Task-Related Factors that Influence the Spontaneous Use of Diagrams in Math Word Problems

Applied Cognitive Psychology

Volumn 26, Issue 2, 2012, Pages 251-260

  Uesaka, Yuri ^a   Manalo, Emmanuel ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b WASEDA UNIVERSITY   (Japan)

Author keywords

Math Word Problems; Spontaneous Use of Diagrams; Task related Factors

Indexed keywords

ADOLESCENT; ARTICLE; COGNITION; DIAGRAM; DRAWING; HUMAN; MATHEMATICAL COMPUTING; MENTAL TASK; PRIORITY JOURNAL; PROBLEM SOLVING;

EID: 84857797244     PISSN: 08884080     EISSN: 10990720     Source Type: Journal    
DOI: 10.1002/acp.1816     Document Type: Article

References (51)

1. Ainsworth, S., & Th Loizou, A. (2003). The effects of self-explaining when learning with text or diagrams. Cognitive Science, 27, 669-681.
2. Blackwell, A., & Engelhardt, Y. (2002). A meta-taxonomy for diagram research. In M. Anderson, B. Meyer, & P. Olivier (Eds.), Diagrammatic representation and reasoning (pp. 47-64). London: Springer-Verlag.
3. Cheng, P. C. H. (2002). Electrifying diagrams for learning: principles for complex representational systems. Cognitive Science, 26, 685-736.
4. Cheng, P. C. H. (2004). Why diagrams are (sometimes) six times easier than words: Benefits beyond locational indexing. In A. Blackwell, K. Marriott, & A. Shimojima (Eds.), Diagrams 2004, LNAI 2980 (pp. 242-254). Heidelberg: Springer-Verlag.
5. Cheng, P. W., & Holyoak, K. J. (1985). Pragmatic reasoning schemas. Cognitive Psychology, 17, 391-416.
6. Cohen, J. (1988). Statistical power analysis for the behavioral sciences, 2nd edn. Hillsdale, NJ: Lawrence Erlbaum Associates.
7. Collins, A., Brown, J. S., & Newman, S. E. (1989). Cognitive apprenticeship: Teaching the crafts of reading, writing and mathematics. In L. B. Resnick (Ed.), Knowing, learning and instruction: Essays in honor of Robert Glasser (pp. 453-494). Hillsdale, NJ: Lawrence Erlbaum Associates.
8. Cox, R. (1999). Representation construction, externalised cognition and individual differences. Learning and Instruction, 9, 343-363.
9. Cox, R., & Grawemeyer, B. (2003). The mental organisation of external representations. Proceedings of the European Cognitive Science Conference (EuroCogSci - joint Cognitive Science Society and German Cognitive Science Society conference), Osnabrück, September, 2003. Available from:.
10. De Corte, E., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In D. C. Berliner, & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 491-549). New York: Macmillan.
11. Dufour-Janvier, B., Bednarz, N., & Belanger, M. (1987). Pedagogical considerations concerning the problem of representation. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 110-120). Hillsdale, NJ: Erlbaum.
12. Evans, J. St. B. T. (1982). The psychology of deductive reasoning. London: Routledge and Kegan Paul.
13. Grawemeyer, B., & Cox, R. (2004). The effect of knowledge-of-external-representations upon performance and representational choice in a database query task. In A. F. Blackwell, K. Marriott, & A. Shimojima (Eds.), Diagrams 2004, LNAI 2980 (pp. 351-354). Heidelberg: Springer-Verlag.
14. Griggs, R. A. (1983). The role of problem content in the selection task and in the THOG problem. In J. St. B. T. Evans (Ed.), Thinking and reasoning: Psychological approaches (pp. 16-43). London: Routledge and Kegan Paul.
15. Gronich, L. H. (2006). The cognitive miser theory and decisions for war and peace. Paper presented at the 2006 Annual Meeting of the International Studies Association, San Diego, California, March 22-25. Retrieved September 10, 2009 from:.
16. Hall, R., Kibler, D., Wenger, E., & Truxaw, C. (1989). Exploring the episodic structure of algebra story problem solving. Cognition and Instruction, 6, 223-283.
17. Hayes, J. R., & Simon, H. A. (1974). Understanding written problem instructions. In L. W. Gregg (Ed.), Knowledge and cognition (pp. 169-200). Hillsdale, N. J.: Erlbaum.
18. Hegarty, M., Carpenter, P. A., & Just, M. A. (1991). Diagrams in the comprehension of scientific texts. In R. Barr, M. L. Kamil, P. Mosenthal, & P. D. Pearson (Eds.), Handbook of reading research, Vol. 2 (pp. 641-668). New York: Longman.
19. Hembree, R. (1992). Experiments and relational studies in problem-solving: A meta-analysis. Journal for Research in Mathematics Education, 23, 242-273.
20. Ichikawa, S. (1993). Suugakuteki na kangaekata wo megutte no soudan to sidou [Case report of cognitive counseling in mathematical thinking]. In S. Ichikawa (Ed.), Cognitive counseling that supports learning: A new approach bridging psychology and education [Gakusyuu wo sasaeru ninnchi-kaunsering -shinrigaku to kyouiku no aratana setten] (pp. 36-61). Tokyo: Brain Press.
21. Ichikawa, S. (2000). Benkyou-hou ga kawaru hon [A book about changing the approach to learning]. Tokyo: Iwanami Press.
22. Ichikawa, S., Seo, M., Kiyokawa, S., & Uesaka, Y. (2007). Development and application of COMPASS: Componential assessment for basic competence and learning activities in mathematics. Proceedings of 2007 International Conference of Competences Based Education Reform (pp. 379-430). Seoul: BK21 Academic Leadership Institute for Competency-based Education, Seoul National University.
