Mutual Expectations Between Mathematicians and Mathematics Educators
Four authors whose education and current position place them at different locations on the continuum from mathematician to mathematics educator use their experience to consider what contribution towards mathematics education mathematics educators might ex
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Mutual Expectations Between Mathematicians and Mathematics Educators Tommy Dreyfus
Abstract Four authors whose education and current position place them at different locations on the continuum from mathematician to mathematics educator use their experience to consider what contribution towards mathematics education mathematics educators might expect from mathematicians and what mathematicians might expect from mathematics educators and from mathematics education as a domain. Keywords Expectations · Mutual expectations · Mathematics · Mathematics education · Mathematicians · Mathematics educators
Introduction The purpose of this chapter is to make a start in asking what mathematics education should be about and what it should not be about in the eyes of mathematicians and mathematics educators: what do mathematicians as opposed to mathematics educators think the concerns of mathematics education should or should not be, and what do mathematics educators think mathematicians could, should, or should not contribute to mathematics education? What, in short, do these two groups expect from one another? Of course the divide between whom we should call a mathematician and whom we should call a mathematics educator is not sharp; there is almost a continuum in the degrees of involvement in mathematics education and mathematics pure and simple. The authors of this chapter occupy different positions along that continuum and represent different perspectives. From those different perspectives, some of the authors make claims about mutual expectations, some ask questions and some raise issues that suggest questions. All the authors, however, primarily intend With contributions by Uri Onn, Department of Mathematics, Ben-Gurion University, Beer Sheva, Israel Joanna Mamona-Downs, Department of Mathematics, University of Patras, Patras, Greece Stephen Lerman, Department of Education, London South Bank University, London, UK T. Dreyfus (B) Department of Education in Mathematics, Science and Technology, Tel Aviv University, Tel Aviv, Israel e-mail: [email protected] M.N. Fried, T. Dreyfus (eds.), Mathematics & Mathematics Education: Searching for Common Ground, Advances in Mathematics Education, DOI 10.1007/978-94-007-7473-5_5, © Springer Science+Business Media Dordrecht 2014
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that the reader become pointedly aware of questions about points of harmony and discord all along the continuum of mathematics and mathematics education. Many of these questions are taken up and partially answered later in the book in specific contexts.
Expectations of a Mathematician Uri Onn I was asked to sketch what are my expectations, as a mathematician, from researchers in math education. The following is drawn mainly from the teaching part of my work rather than my research.
What I See as a Teacher Most of my students, engineers at all levels who will eventually be part of the technological backbone (high-tech or low-tech) of our country, have a completely damaged perception of mathematical objects. Example 1 In a course on li
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