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Notes
- 1.
Recent work by Ruhama Even (2011), however, has shown that in their own view, teachers see advanced mathematical work helpful on three fronts: that it is a knowledge resource; that it improves their understanding of mathematics and what it is; that it provides a model for what learning mathematics feels like.
- 2.
I am referring to mathematicians and mathematics teachers who, lacking the “critical” outlook, devote themselves to teaching mathematics as if it were a neutral subject. For proponents of critical theory, they, unwittingly, support the power structure rather than reveal it. Thus in his well-known article “Ideology and ideological state apparatuses” (Althusser 1971), Louis Althusser writes: “I ask the pardon of those teachers who, in dreadful conditions, attempt to turn the few weapons they can find in the history and learning they ‘teach’ against the ideology, the system and the practices in which they are trapped. They are a kind of hero. But they are rare and how many (the majority) do not even begin to suspect the ‘work’ the system (which is bigger than they are and crushes them) forces them to do, or worse, put all their heart and ingenuity into performing it with the most advanced awareness (the famous new methods!). So little do they suspect it that their own devotion contributes to the maintenance and nourishment of this ideological representation of the School…” (p. 157).
- 3.
One good example of collaboration that does exist is the Klein Project developed and implemented by ICMI. The project was commissioned in 2008 by the International Mathematical Union (IMU) and the International Commission for Mathematical Instruction (ICMI). Its guiding idea was to revisit Felix Klein’s book “Elementary Mathematics from an Advanced Standpoint” and produce a book for secondary teachers communicating the breadth and vitality of mathematics as research discipline while connecting it to the secondary school curriculum. An international design team for the project was appointed led by two ICMI presidents: Michèle Artigue and Bill Barton and a book is under preparation. In the meantime, Klein Project has produced a set of “vignettes” for teachers and students. The rationale for this phase of the project and examples of the vignettes already produced can be found at the website: http://blog.kleinproject.org/.
- 4.
This is the lament of a recent opinion piece in the New York Times by political scientists (note the name!) Kevin A. Clarke and David M. Primo ((2012, March 30). Overcoming ‘Physics Envy’. Available at http://www.nytimes.com/2012/04/01/opinion/sunday/the-social-sciences-physics-envy.html). Interestingly enough, this phrase, so commonly used regarding the social sciences, was actually coined by Joel E. Cohen with reference to biology. Cohen wrote a book review of a book on dynamical systems in biology (Cohen, J.E. (1971, May 14). Mathematics as Metaphor. Science 172, 674–675), which begins, “Everyone likes to discover general and unifying principles in biology” (p. 674) and then goes on to say, creating the famous phrase, “Physics-envy is the curse of biology” (p. 675)! So, even within the natural sciences, one should be careful to recognize that there may not be uniformity in appropriateness of methods and approaches.
- 5.
The English translation contained in the collection edited by Gertrud Lenzer was produced in Comte’s day and, as Lenzer notes, was “enthusiastically approved” by Comte himself. The original French text can be found in Comte (1975b, leçon 46, p. 66).
- 6.
Comte claimed that education was, in his day, motivated by thinking of the theological, metaphysical and literary types. One of his hopes in laying out the positive philosophy was that education would turn in the positive direction: in effect, Comte was, in effect, pressing for education based more on the sciences and mathematics than on the traditional literary curriculum. This theme, now ubiquitous, was taken up often in the 19th century, for example, by the great biologist Thomas Huxley who suggested that liberal education should be science education.
- 7.
Comte’s sense that progress is impeded by less-than-scientific research can be felt the discussion of mathematics education and “Scientifically Based Research” recorded at the US Department of Education Website (US Department of Education 2002b).
- 8.
This point is also made in Weber’s well-known address, “Science as Vocation” (English translation in the collection Gerth and Mills (1958, pp. 129–156) where he also, as in this place, refers to what university professors in science—specifically social science—can see as part of their vocation and what they cannot—and what they cannot includes pronouncements of value among their students.
- 9.
Weber’s famous 1905 work Die protestantische Ethik und der Geist des Kapitalismus (The Protestant Ethic and the Spirit of Capitalism) is a case in point.
- 10.
In his chapter on the fact-value distinction in Natural Right and History, Leo Strauss (1953) makes a point along these lines.
- 11.
The papers by Eisenberg and Fried and Presmeg were joined by a third written by David Pimm (Pimm 2009), who also discussed the relationships and provinces of the different disciplines contributing to mathematics education.
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Fried, M.N. (2014). Mathematics & Mathematics Education: Searching for Common Ground. In: Fried, M., Dreyfus, T. (eds) Mathematics & Mathematics Education: Searching for Common Ground. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7473-5_1
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