Abstract
The purpose of this exploratory study was to investigate the impact of writing during mathematical problem solving. The study involved an analysis of ninth grade algebra students' written and verbal descriptions of their mathematical problem solving processes. Through this comparison, a better understanding of the connection between problem solving and writing is realized. The written and verbal data show a relationship between the number of problem solving strategies tried by students and their success. The majority of problem solving behaviors involve execution actions such as carrying out goals and performing calculations. Students who construct global plans are more successful problem solvers. Students engage in verification behaviors at various stages of problem solving though the majority of students do not verify their final answers. While both oral and written descriptions serve as a tool for understanding students' thinking processes, a comparison of the two modes of reporting, using a metacognitive framework as the lens of analysis, reveals some important variations. Students who wrote descriptions of their thinking were significantly more successful in the problem solving tasks (p< 0.05) than students who verbalized their thinking. Differences in metacognitive behaviors also support the premise that writing can be an effective tool in supporting metacognitive behaviors.
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REFERENCES
Allen, B.R.: 1991, A Study of Metacognitive Skill as Influenced by Expressive Writing in College Introductory Algebra Classes, Unpublished doctoral dissertation, Louisiana State University and Agricultural And Mechanical College.
Applebee, A.N.: 1981', Writing in the Secondary School, National Council of Teachers of English, Urbana, IL.
Artz, A.F. and Armour-Thomas, E.: 1992, 'Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups', Cognition and Instruction 9(2), 137–175.
Barnett, J.: 1979, 'The study of syntax variables', in G.A. Goldin and C.E. McClintock (eds.), Task Variables in Mathematical Problem solving, ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Columbus, OH, pp. 23–68. (ERIC Document Reproduction Service No. ED178366) Retrieved July 22, 2003, from the ERIC database.
Brown, T.: 1997, Mathematics Education and Language: Interpreting Hermeneutics and Post-Structuralism, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Bruning, J.L. and Kintz, B.L.: 1987, Computational Handbook of Statistics, Scott, Foresman and Company, Glenview, IL.
Carpenter, T.P. and Lehrer, R.: 1999, 'Teaching and learning mathematics with understanding', in E. Fennema and T. Romberg (eds.), Mathematics Classrooms that Promote Understanding, Lawrence Erlbaum Associates, Mahweh, NJ, pp. 19–32.
Carr, M. and Biddlecombe, B.: 1998, 'Metacognition in mathematics: From a constructivist perspective', in D.J. Hacker, J. Dunlosky and A.C. Graesser (eds.), Metacognition in Educational Theory and Practice, Lawrence Erlbaum Associates, Mahweh, NJ.
Davidson, J.E. and Sternberg, R.J.: 1998, 'Verbalization and problem solving', in D.J. Hacker, J. Dunlosky and A.C. Graesser (eds.), Metacognition in Educational Theory and Practice, Lawrence Erlbaum Associates, Mahweh, NJ, pp. 47–68.
Emig, J.: 1977, 'Writing as a mode of learning', College Composition and Communication 28, 122–127.
Flower, L.: 1989, 'Taking thought: The role of conscious processing in the making of meaning', in E.P. Maimon, B.F. Nodine and F.W. O'Connor (eds.), Thinking, Reasoning and Writing, Longman, New York, pp. 185–212.
Flower, L. and Hayes, J.R.: 1983, 'Uncovering cognitive processes in writing: An introduction to protocol analysis', in P. Mosenthal, L. Tamor and S.A.Walmsley (eds.), Research on Writing, Longman, New York.
Gay, L.R. and Airasian, P.: 2003, Educational Research: Competencies for Analysis and Applications, Pearson Education, Inc., Upper Saddle River, NJ.
Garofalo, J. and Lester, F.: 1985, 'Metacognition, cognitive monitoring and mathematical performance', Journal for Research in Mathematics Education 16(3), 163–176.
