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Dialogue on mathematics education: two points of view on the state of the art

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Abstract

On many fronts, the field of mathematics education does not speak with a single voice. There appears to be no firm consensus regarding the scientific character of mathematics education, the research methodologies it deems legitimate, the kinds of questions it addresses, the appropriate preparation for its practitioners, and its relationship with other disciplines, including, ironically, mathematics itself. Our field seems to be going through a new phase of self-definition, a crisis from which we shall have to decide who we are and what direction we are going. The authors of the present paper themselves tend towards different positions on these questions. The paper, then, takes the form of a letter in which one of us raises issues about the current state of mathematics education and the other responds. We see this as an attempt to initiate a dialogue on our field, which we consider urgently needed.

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Notes

  1. Considerably earlier origins of research in mathematics education in European traditions are discussed in (Sriraman, B., & Törner, G. 2008).

  2. See pp. 17–18 of (Kilpatrick, J. 1992).

  3. See, for example, Hagstrom, (1974); Merton (1957) and Fisher (1973).

  4. Especially, p. 192 of (Polanyi, M. 1964).

  5. Francis Bacon, Novum Organum, Book I, Sect. 59.

  6. I do not think this concern is yours only. If you recall, PME30 in 2006 was given the title: “Mathematics in the Center.” Such an obvious thing would be unnecessary to say if it were not that mathematics had moved away from the center, or even off to the periphery.

  7. Nathalie Sinclair has argued (e.g. in (Sinclair, N. 2004) that we should not assume esthetic experience belongs exclusively to professional mathematicians, but that all students have a kind of esthetic faculty allowing this kind of experience. She might be right about that; however, I would argue that the depth of one’s mathematical esthetic experience reflects the depth of one’s mathematical understanding.

  8. “Das Geschlecht ist schwer; ja. Aber es ist Schweres, was uns aufgetragen wurde, fast alles Ernste ist schwer, und alles ist ernst” (Briefe an einen jungen Dichter, #4).

  9. “Having changed what needed to be changed.”

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Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University of the Negev, Beersheba, Israel

    Theodore Eisenberg

  2. Program for Science and Technology Education, Ben-Gurion University of the Negev, Beersheba, Israel

    Michael N. Fried

Authors
  1. Theodore Eisenberg
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  2. Michael N. Fried
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Correspondence to Michael N. Fried.

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Eisenberg, T., Fried, M.N. Dialogue on mathematics education: two points of view on the state of the art. ZDM Mathematics Education 41, 143–149 (2009). https://doi.org/10.1007/s11858-008-0112-1

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