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Mathematics has many applications in industry. Here I would like to focus on a special part of these industries and the role of mathematics in its development.

Question: Consider the countries which invested heavily in mathematics for military purposes. How did they format their math education programs in light of their warlike or expansionist nature? Is there information on particular methods or books they have used to effectively increase the country's mathematics education and knowledge? Was their focus exclusively on applied mathematics or was pure mathematics as important, possibly having a higher place?

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  • $\begingroup$ What is the context of a question like this with respect to math ed in particular? In fact, the failure of new math and the successful math educated countries currently (the highly ranked ones that is) might show that math ed might be inversely related to warlike tendencies. $\endgroup$
    – Chris C
    Jul 31, 2014 at 20:14
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    $\begingroup$ What? Why would this question get downvotes and be voted to close? Do you really feel like closing the only questions we get is a good policy? This question is fine, and people are misreading it. It asks "Did militaristic countries take any special actions to format their math education programs in light of their warlike or expansionist nature?" $\endgroup$ Aug 1, 2014 at 19:26
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    $\begingroup$ @chriscunningham: It also asks this question: " Consider a country which has a plan to expand its military power, which parts of "pure" mathematics may help in this direction?" Which is very different from what you pointed to. And, rather alarming, at least to me. ("Tell me parts of math that are useful in war"?!?!) $\endgroup$ Aug 1, 2014 at 20:46
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    $\begingroup$ Georg, I have opened a meta thread about this question here. There's a proposed edit there and your input about it is valuable and desired! $\endgroup$ Aug 3, 2014 at 0:24
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    $\begingroup$ @ChrisCunningham: though "maths education" is explicitely written, it feels to me that the question, as currently written, also/mainly addresses mathematical research. IMHO, this question should be moved to math.SE for a more complete answer. $\endgroup$
    – Taladris
    Aug 5, 2014 at 15:43

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I can see several ways of addressing the question, although I'm afraid that a comprehensive answer would require a number of chapters and quite a bit of scholarship. I also think this question's premises raise interesting issues on their own: are arguments underlying mathematics education programs ever so explicitly about militarism, or are they always made on a basis of diverse views of utility and value of mathematics knowledge? How easy or difficult is it to tie national trends and concerns to the very specific materials (books) mentioned in the question, especially considering how some nations (notably, the U.S.) have historically and intentionally decoupled local education from national policy? Is mathematics education, the bulk of which exists in K-12 classrooms (where policy has most of its focus), thought of as a dichotomy of applied vs. pure mathematics?

For my part, I will touch on one small aspect of the question: a cycle in the justification for mathematics education in the school curricula of the U.S.A. that sometimes involves concerns of war. The preparation for or looming of war has been a part of education policy in the USA. Some in mathematics education research and policy research have noted that there is a cycle of recurring themes in the choices made to determine the place of mathematics education within the American school curriculum (Garrett & Davis Jr, 2003). War concerns are one kind of concern that has acted as a type of critical event in this set of themes.

Drawing directly from, but paraphrasing, Garrett and Davis (2003), the themes fit together like this:

  1. Math in school curriculum is seen to come under attack (Why do we need so much math!? and/or Isn't this math useless for many of these students? -- Shouldn't most of them just learn arithmetic?)
  2. People (university professors and others outside of schools) come to the defense of mathematics in the K-12 curriculum.
  3. Everyone notices some looming threat, or some threatening event occurs (such as war). Arguments turn to using this threat to justify the role of mathematics.
  4. For a time, people accept the role of mathematics in the curriculum.

(see pp. 493-494)

As part of the cyclical nature of this set of themes, Garrett and Davis noted that mathematicians and math educators have failed to make a deep argument for the role of mathematics in the curriculum that is lasting. Consequently, we will all see the same arguments again in the future when memory of the critical event fades. So these events have acted as a ready justification for mathematics in the curriculum, but the strength of their emotional impact has obviated the need for a deeper logical argument.

A number of the chapters in the Stanic and Kilpatric (2003) volumes deal with the different motivations behind mathematics education policy and related reforms, including intervention from notable military voices who were concerned about mathematics.

