Representations and strategies for solving dynamic and static arithmetic word problems: The role of working memory capacities

European Journal of Cognitive Psychology

Volumn 18, Issue 5, 2006, Pages 756-775

  Thevenot, Catherine ^a,b   Oakhill, Jane ^a  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

^b UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARITHMETIC; ARTICLE; COGNITION; DYNAMICS; HUMAN; HUMAN EXPERIMENT; NORMAL HUMAN; PREDICTION; PRIORITY JOURNAL; PROBABILITY; PROBLEM SOLVING; UNITED KINGDOM; WORKING MEMORY;

EID: 33747599907     PISSN: 09541446     EISSN: 14640635     Source Type: Journal    
DOI: 10.1080/09541440500412270     Document Type: Article

References (60)

1. Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14, 219-234.
2. Bilsky, L. H., & Judd, T. (1986). Sources of difficulty in the solution of verbal arithmetic problems by mentally retarded and non-retarded individuals. American Journal of Mental Deficiency, 90, 395-402.
3. Carpenter, T. P., & Moser, J. M. (1982). The development of addition and subtraction problem-solving skills. In T. P Carpenter, J.M.Moser, & T. A. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 9-24). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
4. Coquin-Viennot, D. (2000). Lecture d'énoncés de problèmes arithmétiques: Effet d'une introduction thématique sur la construction de la représentation. Archives de Psychologie, 68, 41-58.
5. Coquin-Viennot, D., & Moreau, S. (2003). Highlighting the role of the episodic situation model in the solving of arithmetical problems. European Journal of Psychology of Education , 3, 267-279.
6. Cummins, D., Kintsch, W., Reusser, K., & Weimer, R. (1988). The role of understanding in solving word problems. Cognitive Psychology, 20, 405-438.
7. Crutcher, R. J. (1994). Telling what we know: The use of verbal report methodologies in psychological research. Psychological Science, 5, 241-244.
8. Daneman, M., & Carpenter, P. (1980). Individual differences in working memory and reading. Journal of Verbal Learning and Verbal Behavior, 19, 450-466.
9. Davis-Dorsey, J., Ross, J. M., & Morrison, G. R. (1991). The role of rewording and context personalization in the solving of mathematical word problems. Journal of Educational Psychology, 83, 61-68.
10. De Corte, E., & Verschaffel, L. (1981). Children's solution processes in elementary arithmetic problems: Analysis and improvement. Journal of Educational Psychology, 73, 765-779.
11. De Corte, E., & Verschaffel, L. (1985). Beginning first graders' initial representation of arithmetic word problems. Journal of Mathematical Behavior, 4, 3-21.
12. De Corte, E., & Verschaffel, L. (1991). Some factors influencing the solution of addition and subtraction word problems. In K. Durkin & B. Shire (Eds.), Language and mathematical education (pp. 117-130). Milton Keynes, UK: Open University Press.
13. De Corte, E., Verschaffel, L., & de Win, L. (1985). Influence of rewording verbal problems on children's problem representations and solutions. Journal of Educational Psychology, 77, 460-470.
14. De Corte, E., Verschaffel, L., & Pauwels, A. (1990). Influence of the semantic structure of word problems on second graders' eye movements. Journal of Educational Psychology, 82, 359-365.
15. Devidal, M., Fayol, M., & Barrouillet, P. (1997). Stratégies de lecture et résolution de problèmes arithmétiques. L'Anné e Psychologique, 97, 9-31.
16. Ericsson, K. A., & Simon, H. A. (1980). Verbal reports as data. Psychological Review, 87, 215-251.
17. Ericsson, K. A., & Simon, H. A. (1993). Protocol analysis: Verbal reports as data . Cambridge, MA: Bradford/MIT Press.
18. Evans, J. St. B. T. (2000). What could and could not be a strategy in reasoning. In W. Schaeken, G. de Vooght, A. Vandierendonck, & G. d'Ydewalle (Eds.), Deductive reasoning and strategies (pp. 1-22). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
19. Evans, J. St. B. T., Handley, S. J., Harper, C. N. J., & Johnson-Laird, P. N. (1999). Reasoning about necessity and possibility: A test of the mental model theory of deduction. Journal of Experimental Psychology: Learning, Memory, and Cognition, 25, 1495-1513.
20. Fayol, M., Abdi, H., & Gombert, J. E. (1987). Arithmetic problem formulation and working memory load. Cognition and Instruction, 4, 183-202.
21. Gattis, M. (2004). Mapping relational structure in spatial reasoning. Cognitive Science, 28, 589-610.
22. Gernsbacher, M. A. (1990). Language comprehension as structure building . Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
23. Gonzales, J., & Espinel, I. (2002). Strategy choice in solving arithmetic word problems: Are there differences between students with learning disabilities, G-V poor performance and typical achievement students. Learning Disability Quarterly, 25, 113-122.
24. Hegarty, M., Mayer, R. E., & Green, C. E. (1992). Comprehension of arithmetic word problems: Evidence from students' eye fixations. Journal of Educational Psychology, 84, 76-84.
25. Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87 (1), 18-32.
26. Hudson, T. (1983). Correspondences and numerical differences between disjoint set. Child Development, 54, 84-90.
27. Johnson-Laird, P. N. (1983). Mental models: Towards a cognitive science of language, inference, and consciousness. Cambridge, MA/Cambridge, UK: Harvard University Press.
