symmetry. Contemporary Educational Psychology 28 (2003) 187-204
79. VanLehn K., Jones R.M., and Chi M.T.H. A model of the self-explanation effect. Journal of the Learning Sciences 2 (1992) 1-59
80. Wagner S.M., Nusbaum H., and Goldin-Meadow S. Probing the mental representation of gesture: Is handwaving spatial?. Journal of Memory and Language 50 (2004) 395-407
81. Wesp R., Hess J., Keutmann D., and Wheaton K. Gestures maintain spatial imagery. The American Journal of Psychology 114 (2001) 591-600
82. Wong R.M.F., Lawson M., and Keeves J. The effects of self-explanation training on students' problem solving in high-school mathematics. Learning and Instruction 12 (2002) 233-262