Advertisement

CREATING OPTIMAL MATHEMATICS LEARNING ENVIRONMENTS: COMBINING ARGUMENTATION AND WRITING TO ENHANCE ACHIEVEMENT

  • Dionne I. Cross
Article

Abstract

The issue of mathematics underachievement among students has been an increasing international concern over the last few decades. Research suggests that academic success can be achieved by focusing on both the individual and social aspects of learning. Within the area of mathematics education, the development of metacognitive skills and the incorporation of discourse in classroom instruction has resulted in students having deeper conceptual understandings of the content and increased mathematical achievement. However, studies in this field tend to focus on the effects of these practices separately, making research that seeks to harness the potential of both quite rare. This paper reports on a study that was aimed at addressing this gap in the literature by examining the effects of writing and argumentation on achievement. Two hundred and eleven students and five teachers participated in this multimethod study that investigated the effects of three treatment conditions on mathematical achievement. These conditions were writing alone, argumentation alone, and writing and argumentation combined. Analysis of covariance revealed significant differences between the groups, and tests of the contrasts showed that students who engaged in both argumentation and writing had greater knowledge gains than students who engaged in argumentation alone or neither activity.

Key words

learning environments mathematics achievement mathematical argumentation writing 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bereiter, C. & Scardamalia, M. (1987). The psychology of written composition. Hillsdale, NJ: Erlbaum.Google Scholar
  2. Boe, E. & Shin, S. (2005). Is the United States really losing the international horse race in academic achievement? Phi Delta Kappan, 86(9), 688–695.Google Scholar
  3. Brown, A. (1987). Metacognition, executive control, self-regulation and other more mysterious mechanisms. In F. Weinert & R. Klume (Eds.), Metacognition, motivation and understanding. Mahwah, NJ: Erlbaum.Google Scholar
  4. Case, R. (1996). Changing views of knowledge and their impact on educational research and practice. In D. R. Olson & N. Torrance (Eds.), The handbook of education and human development: New models of learning, teaching and schooling (pp. 75–99). Oxford: Blackwell Publishers.Google Scholar
  5. Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23, 13–20.Google Scholar
  6. Cobb, P., Yackel, E., Wood, T., Nicholls, J., Wheatley, G. & Trigatti, B. (1991). Assessment of a problem-centered second-grade mathematics project. Journal for Research in Mathematics Education, 22(1), 3–29.CrossRefGoogle Scholar
  7. Cornoldi, C. & Lucangeli, D. (1997). Mathematics and metacognition: What is the nature of the relationship? Mathematical Cognition, 3(2), 121–139.CrossRefGoogle Scholar
  8. Cross, D. (2007). Creating optimal mathematics learning environments: Combining argumentation and writing to enhance achievement. Unpublished dissertation. University of Georgia, Athens, GA.Google Scholar
  9. Cross, D., Taasoobshirazi, G., Hendricks, S. & Hickey, D. (2008). Argumentation: A strategy for enhancing achievement and improving scientific identities. International Journal of Science Education, 30(6), 837–861.CrossRefGoogle Scholar
  10. Flower, L. & Hayes, J. (1980). The dynamics of composing: Making plans and juggling constraints. In L. Gregg & E. Steinberg (Eds.), Cognitive processes in writing (pp. 31–50. ) Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  11. Forman, E. (1989). The role of peer interaction in the social construction of mathematical knowledge. International Journal of Educational Research, 13, 55–70.CrossRefGoogle Scholar
  12. Forman, E., Larreamendy-Joerns, J., Stein, M. K. & Brown, C. (1998). "You’re going to want to find out which and prove it’: Collective argumentation in a mathematics classroom. Learning and Instruction, 8(6), 527–548.CrossRefGoogle Scholar
  13. Garii, B. (2002). That ‘aha’ experience: Meta-cognition and student understanding of learning and knowledge. Paper presented at the American Educational Research Association, New Orleans, LA.Google Scholar
  14. Hatano, G. & Inagaki, K. (2003). When is conceptual change intended? A cognitive sociocultural view. In G. Sinatra & P. Pintrich (Eds.), Intentional conceptual change (pp. 407–427.) Mahwah, NJ: Lawrence Erlbaum Associates, Inc.Google Scholar
