Mathematics at the Center of Distinct Fields: A Response to Michael and Ted
This response to Ted and Michael points out that we are unified in considering mathematics to be central in the work of mathematicians, mathematics educators, and mathematics education researchers. However, there are distinctions between the fields of pur
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Mathematics at the Center of Distinct Fields: A Response to Michael and Ted Norma Presmeg
Abstract This response to Ted and Michael points out that we are unified in considering mathematics to be central in the work of mathematicians, mathematics educators, and mathematics education researchers. However, there are distinctions between the fields of pure mathematics research, the teaching and learning of mathematics, and research in mathematics education, and unless these differences are honored it is possible for researchers to talk past one another. The case of Swedish mathematics education research is examined to exemplify the distinctions. Another distinction is that between “training” and “education”. To further characterize mathematics education research, submission of manuscripts to Educational Studies in Mathematics is explored. Values and aesthetics in various relevant fields are touched upon. Finally, an example is given of the mutual enhancement that exists when mathematicians and mathematics education researchers work together in university mathematics departments. Keywords Distinct fields · Pure mathematics research · Mathematics education · Mathematics education research · Sweden · Training · Research manuscript submissions · Aesthetics · Mutual enhancement
What Are We Talking About? I want to say at the outset that Ted, Michael and I have much in common in our sentiments about mathematics. There is no doubt in my mind that mathematics is central to the endeavors of mathematicians, mathematics educators, and mathematics education researchers alike. However, it appears at times as if we are talking past each other, because there are distinct fields in question. Thus I have constructed a diagram to portray the distinctness of mathematics itself, mathematics education, and research in pure mathematics and in mathematics education respectively. Each of the subsets in the ellipses Professor Emerita N. Presmeg (B) Illinois State University Maryville, TN, USA 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_4, © Springer Science+Business Media Dordrecht 2014
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may be regarded as the topic of the wider set in which it rests. Mathematics, mathematics education, and mathematics education research may be conceptualized as being nested, like Russian dolls, with mathematics at the center, nested in mathematics education, which is nested in turn in mathematics education research. The topic addressed in mathematics research is mathematics; the topic of mathematics education is also mathematics; and the topic of mathematics education research in not mathematics per se, but mathematics education.
On the one hand, mathematicians are engaged in research in various fields of mathematics, and in mathematics education insofar as they teach mathematics. On the other hand, mathematics education researchers are not engaged primarily with research in pure mathematics, e
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