The problem described by Garrett and Davis can be thought of as not only a failure to give a deeper argument for mathematics education in the curriculum, but a failure to confront the fact that these curricular choices are value-laden, and that education reform is values driven (Stanic & Kilpatrick, 1992).

Speaking to the question of what mathematics to teach (e.g. where applied vs. pure might be one dimension considered) and whether or not it is driven by war, Stanic and Kilpatrick (1992) wrote that we are divided by some of the same faith (and arrogance) that has led us to promote mathematics in the first place. Their paper concluded:

The mathematics education community has traditionally acted from and defended a fundamental faith in the importance of mathematics for everyone. According to this faith, more people should study more mathematics in school, for their own sakes as well as the sake of our society. Ironically, the same faith that established and sustained the community gets in the way of seeing and dealing with the important differences that divide it and that hamper curriculum reform. Competing visions – that is, competing answers to the questions of what we should teach, why we should teach one thing rather than another, and who should have access to what knowledge – can be healthy, but only if the are recognized and dealt with. It is naïve, moreover, to assume that wide-ranging reform in school mathematics will result from any effort that focuses only on schools and is not somehow linked to reform of the wider society. (p. 414)

Often we seem so focused on these kinds of differences within the broader field of those who promote mathematics education, we lose the ability to get traction with reform until a looming national concern, such as war or the surprising advancement of a feared enemy (e.g. the U.S reaction to the launch of Sputnik) creates an impetus to stray from "basics" into more research-based approaches (e.g. the boom in exploratory approaches to mathematics education in the U.S. collectively referred to as "New Math").

As an aside, I think that war and other impactful events that have reforms associated them garner a disproportionate amount of attention, distorting our view of history. For instance, our "back to basics" movement of the 1970's was a reaction to the (not entirely justified) perceptions of New Math-era reforms, especially based on misunderstandings of their effects and scope. However, during the "back to basics" era, researchers remarked on impoverished middle school curriculum, an over-focus on processes, and a public's perception of mathematics as limited to arithmetic (Fey & Graeber, 2003).

As a second aside, we might ask whether actual war or threat of war are even needed when war metaphor can be used to generate a sense of urgency. This linguistic theme in calls for reform is notably present in the oft-cited report A Nation at Risk: The Imperative for Educational Reform (National Commission on Excellence in Education, 1983). As you have undoubtedly heard before, they summed up the decade of "back to basics" mathematics reforms with this call to action:

If an unfriendly foreign power had attempted to impose on America the mediocre educational performance that exists today, we might well have viewed it as an act of war. As it stands, we have allowed this to happen to ourselves. We have even squandered the gains in student achievement made in the wake of the Sputnik challenge. Moreover, we have dismantled essential support systems which helped make those gains possible. We have, in effect, been committing an act of unthinking, unilateral educational disarmament. (p. 6)

We might ask whether it is really productive (i.e. aligned with our goals and values) to create, or at least attempt to create a sort of hysterical urgency to drive education reform. Or, at least, what problems it creates for us in the longer term if we agree that there is something fundamentally important about the understanding to be gained via school mathematics apart from its utility in defense and offense.


Cited:

Fey, J. T., & Graeber, A. O. (2003). From the new math to the Agenda for Action. In G. Stanic & J. Kilpatrick, A history of school mathematics (Vol. 1, pp. 521–558).

Garrett, A. W., & Davis Jr, O. (2003). A time of uncertainty and change: School mathematics from World War II until the new math. In G. M. A. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (Vol. 1, pp. 493–520). Reston, VA: National Council of Teachers of Mathematics.

National Commission on Excellence in Education. (1983). A nation at risk: The imperative for educational reform. Washington, D.C.: U.S. Government Printing Office.

Stanic, G., & Kilpatrick, J. (1992). Mathematics curriculum reform in the United States: A historical perspective. International Journal of Educational Research, 17(5), 407–417.

Stanic, G. M. A., & Kilpatrick, J. (Eds.). (2003). A history of school mathematics. National Council of Teachers of Mathematics.

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