The mathematics-for-teachers tasks we discuss in this chapter have two qualities: (1) they offer teachers opportunities to experience the pleasure of mathematical insight; and (2) they aim to disrupt and reorganize teachers' views of what it means to do and learn mathematics. Given that many future and inservice elementary teachers fear and dislike mathematics, it is perhaps not too far-fetched to suggest that there is a need for “math therapy.” We believe that a form of mathematics therapy may involve new and different experiences with mathematics. Such experiences, considered broadly to include questions or prompts for mathematical exploration, draw attention to deep mathematical ideas and offer the potential of experiencing the pleasure of significant mathematical insight. In our work with teachers we have developed and used a variety of mathematics tasks as opportunities for experiential therapy. The tasks aim to challenge some of the mathematical myths that future teachers believe to be true and are typically assumed by them in mathematics classrooms. The tasks have potential to disrupt teachers' view of mathematics, and to start the process for reorganizing their thinking about what mathematics is and what it means to do and learn mathematics.
In this chapter we describe and discuss four of the mathematics tasks which involve non-routine mathematics problems that we use in our mathematics-forteachers program. This program is offered annually to our 440 future elementary school (K-8) teachers, who generally lack confidence in mathematics and often fear and/or dislike the subject. It is also offered to inservice teachers through a series of mathematics-for-teachers courses. A student response summarizes the effects of our approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barnes, M. (2000). Magical moments in mathematics: Insights into the process of coming to know.For the Learning of Mathematics 20(1), 33–43.
Berg, B. L. (2004).Qualitative research methods for the social sciences. New York: Pearson.
Blanton, L. M.,&Kaput, J. J. (2003). Developing elementary teachers algebra eyes and ears.Teaching Children Mathematics 10(2), 70–77.
Borba, M. C.,&Confrey, J. (1996). A student's construction of transformations of functions in a multiple representational environment.Educational Studies in Mathematics 31, 319–337.
Burton, L. (1999). Why is intuition so important to mathematicians but missing from mathematics education?For the Learning of Mathematics 19(November), 27–32.
Buzeika, A. (1999). Teachers' doubts about invented algorithms. In O. Zaslavsky (Ed.)Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education(Vol. 2, pp. 161–168). Haifa, Israel: PME.
Carroll, L. (1885).A tangled tale. Accessed April 20, 2008, fromhttp://etext.library.adelaide.edu.au/c/carroll/lewis/tangled/tangled.html.
Davey, N. (1999). The hermeneutics of seeing. In I. Heywood&B. Sandywell (Eds.)Interpreting visual culture: Explorations in the hermeneutics of the visual(pp. 3–29). New York: Routledge.
Davis, P. J.,&Hersh, R. (1981).The mathematical experience. Boston: Birkhäuser.
Dissanakye, E. (1992).Homo aestheticus. New York: Free Press.
Egan, K. (1997). The arts as the basics of education.Childhood Education 73(6), 341–345.
Ensor, P. (1998). Teachers' beliefs and the problem of the social. In A. Olivier&K. Newstead (Eds.)Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education(pp. 280–287). Stellenbosch, South Africa: PME.
Fosnot, C. T.,&Dolk, M. (2001).Young mathematicians at work. Constructing multiplication and division. Portsmouth, NH: Heinemann.
Gadanidis, G. (2004). The pleasure of attention and insight.Mathematics Teaching 186(1), 10–13.
Gadanidis, G.,&Hoogland, C. (2004). Mathematics as story. In G. Gadanidis, C. Hoogland,&C. Sedig (Eds.)Mathematics as story: Mathematics through the lenses of art&technology(pp. 128–135). Toronto, ON: Fields Institute for Research in Mathematical Sciences.
Gadanidis, G., Simmt, E., Sterenberg, G.,&Tumanov, V. (2004). Mathematics as story. In G. Gadanidis, C. Hoogland,&C. Sedig (Eds.)Mathematics as story: Mathematics through the lenses of art&technology(pp. 62–65). Toronto, ON: Fields Institute for Research in Mathematical Sciences.
Ginsburg, H. G. (2002). Little children, big mathematics: Learning and teaching in the pre-school.Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education(Vol. 1, pp. 3–14).University of East Anglia.
Hadamard, J. (1996/1945).The mathematician's mind: The psychology of invention in the mathematical field. Princeton, NJ: Princeton University.
Heidegger, M. (1927–1964). Basic writings. In D. F. Krell (Ed.)Revised&expanded edition. New York: Harper Collins.
Jonassen, D. H. (2000).Computers as mindtools for schools. Engaging critical thinking(2nd ed.). Upper Saddle River, NJ: Merrill/Prentice-Hall.
Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.)Handbook of research on mathematics teaching and learning(pp. 390–419). New York: MacMillan.
Kieran, C.,&Sfard, A. (1999). Seeing through symbols: The case of equivalent expressions.Focus on Learning Problems in Mathematics 21(1), 1–17.
Liljedahl, P. (2002). The àha moment: Students' insight into the learning of mathematics.Proceedings of the 24th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education(pp. 887–896). University of Georgia.
McGowen, M. A.,&Davis, G. E. (2001). What mathematics knowledge do preservice elementary teachers value and remember? In R. Speiser, C. A. Maher,&C. N. Walter (Eds.)Proceedings of the 23rd Annual Meeting, North American Chapter of International Group for the Psychology of Mathematics Education(pp. 875–884). Snowbird, Utah.
Nathan, M. J.,&Koedinger, K. R. (2000). An investigation of teachers' beliefs of students' algebra development.Cognition and Instruction 18(2), 209–237.
Peacock, M. (1999).How to read a poem … and start a poetry circle. Toronto, ON: McClelland and Stewart.
Skott, J. (1999). The multiple motives of teaching activity and the role of the teacher's school mathematical images. In O. Zaslavsky (Ed.)Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education(Vol. 4, pp. 209–216). Haifa, Israel: PME.
Sumara, D. (2002).Why reading literature in schools still matters: Imagination, interpretation, insight. Mahwah, NJ: L. Erlbaum.
Zwicky, J. (2003).Wisdom&metaphor. Kentville, Nova Scotia: Gaspereau Press.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Gadanidis, G., Namukasa, I. (2009). Teacher Tasks for Mathematical Insight and Reorganization of What it Means to Learn Mathematics. In: Clarke, B., Grevholm, B., Millman, R. (eds) Tasks in Primary Mathematics Teacher Education. Mathematics Teacher Education, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09669-8_9
Download citation
DOI: https://doi.org/10.1007/978-0-387-09669-8_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-09668-1
Online ISBN: 978-0-387-09669-8
eBook Packages: Humanities, Social Sciences and LawEducation (R0)