# Examining the effects of writing on conceptual and procedural knowledge in calculus

## Abstract

It has been claimed that writing to learn mathematics (WTLM) may benefit students' conceptual understanding as well as their procedural ability. To investigate this claim, we collected data from students in two sections of an introductory calculus course. In one of the sections, students used WTLM activities and discussed the activities after completing the writing; in the other section, students used similar activities that did not involve writing but engaged them in thinking about the mathematical ideas and in discussing the activities. The errors from the in-class and final exams of both groups of students were categorized and analyzed for information about the students' conceptual and procedural understanding. We found no significant differences between the WTLM group and the non-writing group, which suggests that the real benefit from writing activities may not be in the actual activity of writing, but rather in the fact that such activities require students to struggle to understand mathematical ideas well enough to communicate their understanding to others.

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## REFERENCES

- Allen, N.B.R.: 1992, 'A study of metacognitive skill as influenced by expressive writing in college introductory algebra classes', (Doctoral dissertation, Louisiana State University, 1991).
*Dissertation Abstracts International*53, 432A.Google Scholar - Brandau, L.: 1990, 'Rewriting our stories of mathematics', in A. Sterrett (ed.),
*Using Writing to Teach Mathematics,*Mathematical Association of America, Washington, DC, pp. 73-77.Google Scholar - Doherty, B.J.: 1996, 'The write way: A look at journal writing in first-year algebra',
*Mathematics Teacher*89, 556-560.Google Scholar - Gopen, G.D. and Smith, D.A.: 1990, 'What's an assignment like you doing in a course like this?: Writing to learn mathematics',
*The College Mathematics Journal*21, 2-19.CrossRefGoogle Scholar - Guckin, A.M.: 1992, 'The role of mathematics informal writing in college mathematics instruction', (Doctoral dissertation, University of Minnesota, 1992).
*Dissertation Abstracts International*53, 1435A.Google Scholar - Harel, G. and Sowder, L.: 1998, 'Students' proof schemes: Results from exploratory studies', in A.H. Schoenfeld, J. Kaput, E. Dubinsky (eds),
*Research in Collegiate Mathematics Education III*, American Mathematical Society, Providence, RI, pp. 234-283.Google Scholar - Heid, M.K.: 1988, 'Resequencing skills and concepts in applied calculus using the computer as a tool',
*Journal for Research in Mathematics Education*19, 3-25.CrossRefGoogle Scholar - Hiebert, J. and Carpenter, T.: 1992, 'Learning and teaching with understanding', in D. Grouws (ed.),
*Handbook of Research on Mathematics Teaching and Learning*, Macmillan Publishing Company, New York, pp. 65-97.Google Scholar - Hiebert, J. and Lefevre, P.: 1986, 'Conceptual and procedural knowledge in mathematics: An introductory analysis', in J. Hiebert (ed.),
*Conceptual and Procedural Knowledge: The Case of Mathematics*, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 1-27.Google Scholar - Judson, P.T.: 1988, 'Effects of modified sequencing of skills and applications in introductory calculus', Doctoral dissertation, University of Texas at Austin, 1988,
*Dissertation Abstracts International*49, 1397A.Google Scholar - Judson, P.T.: 1990, 'Elementary business calculus with computer algebra',
*Journal of Mathematical Behavior*9, 153-157.Google Scholar - Miller, L.D.: 1992, 'Teacher benefits from using impromptu writing prompts in algebra classes',
*Journal for Research in Mathematics Education*23, 329-340.CrossRefGoogle Scholar - Morgan, C.: 1998,
*Writing Mathematically: The Discourse of Investigation,*Falmer Press, London.Google Scholar - Movshovitz-Hadar, N., Zaslavsky, O. and Inbar, S.: 1987, 'An empirical classification model for errors in high school mathematics',
*Journal for Research in Mathematics Education*18, 3-14.CrossRefGoogle Scholar - Nahrgang, C.L. and Petersen, B.T.: 1986, 'Using writing to learn mathematics',
*Mathematics Teacher*79, 461-465.Google Scholar - Oaks, A.B.: 1988, 'The effects of the interaction of conception of mathematics and affective constructs on college students in remedial mathematics', Doctoral dissertation, University of Rochester, 1987.
*Dissertation Abstracts International*49, 54A.Google Scholar - Oaks, A.B.: 1990, 'Writing to learn mathematics: Why do we need it and how can it help us?', paper presented at Association of Mathematics Teachers of New York State Conference, November 1990, Ellenville, NY.Google Scholar
- Orton, A.: 1983a, 'Students' understanding of differentiation',
*Educational Studies in Mathematics*14, 235-250.CrossRefGoogle Scholar - Orton, A.: 1983b, 'Students' understanding of integration',
*Educational Studies in Mathematics*14, 1-18.CrossRefGoogle Scholar - Palmiter, J.R.: 1986, 'The impact of a computer algebra system on college calculus', Doctoral dissertation, The Ohio State University, 1986.
*Dissertation Abstracts International*47, 1640A.Google Scholar - Palmiter, J.R.: 1991, 'Effects of computer algebra systems on concept and skill acquisition in calculus',
*Journal for Research in Mathematics Education*22, 151-156.CrossRefGoogle Scholar - Porter, M.K.: 1996, 'The effects of writing to learn mathematics on conceptual understanding and procedural ability in introductory college calculus', Doctoral dissertation, Syracuse University, 1996.
*Dissertation Abstracts International*58, 2576A.Google Scholar - Pugalee, D.: 1997, 'Connecting writing to the mathematics curriculum',
*Mathematics Teacher*90, 308-310.Google Scholar - Rose, B.J.: 1989, 'Using expressive writing to support the learning of mathematics', Doctoral dissertation, University of Rochester, 1989.
*Dissertation Abstracts International*50, 867A.Google Scholar - Rose, B.J.: 1990, 'Using expressive writing to support mathematics instruction: Benefits for the student, teacher, and classroom', in A. Sterrett (ed.),
*Using Writing to Teach Mathematics,*Mathematical Association of America, Washington, DC, pp. 63-72.Google Scholar - Schoenfeld, A.H.: 1985,
*Mathematical Problem Solving,*Academic Press, New York.Google Scholar - Skemp, R.R.: 1976, 'Relational understanding and instrumental understanding',
*Mathematics Teaching*77, 20-26.Google Scholar - Stehney, A.K.: 1990, 'A writing program and its lessons for mathematicians', in A. Sterrett (ed.),
*Using Writing to Teach Mathematics,*Mathematical Association of America, Washington, DC, pp. 26-29.Google Scholar - Youngberg, S.A.T.: 1990, 'The effect of writing assignments on student achievement in a college level elementary algebra class', Doctoral dissertation, University of Iowa, 1989.
*Dissertation Abstracts International*50, 2819A.Google Scholar