The Influence of Teaching on Student Learning: The Notion of Piecewise Function

Ibrahim Bayazit

doi:10.29333/iejme/255

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Ibrahim Bayazit

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Abstract

This paper examines the influence of classroom teaching on student understanding of the piecewise function. The participants were two experienced mathematics teachers and their 9th grade students. Using a theoretical standpoint that emerged from an analysis of APOS theory, the paper illustrates that the teachers differ remarkably in their approaches to the essence of the piecewise function and this, in turn, affects greatly their students‟ understanding of this notion. Action-oriented teaching, which is distinguished by the communication of rules, procedures and factual knowledge, confines students‟ understanding to an action conception of piecewise function. Process-oriented teaching, which priorities the concept and illustrates it across the representations, promotes students‟ understanding towards a process conception of function.

Keywords

action-oriented teaching
process-oriented teaching
student learning
piecewise function
action conception of piecewise function
process conception of piecewise function

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2010, Volume 5, Issue 3, 146-164

https://doi.org/10.29333/iejme/255

Publication date: 12 Dec 2010

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References

Askew, M., Brown, M., Rhodes, V., William, D., & Johnson, D. (1996). Effective teachers of numeracy. London: King's College.
Ball, D. L. (1991). Research on teaching mathematics: Making subject-matter knowledge part of the equation. In J. Brophy (Ed.), Advances in Research on Teaching (pp. 1-48). Greenwich, CT: JAI Press, 2.
Bayazit, İ. (2006). The relationship between teaching and learning through the context of functions. Unpublished PhD dissertation, University of Warwick, UK.
Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23(3), 247-285.
Brophy, J., & Good, T. L. (1986). Teacher Behavior and student achievement. In M. C. Wittrock (Ed.), Handbook of Research on Teaching (pp.328-375), New York: Macmillan.
Cobb, P., McClain, K., & Whitenack, J. (1997). Reflective discourses and collective reflection. Journal for Research in Mathematics Education, 28(3), 258-277.
Cottrill, J., Dubinsky, E., Nichols, D., Schwingendorf, K., Thomas, K., & Vidakovic, D. (1996). Understanding the Limit Concept: Beginning with a Coordinated Process Scheme. Journal for Mathematical Behavior, 15(2), 167-192.
Dubinsky, E. (1991). Reflective abstraction. In D. O. Tall (Ed.), Advanced Mathematical Thinking (pp.95-123). Dordrecht: Kluwer Academic Publishers.
Dubinsky, E., & Harel, G. (1992). The nature of the process conception of function. In G. Harel & E. Dubinsky (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy (85-107). United States of America: Mathematical Association of America.
Eisenberg, T. (1991). Function and associated learning difficulties. In D. O. Tall (Ed.), Advanced Mathematical Thinking (pp.140-152). Dordrecht: Kluwer Academic Publishers.
English, L. D. (1997). Analogies, metaphors, and images: Vehicles for mathematical reasoning. In L. D. English (Ed.), Mathematical Reasoning: Analogies, Metaphors, and Images (p. 3-18). New Jersey: Lawrence Erlbaum Associates Inc.
Even, R. (1990). Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21(6), 521-544.
Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning use children‟s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27(4), 403-434.
Goldin, G. (2001). Systems of representations and the development of mathematical concepts. In Cuoco, A. A., & Curcio, F. R. (Eds.), The role of representation in school mathematics (p. 1-23). Reston. NCTM Yearbook.
Good, T., & Grouws, D. (1977). Teaching effects: A process-product study in fourth grade mathematics classrooms. Journal of Teacher Education, 28, 49-54.
Helmke, A., Schneider, W., & Weiner, F. E. (1986). Quality of instruction and classroom learning outcomes: The German contribution to the IEA classroom environment study. Teaching and Teacher Education, 2(1), 1-18.
Leinhardt, G. (1988). Expertise in instructional lessons: An example from fractions. In D. A. Grouws, & T. J. Cooney (Eds.), Perspectives on Research on Effective Mathematics Teaching (pp.44-66). Hillsdale, NJ: Lawrence Erlbaum.
Leinhardt, G., Putnam, R. T., Stein, M. K., & Baxter, J. (1991). Where subject knowledge is matter. In J. Brophy (Ed.), Advances in Research on Teaching: Teacher's Knowledge of Subject Matter as it Relates to Their Teaching Practice (v2, pp.87-113). London: JAI Press Inc.
Markovits, R., Eylon, B. S., & Brukheimer, M. (1986). Functions today and yesterday. For the Learning of Mathematics, 6(2), 18-28.
Merriam, S. B. (1988). Case study research in education: Qualitative approach. London: Jossey-Bass Publishers.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis (An expanded sourcebook). London: Sage Publications.
Phillips, N., & Hardy, C. (2002). Discourse analysis: investigating processes of social construction. United Kingdom: Sage Publications Inc.
Pirie, S., & Kieren, T. (1992). Creating constructivist environments and constructing creative mathematics. Educational Studies in Mathematics, 23, 505-528.
Schwarz, B., & Dreyfus, T. (1995). New actions upon old objects: A new ontological perspective on functions. Educational studies in mathematics, 29(3), 259-291.
Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reificationthe case of function. In G. Harel, & E. Dubinsky (Eds.), The Concept of Function Aspects of Epistemology and Pedagogy (pp.59-85). USA: Mathematical Association of America.
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4-14.
Tall, D. O. (1999). Reflections on APOS theory in elementary and advanced mathematical thinking. In O. Zaslavsky (Ed.,), Proceeding of the 23rd Conference of the International Group for the Psychology of Mathematics Education (v1, pp.11-118). Israil: Haifa
Tobin, K., & Capie, W. (1982). Relationships between classroom process variables and middle-school science achievement. Journal of Educational Psychology, 74, 441-454.
Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293- 305.
Weinert, F. E., Schrader, F-W., & Helmke, A. (1989). Quality of instruction and achievement outcomes. International Journal of Educational Research, 13(8), 895-914.

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APA

Bayazit, I. (2010). The Influence of Teaching on Student Learning: The Notion of Piecewise Function. International Electronic Journal of Mathematics Education, 5(3), 146-164. https://doi.org/10.29333/iejme/255

Vancouver

Bayazit I. The Influence of Teaching on Student Learning: The Notion of Piecewise Function. INT ELECT J MATH ED. 2010;5(3):146-64. https://doi.org/10.29333/iejme/255

AMA

Bayazit I. The Influence of Teaching on Student Learning: The Notion of Piecewise Function. INT ELECT J MATH ED. 2010;5(3), 146-164. https://doi.org/10.29333/iejme/255

Chicago

Bayazit, Ibrahim. "The Influence of Teaching on Student Learning: The Notion of Piecewise Function". International Electronic Journal of Mathematics Education 2010 5 no. 3 (2010): 146-164. https://doi.org/10.29333/iejme/255

Harvard

Bayazit, I. (2010). The Influence of Teaching on Student Learning: The Notion of Piecewise Function. International Electronic Journal of Mathematics Education, 5(3), pp. 146-164. https://doi.org/10.29333/iejme/255

MLA

Bayazit, Ibrahim "The Influence of Teaching on Student Learning: The Notion of Piecewise Function". International Electronic Journal of Mathematics Education, vol. 5, no. 3, 2010, pp. 146-164. https://doi.org/10.29333/iejme/255