28. Just, M. A., & Carpenter, P. A. (1987). The psychology of reading and language comprehension. Pittsburgh, PA: Carnegie Mellon University.
29. Kintsch, W. (1986). Learning from text. Cognition and Instruction, 3, 87-108.
30. Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92, 109-129.
31. Kirk, E. P., & Ashcraft, M. K. (2001). Telling stories: The perils and promise of using verbal reports to study math strategies. Journal of Experimental Psychology: Learning, Memory, and Cognition, 27, 157-175.
32. Knoblich, G., Ohlsson, S., & Raney, G. E. (2001). An eye movement study of insight problem solving. Memory and Cognition, 29, 1000-1009.
33. Lewis, A., & Mayer, R. E. (1987). Students' miscomprehension of relational statements in arithmetic word problems. Journal of Educational Psychology, 79, 363-371.
34. Luchins, A. S., & Luchins, E. H. (1959). Rigidity of behavior: A variational approach to the effect of Einstellung . Eugene, OR: University of Oregon Press.
35. Markman, A. B., & Gentner, D. (1993). Structural alignment during similarity comparisons. Cognitive Psychology, 25, 431-467.
36. Moreau, S., & Coquin-Viennot, D. (2003). Comprehension of arithmetic word problem by fifth-grade pupils: Representation and selection of information. British Journal of Educational Psychology, 73, 109-121.
37. Nathan, M. J., Kintsch, W., & Young, E. (1992). A theory of algebra word problem comprehension and its implication for the design of learning environments. Cognition and Instruction, 4, 329-390.
38. Nescher, P., Greeno, J. G., & Riley, M. S. (1982). The development of semantics categories for addition and subtraction. Educational Studies in Mathematics, 13, 373-394.
39. Newstead, S. E., & Griggs, R. A. (1999). Premise misinterpretation and syllogistic reasoning. Quarterly Journal of Experimental Psychology, 52A, 1057-1075.
40. Newstead, S. E., Handley, S. J., & Buck, E. (1999). Falsifying mental models: Testing the predictions of theories of syllogistic reasoning. Memory and Cognition, 27, 344-354.
41. Newstead, S. E., Thompson, V. A., & Handley, S. J. (2002). Generating alternatives: A key component in human reasoning? Memory and Cognition, 30, 129-137.
42. Norris, D. G. (1984). A computer-based programmable tachistoscope for nonprogrammers. Behavior Research Methods, Instruments and Computers, 16, 25-27.
43. Palladino, P., Cornoldi, C., de Beni, R., & Pazzaglia, F. (2001). Working memory and updating processes in reading comprehension. Memory and Cognition, 29, 344-354.
44. Pape, S. J. (2003). Compare word problems: Consistency hypothesis revisited. Contemporary Educational Psychology, 28, 396-421.
45. Pape, S. J., & Wang, C. (2003). Middle school children's strategic behavior: Classification and relation to academic achievement and mathematical problem solving. Instructional Science, 31, 419-449.
46. Payne, J.W. (1994). Thinking aloud: Insights into information processing. Psychological Science, 5, 241-248.
47. Polk, T. A., & Newell, A. (1995). Deduction as verbal reasoning. Psychological Review, 102, 533-566.
48. Rayner, K., & McConkie, G. W. (1976). What guides a reader's eye movements? Vision Research, 16, 829-837.
49. Reusser, K. (1989). Textual and situational factors in solving mathematical word problems. Bern, Switzerland: University of Bern.
50. Riley, M. S., & Greeno, J. G. (1988). Developmental analysis of understanding language about quantities and of solving problems. Cognition and Instruction, 5, 49-101.
51. Riley, M. S., Greeno, J. G., & Heller, J. I. (1983). Development of children's problem solving ability in arithmetic. In H. P. Ginsburg (Ed.), The development of mathematical thinking. New York: Academic Press.
52. Shrager, J., & Siegler, R. S. (1998). SCADS: A model of children's strategy choices and strategy discoveries. Psychological Science, 9, 405-410.
53. Siegler, R. S., & Shipley, C. (1995). Variation, selection, and cognitive change. In T. J. Simon & G. S. Halford (Eds.), Developing cognitive competence: New approaches to process modeling (pp. 31-76). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
54. Staub, F. C., & Reusser, K. (1995). The role of presentational structures in understanding and solving mathematical word problems. In C. A. Weaver, S. Mannes, & C. R. Fletcher (Eds.), Discourse comprehension: Essays in honor of Walter Kintsch (pp. 285-305). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
55. Stern, E., & Lehrndorfer, A. (1992). The role of situational context in solving word problems. Cognitive Development, 2, 259-268.
56. Thevenot, C., Barrouillet, P., & Fayol, M. (2001). Algorithmic solution of arithmetic problems and operands-answer associations in LTM. Quarterly Journal of Experimental Psychology, 54A(2), 599-611.
57. Thevenot, C., Barrouillet, P., & Fayol, M. (2004). Mental representation and procedures in arithmetic word problems: The effect of the position of the question. L'Année Psychologique, 104, 683-699.
58. Thevenot, C., & Oakhill, J. (2005). The strategic use of alternative representation in arithmetic word problem solving. Quarterly Journal of Experimental Psychology, 58A, 1311-1323.
59. Verschaffel, L., de Corte, E., & Pauwels, A. (1992). Solving compare problems: An eye movement test of Lewis and Mayer's consistency hypothesis. Journal of Educational Psychology, 84, 85-94.
60. Wilson, T. D. (1994). The proper protocol: Validity and completeness of verbal reports. Psychological Science, 5, 249-252.