Gravemeijer, K., Cobb, P., Bowers, J. and Whitenack, J.: 2000, 'Symbolizing, modeling, and instructional design', in P. Cobb, E. Yackel and K. McClain (eds.), Symbolizing and Communicating in Mathematics Classrooms, Lawrence Erlbaum Associates, Mahwah, NJ, pp. 225–273.
Kulm, G.: 1979, 'The classification of problem-solving research variables', in G.A. Goldin and C.E. McClintock (eds.), Task Variables in Mathematical Problem Solving, ERIC Clearinghouse for Science, Mathematics and Environmental Education, Columbus, OH, pp. 1–22. (ERIC Document Reproduction Service No. ED178366) Retrieved July 22, 2003, from the ERIC database.
Masingila, J.O. and Prus-Wisniowska, E.: 1996, 'Developing and assessing mathematical understanding in calculus through writing', in P.C. Elliott and M.J. Kenney (eds.), Communication in Mathematics, K-12 and Beyond, National Council of Teachers of Mathematics, Reston, VA, pp. 95–104.
Meir, J. and Rishel, T.: 1998, Writing in the Teaching and Learning of Mathematics, The Mathematical Association of America, Washington, DC.
Miller, L.D. and England, D.A.: 1989, 'Writing to learn algebra', School Science and Mathematics 89(4), 299–312.
Morgan, C.: 1998, Writing Mathematically: The Discourse of Investigation, Falmer Press, London.
National Council of Teachers of Mathematics: 2000, Principles and Standards for School Mathematics, author, Reston, VA.
National Council of Teachers ofMathematics: 1989, Curriculum and Evaluation Standards for School Mathematics, author, Reston, VA.
O'Connor, M.C.: 1998, 'Language socialization in the mathematics classroom: Discourse practices and mathematical thinking', in M. Lampert and M.L. Blunk (eds.), Talking Mathematics in School: Studies of Teaching and Learning, Cambridge University Press, Cambridge, UK, pp. 17–55.
Patton, M.Q.: 2001, Qualitative Research and Evaluation Methods, Sage, Thousand Oaks, CA.
Porter, M.K. and Masinglila, J.O.: 2000, 'Examining the effects of writing on conceptual and procedural knowledge in calculus', Educational Studies in Mathematics 42(2), 165–77.
Powell, A.B.: 1997, 'Capturing, examining and responding to mathematical thinking through writing', The Clearing House 71(1), 21–25.
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.
Rose, B.J.: 1989, 'Writing and math: Theory and practice', in P. Connolly and T. Vilardi (eds.), Writing to Learn Mathematics and Science, Teachers College Press, New York, pp. 15–30.
Schurter, W.A.: 2002, 'Comprehension monitoring: An aid to mathematical problem solving', Journal of Developmental Education 26(2), 22–33.
Sierpinska, A.: 1998, 'Three epistemologies, three views of classroom communication: Constructivism, sociocultural approaches, interactionism', in H. Steinbring, M.G. Bartolini Bussi and A. Sierpinska (eds.), Language and Communication in the Mathematics Classroom, National Council of Teachers of Mathematics, Reston, VA, pp. 30–62.
Smagorinsky, P.: 1989, 'The reliability and validity of protocol analysis', Written Communication 6(4), 463–479.
Vygotsky, L.S.: 1987, 'Thinking and speech', in R.W. Rieber and A.S. Carton (eds.), The Collected Works of L.S. Vygotsky, Plenum Press, New York, pp. 39–243.
Webb, N.: 1979, 'Content and context variables in problem tasks', in G.A. Goldin and C.E. McClintock (eds.), Task Variables in Mathematical Problem Solving, ERIC Clearinghouse for Science, Mathematics and Environmental Education, Columbus, OH, pp. 69–102. (ERIC Document Reproduction Service No. ED178366) Retrieved July 22, 2003, from the ERIC database.
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Pugalee, D.K. A Comparison of Verbal and Written Descriptions of Students' Problem Solving Processes. Educational Studies in Mathematics 55, 27–47 (2004). https://doi.org/10.1023/B:EDUC.0000017666.11367.c7
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DOI: https://doi.org/10.1023/B:EDUC.0000017666.11367.c7