Promoting Writing in Mathematics: Prospective Teachers’ Experiences and Perspectives on the Process of Writing When Doing Mathematics as Problem Solving
Keywords:
Attitudes, Beliefs, Metacognition, Problem solving, Prospective mathematics teachers, Writing in mathematics
Abstract
Despite a great deal of research on the benefits of writing in mathematics, writing plays a minimal role, if any, in secondary and tertiary mathematics education. In order for teachers to use writing in their classrooms, they themselves have to experience writing mathematics within the teacher education programme. The present paper reports on a study aimed at addressing this gap. In a problem-solving seminar, preservice teachers had an opportunity to experience writing in mathematics and report how this affected their problem-solving processes and shaped their attitudes towards incorporating writing in their classrooms. In order to provide a more detailed description of the phenomenon, four participants were chosen based on their beliefs about mathematics. All of the participants struggled with writing their explanations. Those who used writing as a method to support metacognitive processes while exploring mathematics tended to respond positively to the writing process. The others used writing merely as a method to produce a formal document to be evaluated by the instructor. Consequently, those who viewed writing and doing mathematics as an intertwined process expressed a positive attitude towards using writing in their mathematics classroom. This was, unfortunately, not the case when writing and doing mathematics were seen as two separate processes. Implications for teacher education programmes are presented at the end of the report.
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References
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Pugalee, D. K. (2001). Writing, mathematics, and metacognition: Looking for connections through students’ work in mathematical problem solving. School Science and Mathematics, 101(5), 236–245.
Schoenfeld, A. H. (1987). What’s all the fuss about metacognition? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 189–215). Hillsdale, NJ: Erlbaum.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.
Sfard, A. (2001). Learning mathematics as developing a discourse. In R. Speiser, C. Maher, & C. Walter (Eds.), Proceedings of the Twenty-first Conference of PME-NA (pp. 23–44). Columbus, OH: ERIC Clearing House for Science, Mathematics, and Environmental Education.
Silver, E. A. (1987). Foundations of cognitive theory and research for mathematics problem-solving instruction. In A. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 33–60.) Hillsdale, NJ: Erlbaum.
Thompson, A. (1992). Teacher’s beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
Wilson, M., & Cooney, T. J. (2002). Mathematics teacher change and development. In G. C. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 127–147). Dordrecht, The Netherlands: Kluwer.
Yoo, S. (2008). Effects of traditional and problem-based instruction on conceptions of proof and pedagogy in undergraduates and prospective mathematics teachers. Doctoral dissertation. The University of Texas, Austin.
Brown, A. (1987). Metacognition, executive control, self-regulation and other more mysterious mechanisms. In F. Weinert & R. Klume (Eds.), Metacognition, motivation and understanding (pp. 65–116). Mahwah, NJ: Erlbaum.
Bruder, R., & Collet, C. (2011). Problemlösen lernen im Mathematikunterricht. Berlin: Cornelsen.
Carlson, M. P. (1999). The mathematical behavior of six successful mathematics graduate students: Influences leading to mathematical success. Educational Studies in Mathematics, 40(3), 237–258.
College Entrance Examination Board. (1983). Academic preparation for college: What students need to know and be able to do. New York: Author.
Cooney, T. J. (1999). Conceptualizing teachers’ ways of knowing. Educational Studies in Mathematics, 38, 163–187.
Countryman, J. (1992). Writing to learn mathematics. Portsmouth, NH: Heinemann.
Cross, D. I. (2009). Creating optimal mathematics learning environments: Combining argumentation and writing to enhance achievement. International Journal of Science and Mathematics Education, 7(5), 905–930.
deFreitas, E. (2008). Troubling teacher identity: Preparing mathematics teachers to teach for diversity. Teaching Education, 19(1), 43–55.
Ernest, P. (1989). Philosophy, mathematics and education: The state of the art. International Journal of Mathematics Education in Science and Technology, 20, 555–559.
Ernest, P. (1991). The philosophy of mathematics education. Abingdon, Oxon, UK: Routledge Farmer.
Flores, A., & Brittain, C. (2003). Writing to reflect in a mathematics methods course. Teaching Children Mathematics, 10, 112–118.
