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Asia Pacific Education Review

, Volume 9, Issue 2, pp 101–112 | Cite as

Cognitive models: The missing link to learning fraction multiplication and division

  • Belinda V. de Castro
Article

Abstract

This quasi-experimental study aims to streamline cognitive models on fraction multiplication and division that contain the most worthwhile features of other existing models. Its exploratory nature and its approach to proof elicitation can be used to help establish its effectiveness in building students’ understanding of fractions as compared to the traditional algorithmic way of teaching, vis-à-vis the students’ negative notions about learning fractions. Interestingly, the study showed the benefits and drawbacks of using these cognitive models in the teaching and learning of mathematics.

Key words

cognitive models fraction multiplication and division instructional intervention 

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References

  1. Albacete, P., & VanLehn, K. (2000).Evaluating the effectiveness of a cognitive tutor for fundamental physics concepts. Retrieved August, 2003, from http://www.pitt.edu/vanlehn/distrib/Papers/last-cogsci-albacete.pdf.Google Scholar
  2. Cramer, K., Post, T., & delMas, R. (2002). Initial fraction learning by fourth and fifth grade students: a comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum.Journal of Research in Mathematics Education, 33(2), 111–144.CrossRefGoogle Scholar
  3. de Castro, B. (2004). Pre-service teachers’ mathematical reasoning as an imperative for codified conceptual pedagogy in Algebra: A case study in teacher education.Asia Pacific Education Review, 5(2), 157–166.CrossRefGoogle Scholar
  4. Freiman, V., & Volkov, A. (2004).Fractions and fractions again? A comparative analysis of the presentation of common fractions in the textbooks belonging to different didactical tradition. Paper presented at ICME-10, Discussion Group 14, Copenhagen, Denmark.Google Scholar
  5. Hunting, R. (1999). Rational-number learning in the early years: what is possible?Mathematics in the Early Years, 80-87.Google Scholar
  6. Ibe, M. (2001). Confluence of mathematics teaching methods, textbook preparation and testing: explaining RP TIMSS student performance.Intersection Proceedings Biennial Conference. Curricular Issues and New Technologies. Phil. Council of Mathematics Teachers Educators MATHTED Inc.Google Scholar
  7. Lubinski, C., & Fox, T. (1998). Learning to make sense of division of fractions: one K-8 preservice teacher’s perspective.School Science and Mathematics.98(7), 247–252.Google Scholar
  8. Johnson, B., & Koedinger, K. (2001).Using cognitive models to guide instructional design: the case of fraction division. Retrieved August, 2003, from http://act-r.psy.cmu.edu/papers/361/br_krk_2001_a.pdf.Google Scholar
  9. Kinach, B. (2002). A cognitive strategy for developing pedagogical content knowledge in the secondary mathematics methods course: toward a model of effective practice.Teaching and Teacher Education, 18(1), 51–71.CrossRefGoogle Scholar
  10. Kort, B., & Reilly, R. (2002).A pedagogical model for teaching scientific domain knowledge. Paper presented at the32 nd ASEE/IEEE Frontiers in Education Conference, November 6-9, 2002. Google Scholar
  11. Mack, N. (1998). Building a foundation for understanding the multiplication of fractions.Teaching Children Mathematics, 5(1), 34–38.Google Scholar
  12. Mayer, R. E. (1987).Educational Psychology: A Cognitive Approach. Boston: Little Brown.Google Scholar
  13. Meagher, M. (2002). Teaching fractions, new methods, new resources.ERIC Digest. Moss, J., & Case, R. (1999). Developing children’s understanding of the rational numbers: a new model and experimental curriculum.Journal for Research in Mathematics Education,30(2), 122-147.Google Scholar
  14. NCTM standards (2000). Retrieved May, 2002, from http://www.standards.nctm.org/document.Google Scholar
  15. Norris, S., Leighton, J., & Phillips, L. (2004). What is at stake in knowing the content and capabilities of the children’s minds? A case of basing high stakes test on cognitive models.Theory and Research in Education, 2(3), 283–308.CrossRefGoogle Scholar
  16. Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: an example from a longitudinal trajectory on percentage.Education Studies in Mathematics, 54, 9–35.CrossRefGoogle Scholar
  17. Parmar, R. (2003). Understanding the concept of “division”: Assessment considerations.Exceptionality, 11(3), 177–189.CrossRefGoogle Scholar
  18. Reiman, A., & Sprinthall, L. (1998). Identifying models and methods of instruction.Mentoring and Supervision for Teacher Development. New York: Addison Wesley Longman Inc.Google Scholar
  19. Shulman, L.S. (1987). Knowledge and teaching: Foundations of the new reform.Harvard Educational Review, 57(1), 1–22.Google Scholar
  20. Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions.Learning and Instruction, 14, 503–518.CrossRefGoogle Scholar
  21. Sternberg, R.J. (1985).Beyond IQ: a triarchic theory of human intelligence. New York: Cambridge University Press.Google Scholar
  22. Streefland, L. (1991).Fractions in realistic mathematics education: a paradigm of developmental research. Dordrecht: Kluwer Academic Publishers.Google Scholar
  23. TIMSS-R results. (2000). Retrieved April, 2002, from http://nces.ed.gov/timss/results.asp.Google Scholar
  24. Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: the case of division of fractions.Journal for Research in Mathematics Education, 31(1), 5–25.CrossRefGoogle Scholar
  25. Tzur, R. (1999). An integrated study of children’s construction of improper fractions and the teacher’s role in promoting that learning.Journal for Research in Mathematics Education, 30(4), 390–416.CrossRefGoogle Scholar
  26. Wilson, B., & Cole, P. (1996).Cognitive teaching models. Retrieved August, 2003, from http://carbon. cudenver.edu/-bwilson/hndbkch.html.Google Scholar
  27. Yoshida, H., & Sawano, K. (2002). Overcoming cognitive obstacles in learning fractions: equal-partitioning and equal-whole.Japanese Psychological Research, 44(4), 183–195.CrossRefGoogle Scholar

Copyright information

© Education Research Institute 2008

Authors and Affiliations

  1. 1.Center for Educational Research and DevelopmentUniversity of Santo Tomas, EspañaManilaPhilippines

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