  15. Hayes, J. & Flower, L. (1980). Identifying the organization of writing processes. In L. Gregg & E. Steinberg (Eds.), Cognitive Processes in Writing (pp. 3–30.) Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  16. Inagaki, K., Hatano, G. & Morita, E. (1998). Construction of mathematical knowledge through whole-class discussion. Learning and Instruction, 8(6), 503–526.CrossRefGoogle Scholar
  17. Keys, C. (2000). Investigating the thinking processes of eighth grade writers during the composition of a scientific laboratory report. Journal of Research in Science Teaching, 37(7), 676–690.CrossRefGoogle Scholar
  18. Kramarski, B., Mevarech, Z. & Arami, M. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 49, 225–250.CrossRefGoogle Scholar
  19. Leonard, J. (2000). Let’s talk about the weather: lessons learned in facilitating mathematical discourse. Mathematics Teaching in the Middle School, 5(8), 518–523.Google Scholar
  20. Lesh, R., Doerr, H., Carmona, G. & Hjalmarson, M. (2003). Beyond constructivism. Mathematical Thinking & Learning, 5(2/3) 211–233.CrossRefGoogle Scholar
  21. Mayer, R. (1998). Cognitive, metacognitive and motivational aspects of problem solving. Instructional Science 26, 49–63.CrossRefGoogle Scholar
  22. McClain, K. & Cobb, P. (2001). An analysis of development of sociomathematical norms in one first-grade classroom. Journal of Research in Mathematics Education, 32(3), 236–266.CrossRefGoogle Scholar
  23. McClain, K., McGatha, M. & Hodge, L. (2000). Improving data analysis through discourse. Mathematics Teaching in the Middle School, 5(8), 548–553.Google Scholar
  24. Nasir, N. (2005). Individual cognitive structuring and the sociocultural context: strategy shifts in the game of dominoes. The Journal of the Learning Sciences, 14(1), 5–34.CrossRefGoogle Scholar
  25. NCES (2003). National assessment of educational progress report. Washington, DC: National Center for Educational Statistics.Google Scholar
  26. Pontecorvo, C. (1993). Social interaction in the acquisition of knowledge. Educational Psychology Review, 5(3), 293–310.CrossRefGoogle Scholar
  27. Prawat, R. S. (1996). Constructivisms, modern and postmodern. Educational Psychologists, 31, 215–225.CrossRefGoogle Scholar
  28. Rittenhouse, P. (1998). The teacher’s role in mathematical conversation: stepping in and stepping out. In M. Lampert & M. Blunk (Eds.), Talking mathematics in school: Studies of teaching and learning (pp. 163–189.) Cambridge: University Press.Google Scholar
  29. Rivard, L. & Straw, S. (2000). The effect of talk and writing on learning science: an exploratory study. Science Education, 85(5), 566–593.CrossRefGoogle Scholar
  30. Rogoff, B. (1995). Observing sociocultural activity in three planes: participatory appropriation, guided participation, and apprenticeship. Cambridge, UK: Cambridge University Press.Google Scholar
  31. Scardamalia, M. & Bereiter, C. (1986). Research on written composition. In M. Wittrock (Eds.), Handbook of research on teaching (pp. 778–803.) New York: MacMillan.Google Scholar
  32. Schmidt, W., Wang, H. & McKnight, C. (2005). Curriculum coherence: an examination of US mathematics and science content standards from an international perspective. Journal of Curriculum Studies, 37(5), 525–559.CrossRefGoogle Scholar
  33. Schoenfeld, A. (1987). What’s all the fuss about metacognition? In A. Schoenfeld (Eds.), Cognitive Science and Mathematics Education (pp. 189–215.) Hillsdale, NJ: Lawrence Erlbaum Associates Inc.Google Scholar
  34. Schoenfeld, A. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In D. Grouws (Eds.), Handbook of research on teaching and mathematics learning. New York: Macmillan Publishing Company.Google Scholar
  35. Silver, E. A. (1987). Foundations of cognitive theory and research for mathematics problem-solving instruction. In A. Schoenfeld (Eds.), Cognitive science and mathematics education (pp. 33–60.) Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  36. Stein, M. (2001). Mathematical argumentation: putting umph into classroom discussions. Mathematics Teaching in the Middle School, 7(2), 110–112.Google Scholar
  37. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.Google Scholar
  38. Yackel, E. & Cobb, P. (1996). Sociomathematical norms, argumentation and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.CrossRefGoogle Scholar
  39. Zan, R. (2000). A metacognitive intervention in mathematics at the university level. International Journal of Mathematical Education in Science and Technology, 31(1), 143–150.CrossRefGoogle Scholar

Copyright information

© National Science Council, Taiwan 2008

Authors and Affiliations

  1. 1.Mathematics EducationIndiana UniversityBloomingtonUSA

Personalised recommendations