Flower, L., & Hayes, J. R. (2009). The cognition of discovery: Defining a rhetorical problem. In S. Miller (Ed.), The Norton book of composition studies (pp. 467–478). New York: W.W. Norton.
Geeslin, W. E. (1977). Using writing about mathematics as a teaching technique. Mathematics Teacher, 70, 112–115.
Halloun, I., & Hestenes, D. (1996). Views About Sciences Survey: VASS. Paper presented at the annual meeting of the National Association of Research in Science Teaching, St. Louis, MO. (ERIC Document Reproduction Service No. ED394840).
Komorek, E. (2009). Mit Hausaufgaben Problemlösen und eigenverantwortliches Lernen in der Sekundarstufe I fördern. Entwicklung und Evaluation eines Ausbildungsprogramms für
Mathematiklehrkräfte. Berlin: Logos Verlag.
Kramarski, B., Mevarech, Z. R., & Arami, M. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 48, 225–250.
Kuzle, A. (2011). Preservice teachers’ patters of metacognitive behavior during mathematics problem solving in a dynamic geometry environment. Doctoral dissertation. The University of Georgia–Athens.
Kuzle, A. (2013). Patterns of metacognitive behavior during mathematics problem-solving in a dynamic geometry environment. International Electronic Journal of Mathematics Education, 8(1), 20–40.
Lester, F. K. (1994). Musing about mathematical problem-solving research: 1970-1994. Journal for Research in Mathematics Education, 25(6), 660–675.
Liljedahl, P., Rolka, K., & Rösken, B. (2007b). Affecting affect: The reeducation of preservice teachers’ beliefs about mathematics and mathematics teaching and learning. In W. G. Martin, M. E. Strutchens, & P. C. Elliott (Eds.), The learning of mathematics (pp. 319–330). Reston, VA: National Council of Teachers of Mathematics.
Llinares, S. (2002). Participation and reification in learning to teach: The role of knowledge and beliefs. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 195–209). Dordrecht, The Netherlands: Kluwer.
Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, 26(1–2), 49–63.
Miller, L. D., & Hunt, N. P. (1994). Professional development through action research. In D. B. Aichele & A. F. Coxford (Eds.), Professional development for teachers of mathematics (pp. 296–303). Reston, Va: The National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (1980). An agenda for action: Recommendations for school mathematics of the 1980s. Reston, VA: Author.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Pajares, F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307-332.
Patton, M. Q. (2002). Qualitative research and evaluation methods. Thousand Oaks, CA: Sage.
Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning, Vol. 2 (pp. 257–315). Charlotte, NC: Information Age.
Porter, M., & Masingila, J. (2001). Examining the effects of writing on conceptual and procedural knowledge in calculus. Educational Studies in Mathematics, 42(2), 165–177.
Pugalee, D. K. (2001). Writing, mathematics, and metacognition: Looking for connections through students’ work in mathematical problem solving. School Science and Mathematics, 101(5), 236–245.
Schoenfeld, A. H. (1987). What’s all the fuss about metacognition? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 189–215). Hillsdale, NJ: Erlbaum.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.
Sfard, A. (2001). Learning mathematics as developing a discourse. In R. Speiser, C. Maher, & C. Walter (Eds.), Proceedings of the Twenty-first Conference of PME-NA (pp. 23–44). Columbus, OH: ERIC Clearing House for Science, Mathematics, and Environmental Education.
Silver, E. A. (1987). Foundations of cognitive theory and research for mathematics problem-solving instruction. In A. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 33–60.) Hillsdale, NJ: Erlbaum.
Thompson, A. (1992). Teacher’s beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
Wilson, M., & Cooney, T. J. (2002). Mathematics teacher change and development. In G. C. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 127–147). Dordrecht, The Netherlands: Kluwer.
Yoo, S. (2008). Effects of traditional and problem-based instruction on conceptions of proof and pedagogy in undergraduates and prospective mathematics teachers. Doctoral dissertation. The University of Texas, Austin.
Published
2013-12-31
How to Cite
Kuzle, A. (2013). Promoting Writing in Mathematics: Prospective Teachers’ Experiences and Perspectives on the Process of Writing When Doing Mathematics as Problem Solving. Center for Educational Policy Studies Journal, 3(4), 41-59. https://doi.org/10.26529/cepsj.222
Section
FOCUS
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