23. Japanese Ministry of Education. (1998). Tyuugakkou gakusyuu sidouyouryou [National curriculum standards for junior high school]. Tokyo: Japanese Government Printing Office.
24. Johnson-Laird, P. N. (1983). Mental models: Towards a cognitive science of language, inference, and consciousness. Cambridge: Cambridge University Press.
25. Koedinger, K. R., & Terao, A. (2002). A cognitive task analysis of using pictures to support pre-algebraic reasoning. In C. D. Schunn, & W. Gray (Eds.), Proceedings of the Twenty-Fourth Annual Conference of the Cognitive Science Society (pp. 542-547). Mahwah, NJ: Lawrence Erlbaum Associates.
26. Kool, W., McGuire, J. T., Rosen, Z. B., & Botvinick, M. M. (2010). Decision making and the avoidance of cognitive demand. Journal of Experimental Psychology. General, 139, 665-682.
27. Lahlou, S. (2000). Attracteurs cognitifs et travail de bureau [Cognitive attractors and office work]. Intellectica, 30, 75-113.
28. Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive Science, 11, 65-99.
29. Manalo, E., & Uesaka, Y. (2006). Quantity and quality of diagrams used in math word problem solving: A comparison between New Zealand and Japanese students. Refereed papers of the NZARE (New Zealand Association for Research in Education) National Conference 2006 (CD-ROM; ISSN 1176-4902). Wellington, New Zealand: NZARE. (ERIC Document Reproduction Service No. ED 518 280).
30. Mayer, R. E. (2003). The promise of multimedia learning: Using the same instructional design methods across different media. Learning and Instruction, 13, 125-139.
31. McCombs, B. L. (1988). Motivational skills training: Combining metacognitive, cognitive, and affective learning strategies. In C. E. Weinstein, E. T. Goetz, & P. A. Alexander (Eds.), Learning and study strategies: Issues in assessment, instruction, and evaluation (pp. 141-169). San Diego: Academic Press.
32. Miller, E. K., & Cohen, J. D. (2001). An integrative theory of prefrontal cortex function. Annual Reviews in Neuroscience, 24, 167-202.
33. Murayama, K. (2003). Learning strategy use and short- and long-term perceived utility. Japanese Journal of Educational Psychology, 51, 130-140.
34. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
35. Novick, L. R. (2006). The importance of both diagrammatic conventions and domain-specific knowledge for diagram literacy in science: The hierarchy as an illustrative case. In D. Barker-Plummer, R. Cox, & N. Swoboda (Eds.), Diagrams 2006, LNAI 4045 (pp. 1-11). Berlin, Heidelberg: Springer-Verlag.
36. Novick, L. R., & Hurley, S. M. (2001). To matrix, network, or hierarchy: That is the question. Cognitive Psychology, 42, 158-216.
37. Organisation for Economic Co-operation and Development. (2004). Learning for tomorrow's world: First results from PISA 2003. Paris, VA: Author.
38. Pedone, R., Hummel, J. E., & Holyoak, K. J. (2001). The use of diagrams in analogical problem solving. Memory and Cognition, 29, 214-221.
39. Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.
40. Reed, S. K. (1999). Word problems: Research and curriculum reform. Mahwah, NJ: Erlbaum.
41. Sato, J. (1998). Effects of learners' perceptions of utility and costs, and learning strategy preferences. Japanese Educational Psychology, 46, 367-376.
42. Schoenfeld, A. H. (1985). Mathematical problem solving. San Diego: Academic Press.
43. Stenning, K., & Oberlander, J. (1995). A cognitive theory of graphical and linguistic reasoning: Logic and implementation. Cognitive Science, 19, 97-140.
44. Stern, E., Aprea, C., & Ebner, H. G. (2003). Improving cross-content transfer in text processing by means of active graphical representation. Learning and Instruction, 13, 191-203.
45. Sugisawa, T. (1999). Statistical power of educational psychology research in Japan. Japanese Journal of Educational Psychology, 47, 150-159.
46. Uesaka, Y., & Manalo, E. (2006). Active comparison as a means of promoting the development of abstract conditional knowledge and appropriate choice of diagrams in math word problem solving. In D. Barker-Plummer, R. Cox, & N. Swoboda (Eds.), Diagrams 2006, LNAI 4045 (pp. 181-195). Berlin, Heidelberg: Springer-Verlag.
47. Uesaka, Y., Manalo, E., & Ichikawa, S. (2007). What kinds of perceptions and daily learning behaviors promote students' use of diagrams in mathematics problem solving? Learning and Instruction, 17, 322-335.
48. Uesaka, Y., Manalo, E., & Ichikawa, S. (2010). The effects of perception of efficacy and diagram construction skills on students' spontaneous use of diagrams when solving math word problems. In A. K. Goel, M. Jamnik, & N. H. Narayanan (Eds.), Diagrams 2010, LNAI 6170 (pp. 197-211). Berlin, Heidelberg: Springer-Verlag.
49. Wason, P. C. (1983). Realism and rationality in the selection task. In J. St. B. T. Evans (Ed.), Thinking and reasoning: Psychological approaches (pp. 44-75). London: Routledge and Kagan Paul.
50. Yoshida, H., & Tajika, H. (Eds.). (1995). Ninchisinrigaku kara mita kazu no rikai [Understanding of numbers from the perspective of cognitive psychology]. Kyoto: Kitaouji Press.
51. Zhang, J., & Norman, D. A. (1994). Representations in distributed cognitive tasks. Cognitive Science, 18, 87-122.