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The Effects of Perception of Efficacy and Diagram Construction Skills on Students’ Spontaneous Use of Diagrams When Solving Math Word Problems

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Diagrammatic Representation and Inference (Diagrams 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6170))

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Abstract

Although diagram use is considered to be one of the most effective strategies for solving problems, reports from applied educational research have noted that students lack spontaneity in using diagrams even when teachers extensively employ diagrams in instructions. To address this problem, the present study investigated the effectiveness of teacher-provided verbal encouragement (VE) and practice in drawing diagrams (PD), as additions to typical math classes, for promoting students’ spontaneous use of diagrams when attempting to solve problems. The participants were 86 8th graders who were assigned to one of four instruction conditions: VE+PD, VE only, PD only, and with no addition to typical instruction (Control). The highest improvement in spontaneous diagram use was observed in the VE+PD condition. This finding suggests that, to promote spontaneity in students’ diagram use, helping students appreciate the value of diagram use is important, as well as developing procedural knowledge in using diagrams.

An Erratum for this chapter can be found at http://dx.doi.org/10.1007/978-3-642-14600-8_51

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References

  1. Larkin, J.H., Simon, H.A.: Why a diagram is (sometimes) worth ten thousand words. Cognitive Science 11, 65–99 (1987)

    Article  Google Scholar 

  2. Ainsworth, S., Th Loizou, A.: The effects of self-explaining when learning with text or diagrams. Cognitive Science 27, 669–681 (2003)

    Article  Google Scholar 

  3. Pedone, R., Hummel, J.E., Holyoak, K.J.: The use of diagrams in analogical problem solving. Memory & Cognition 29, 214–221 (2001)

    Article  Google Scholar 

  4. Cheng, P.C.H.: Electrifying diagrams for learning: Principles for complex representational systems. Cognitive Science 26, 685–736 (2002)

    Article  Google Scholar 

  5. Stern, E., Aprea, C., Ebner, H.G.: Improving cross-content transfer in text processing by means of active graphical representation. Leaning and Instruction 13, 191–203 (2003)

    Article  Google Scholar 

  6. Cox, R.: Representation construction, externalised cognition and individual differences. Learning and Instruction 9, 343–363 (1999)

    Article  Google Scholar 

  7. Grawemeyer, B., Cox, R.: The effect of knowledge-of-external-representations upon performance and representational choice in a database query task. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 351–354. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Uesaka, Y., Manalo, E.: Active comparison as a means of promoting the development of abstract conditional knowledge and appropriate choice of diagrams in math word problem solving. In: Barker-Plummer, D., Cox, R., Swoboda, N. (eds.) Diagrams 2006. LNCS (LNAI), vol. 4045, pp. 181–195. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Mokros, J.R., Tinker, R.F.: The impact of microcomputer-based labs on children’s ability to interpret graphs. Journal of Research in Science Teaching 24, 369–383 (1987)

    Article  Google Scholar 

  10. Cox, R.: Analytical reasoning with multiple external representations. Unpublished Ph.D Thesis: The University of Edinburgh, United Kingdom (1996)

    Google Scholar 

  11. Ichikawa, S. (ed.): Gakusyuu wo sasaeru ninnchikaunsering: Shinrigaku to kyouiku no aratana setten (Cognitive counseling that supports learning: A new approach bridging psychology and education). Brain Press, Tokyo (1993)

    Google Scholar 

  12. Dufour-Janvier, B., Bednarz, N., Belanger, M.: Pedagogical considerations concerning the problem of representation. In: Janvier, C. (ed.) Problems of Representation in the Teaching and Learning of Mathematics, pp. 110–120. Erlbaum, Hillsdale (1987)

    Google Scholar 

  13. Uesaka, Y.: How learning skills support through cognitive counseling can provide new perspective in both cognitive research and school curriculum development - Focusing on the strategy of diagram use in problem solving. Cognitive Studies 16, 313–332 (2009)

    Google Scholar 

  14. Mullis, I.V.S., Martin, M.O., Gonzalez, E.J., Chrostowski, S.J.: TIMSS 2003 international mathematics report- Findings from IEA’s trends in international mathematics and science study at the fourth and eighth grades. In: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, Chestnut Hill, MA (2004)

