Mathematics, mathematicians, and mathematics education. (English) Zbl 1208.01017
From the text: I am one of a growing number of research mathematicians who are substantially engaged with school mathematics education. Such outreach has a long and honorable tradition. In this lecture, I illustrate some of the ways that I think this can be helpful, and even essential. …
Mathematics education is not mathematics. It is a domain of professional work that makes fundamental use of highly specialized kinds of mathematical knowledge, and in that sense it can, I suggest, be usefully viewed as a kind of applied mathematics. I will argue that, just as in other domains of “applied mathematics”, the first task of the mathematician who wishes to contribute in this area is to understand sensitively the domain of application, the nature of its mathematical problems, and the forms of mathematical knowledge that are useful and usable in this domain.
The lecture has three parts:
I. A brief look at the work of two major historical figures.
II. Some observations on the contemporary scene.
III. A sample immersion into some of the work in which I have personally been engaged.
Conclusion: Let me conclude here by summing up my argument about productive interactions among mathematics, mathematicians, and mathematics education.
– The mathematics profession has a long and honorable tradition of involvement in mathematics education.
– Eminent mathematicians from around the world, and throughout history, have exemplified this tradition.
– Important contemporary mathematicians are continuing, and expanding, this tradition.
– This work can be productively pursued in the spirit of “applied mathematics” by first deeply understanding the domain of application.
– As practitioners of the discipline, research mathematicians can bring valuable mathematical knowledge, perspectives, and resources to the work of mathematics education.
– This is a tradition worthy of continued development and support.
Mathematics education is not mathematics. It is a domain of professional work that makes fundamental use of highly specialized kinds of mathematical knowledge, and in that sense it can, I suggest, be usefully viewed as a kind of applied mathematics. I will argue that, just as in other domains of “applied mathematics”, the first task of the mathematician who wishes to contribute in this area is to understand sensitively the domain of application, the nature of its mathematical problems, and the forms of mathematical knowledge that are useful and usable in this domain.
The lecture has three parts:
I. A brief look at the work of two major historical figures.
II. Some observations on the contemporary scene.
III. A sample immersion into some of the work in which I have personally been engaged.
Conclusion: Let me conclude here by summing up my argument about productive interactions among mathematics, mathematicians, and mathematics education.
– The mathematics profession has a long and honorable tradition of involvement in mathematics education.
– Eminent mathematicians from around the world, and throughout history, have exemplified this tradition.
– Important contemporary mathematicians are continuing, and expanding, this tradition.
– This work can be productively pursued in the spirit of “applied mathematics” by first deeply understanding the domain of application.
– As practitioners of the discipline, research mathematicians can bring valuable mathematical knowledge, perspectives, and resources to the work of mathematics education.
– This is a tradition worthy of continued development and support.
MSC:
| 01A65 | Development of contemporary mathematics |
| 01A70 | Biographies, obituaries, personalia, bibliographies |
| 97B10 | Mathematics educational research and planning |
| 97B20 | Educational policy for general education |
Online Encyclopedia of Integer Sequences:
Positive integers congruent to 2 (mod 4): a(n) = 4*n+2, for n >= 0.References:
| [1] | Ball, D. L. and Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In B. Davis and E. Simmt , Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 3-14). Edmonton, AB: CMESG/GCEDM. |
| [2] | Hill, H., Rowan, B. and Ball, D. (in press). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal. |
| [3] | Hill, H. C., Schilling, S. and Ball, D. (2004). Developing measures of teachers’ mathematical knowledge for teaching. Elementary School Journal. |
| [4] | Felix Klein, Elementary mathematics from an advanced standpoint. Arithmetic-algebra-analysis, Dover Publications, Inc., New York, N. Y., 1953. Translated by E. R. Hedrick and C. A. Noble. · Zbl 0051.00605 |
| [5] | David E. Rowe, A forgotten chapter in the history of Felix Klein’s Erlanger Programm, Historia Math. 10 (1983), no. 4, 448 – 454. · Zbl 0526.01019 · doi:10.1016/0315-0860(83)90006-X |
| [6] | David E. Rowe, Felix Klein’s ”Erlanger Antrittsrede”, Historia Math. 12 (1985), no. 2, 123 – 141 (English, with French and German summaries). A transcription in German with English translation and commentary. · Zbl 0574.01014 · doi:10.1016/0315-0860(85)90003-5 |
| [7] | Howson, A. G. (2004). Klein and Freudenthal: Two rocks on which to build. Regular Lecture, ICME 10, Copenhagen, July 2004. |
| [8] | National Commission of Excellence in Education (1983). A Nation at Risk: The Imperative for Educational Reform. Washington, DC: U.S. Government Printing Office. |
| [9] | National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics (1989). Professional Standards for Teaching Mathematics (1991). Assessment Standards for School Mathematics (1995). Reston, Virginia. |
| [10] | Conference Board of the Mathematical Sciences (2001). The Mathematical Education of Teachers. Mathematical Association of America, in cooperation with the American Mathematical Society, Providence, Rhode Island. · Zbl 0985.00005 |
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