Abstract
I use the term ”instructional example,” to refer to an example offered by a teacher within the context of learning a particular topic. The important role of instructional examples in learning mathematics stems firstly from the central role that examples play in mathematics and mathematical thinking. Examples are an integral part of mathematics and a significant element of expert knowledge . In particular, examples are essential for generalization, abstraction, and analogical reasoning. Furthermore, from a teaching perspective, there are several pedagogical aspects of the use of instructional examples that highlight the significance and convey the complexity of this central element of teaching.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The generation or selection of examples is a fundamental part of constructing a good explanation… For learning to occur, several examples are needed, not just one; the examples need to encapsulate a range of critical features; and examples need to be unpacked, with the features that make them an example clearly identified.
(Leinhardt, 2001, p. 347)
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215–241.
Ball, D., Bass, H., Sleep, L., & Thames, M. (2005). A theory of mathematical knowledge for teaching. Paper presented at a Work-Session at ICMI-Study15: The Professional Education and Development of Teachers of Mathematics, Brazil, 15–21 May 2005.
Ball, D.L., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
Bills, L., Dreyfus, T., Mason, J., Tsamir, P., Watson, A., & Zaslavsky, O. (2006). Exemplification in mathematics education. In J. Novotná, H. Moraová, M. Krátká, & N. Stehliková (Eds.), Proceedings of the 30th conference of the international group for the psychology of mathematics education (Vol.1, pp. 126–154).
Bishop, A. J. (1976). Decision-making, the intervening variable. Educational Studies in Mathematics, 7(1/2), 41–47.
Hazzan, O., & Zazkis, R. (1999). A Perspective on “give and example” tasks as opportunities to construct links among mathematical concepts. Focus on Learning Problems in Mathematics, 21(4), 1–14.
Harel, G. (2008). DNR perspective on mathematics curriculum and instruction, Part II. Zentralblatt fuer Didaktik der Mathematik, 40, 893–907.
Kennedy, M. M. (2002). Knowledge and teaching [1]. Teachers and Teaching: Theory and Practice, 8, 355–370.
Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge: Cambridge University Press.
Leinhardt, G. (2001). Instructional explanations: A commonplace for teaching and location for contrast. In V. Richardson (Ed.). Handbook of research on teaching (4th ed., pp. 333–357). Washington, DC: American Educational Research Association.
Leinhardt, G. (1990). Capturing craft knowledge in teaching. Educational Researcher, 19(2), 18–25.
Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1–64.
Mason, J. & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics 15(3), 277–290.
Mason, J., Spence, M. (1999). Beyond mere knowledge of mathematics: The importance of knowing-to act in the moment. Educational Studies in Mathematics, 38(1–3), 135–161.
Peled, I., & Zaslavsky, O. (1997). Counter-examples that (only) prove and counter-examples that (also) explain. FOCUS on Learning Problems in Mathematics, 19(3), 49–61.
Rissland, E. L. (1978). Understanding understanding mathematics. Cognitive Science, 2(4), 361–383.
Rissland, E. L. (1991). Example-based reasoning. In J. F. Voss, D. N. Parkins, & J. W. Segal (Eds.), Informal reasoning in education (pp. 187–208). Hillsdale, NJ: Lawrence Erlbaum Associates.
Rowland, T., Thwaites, A., & Huckstep, P. (2003). Novices’ choice of examples in the teaching of elementary mathematics. In A. Rogerson (Ed.), Proceedings of the international conference on the decidable and the undecidable in mathematics education (pp. 242–245) Brno, Czech Republic.
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York: Teachers College Press.
Skemp, R. R. (1971). The psychology of learning mathematics. Harmondsworth, UK: Penguin Books, Ltd.
Watson, A., & Mason, J. (2002). Student-Generated Examples in the Learning of Mathematics. Canadian Journal of Science, Mathematics and Technology Education, 2(2), 237–249.
Zaslavsky, O. (2008). Meeting the challenges of mathematics teacher education through design and use of tasks that facilitate teacher learning. In B. Jaworski & T. Wood (Vol. Eds.), The mathematics teacher educator as a developing professional, Vol. 4, of T. Wood (Series Ed.), The international handbook of mathematics teacher education (pp. 93–114). Rotterdam, The Netherlands: Sense Publishers.
Zaslavsky, O., Harel, G., & Manaster, A. (2006). A teacher’s treatment of examples as reflection of her knowledge-base. In J. Novotná, H. Moraová, M. Krátká, & N. Stehliková (Eds.), Proceedings of the 30th conference of the international group for the psychology of mathematics education (Vol. 5, pp. 457–464).
Zaslavsky, O., & Lavie, O. (2005). Teachers’ use of instructional examples. Paper presented at the 15th Study Conference of the International Commission on Mathematical Instruction (ICMI), on the Professional Education and Development of Teachers of Mathematics. Águas de Lindóia, Brazil.
Zaslavsky, O., & Peled, I. (1996). Inhibiting factors in generating examples by mathematics teachers and student–teachers: The case of binary operation. Journal for Research in Mathematics Education, 27(1), 67–78.
Zaslavsky, O., & Zodik, I. (2007). Mathematics teachers’ choices of examples that potentially support or impede learning. Research in Mathematics Education, 9, 143–155.
Zodik, I., & Zaslavsky, O. (2007). Is a visual example in geometry always helpful? In J-H. Woo, H-C. Lew, K-S. Park, & D-Y. Seo (Eds.), Proceedings of the 31st conference of the international group for the psychology of mathematics education (Vol. 4, pp. 265–272).
Zodik, I., & Zaslavsky, O. (2008). Characteristics of teachers’ choice of examples in and for the mathematics classroom. Educational Studies in Mathematics, 69, 165–182
Zodik, I., & Zaslavsky, O. (2009). Teachers’ treatment of examples as learning opportunities. In Tzekaki, M., Kaldrimidou, M., & Sakonidis, C. (Eds.). Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, v.5, pp. 425–432. Thessaloniki, Greece: PME.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Zaslavsky, O. (2010). The Explanatory Power of Examples in Mathematics: Challenges for Teaching. In: Stein, M., Kucan, L. (eds) Instructional Explanations in the Disciplines. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0594-9_8
Download citation
DOI: https://doi.org/10.1007/978-1-4419-0594-9_8
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-0593-2
Online ISBN: 978-1-4419-0594-9
eBook Packages: Humanities, Social Sciences and LawEducation (R0)