    Google Scholar 

  15. Ichikawa, E., Seo, M., Kiyokawa, S., Uesaka, Y.: Development and application of COMPASS - Componential assessment for basic competence and learning in mathematics. In: Proceedings of 2007 International Conference of Competences Based Education Reform, pp. 379–430. Center for Research of Core Academic Competences, Tokyo (2007)

    Google Scholar 

  16. Uesaka, Y., Manalo, E., Ichikawa, S.: What kinds of perceptions and daily learning behaviors promote students’ use of diagrams in mathematics problem solving? Learning and Instruction 17, 322–335 (2007)

    Article  Google Scholar 

  17. Uesaka, Y., Manalo, E.: Task-related factors that influence the spontaneous use of diagrams in math word problem solving. Paper Presented at the 7th Biennial Meeting of the Society for Applied Research in Memory and Cognition, Lewiston, Main (2007)

    Google Scholar 

  18. Garner, R.: When children and adults do not use learning strategies: Toward a theory of settings. Review of Educational Research 60, 517–529 (1990)

    Article  Google Scholar 

  19. Murayama, K.: Learning strategy use and short- and long-term perceived utility. Japanese Journal of Educational Psychology 51, 130–140 (2003)

    Article  Google Scholar 

  20. Sato, J.: Effects of learners’ perceptions of utility and costs, and learning strategy preferences. Japanese Journal of Educational Psychology 46, 367–376 (1998)

    Article  Google Scholar 

  21. Ames, C., Archer, J.: Achievement goals in the classroom - students’ learning strategies and motivation processes. Journal of Educational Psychology 80, 260–267 (1988)

    Article  Google Scholar 

  22. Murayama, I.: Transformation of tasks and cognitive agents by external resources. Cognitive Studies 2(4), 28–38 (1995)

    Google Scholar 

  23. Brown, A.L., Bransford, J.D., Ferrara, R., Campione, J.: A tetrahedral framework for exploring problems of learning. In: Flavell, J.H., Markman, E.M. (eds.) Handbook of Child Psychology, Cognitive Development, 4th edn., vol. 3, pp. 85–106. Wiley, New York (1983)

    Google Scholar 

  24. Shinogaya, K.: Effects of preparation on learning: Interaction with beliefs about learning. Japanese Journal of Educational Psychology 56, 256–267 (2008)

    Article  Google Scholar 

  25. Ichikawa, S.: Cognitive counseling to improve students’ metacognition and cognitive skills. In: Shwalb, D.W., Nakazawa, J., Shwalb, B.J. (eds.) Applied Developmental Psychology - Theory, practice, and Research from Japan, pp. 57–87. Information Age, Greenwich (2005)

    Google Scholar 

  26. Chan, L.K.S.: Combined strategy and attributional training for seventh grade average and poor readers. Journal of Research in Reading 19, 111–127 (1996)

    Article  Google Scholar 

  27. Borkowski, J.G., Carr, M., Rellinger, L., Pressley, M.: Self-regulated cognition- Interdependence of metacognitions attributions and self-esteem. In: Jones, B.J., Idol, L. (eds.) Dimensions of Thinking and Cognitive Instruction, pp. 53–92. Erlbaum, Hillsdale (1990)

    Google Scholar 

  28. Guthrie, J.T., Wigfield, A., VonSecker, C.: Effects of integrated instruction on motivation and strategy use in reading. Journal of Educational Psychology 92, 331–341 (2000)

    Article  Google Scholar 

  29. Ellis, S., Davidi, I.: After-event reviews - Drawing lessons from successful and failed experience. Journal of Applied Psychology 90, 857–871 (2005)

    Article  Google Scholar 

  30. Rivera, D.M., Smith, D.D.: Using a demonstration strategy to teach midschool students with learning disabilities how to compute long division. Journal of Learning Disabilities 21, 77–81 (1988)

    Article  Google Scholar 

  31. Manalo, E., Bunnell, J.K., Stillman, J.A.: The use of process mnemonics in teaching students with mathematics learning disabilities. Learning Disability Quarterly 23, 137–156 (2000)

    Article  Google Scholar 

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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: Goel, A.K., Jamnik, M., Narayanan, N.H. (eds) Diagrammatic Representation and Inference. Diagrams 2010. Lecture Notes in Computer Science(), vol 6170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14600-8_19

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  • DOI: https://doi.org/10.1007/978-3-642-14600-8_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14599-5

  • Online ISBN: 978-3-642-14600-8

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