Commentary on Theories of Mathematics Education

Surveying Theories and Philosophies of Mathematics Education 21
in the 1930s and aimed to write a thorough (formalized) and unified account of all
mathematics, which could be used by mathematicians in the future (see Bourbaki
1970). The highly formal nature of mathematics textbooks following the Boubarki √
tradition is evident in examples such as the “bourbakized” definition of 2 2 as the
supremum of a suitable set of rational powers of 2 (Sriraman and Strzelecki 2004).
It is commonly agreed that New Math was one of outcomes of the Bourbakists,
who systematized common threads from diverse mathematical domains into
a coherent whole and influenced policy makers in the 1950’s and early 1960’s to
attempt an analogous logical math program for schools (Pitman 1989). The mathematical
community became interested in mathematics education stimulated by both
their war-time experiences as well the new importance that mathematics, science,
and technology had achieved in the public eye. This resulted in mathematicians and
experts from other fields designing curriculums for schools (e.g School Mathematics
Study Group or SMSG). One must understand that the intentions of mathematicians
like Max Beberman and Edward Begle was to change the mindless rigidity
of traditional mathematics. They did so by emphasizing the whys and the deeper
structures of mathematics rather than the hows but it in hindsight with all the new
findings on the difficulties of changing teacher beliefs it seems futile to impose a
top-down approach to the implementation of the New Math approach with teacher
“upgrades” via summer courses on university campuses. The global impact of New
Math as a result of the Royaumont Seminar is not one that is well documented
in the literature, particularly the huge influence it had on changes in mathematics
content taught in schools (Dieudonné 1961; Moon 1986). Given no mention of
this seminar in extant mathematics education histories constructed (Bishop 1992;
Kilpatrick 1992) we deem it important to fill this gap in the literature.
The prominent French mathematician and Bourbakist, Jean Dieudonné played
a significant role in initiating these changes. The Royaumont Seminar was held in
1959 in France (OEEC 1961), organized chiefly by the Organization for European
Economic Co-operation and attended by 18 nations (including Germany, France and
Italy), catalyzed New Math into a more global “Western” phenomenon. Dieudonné,
who chaired one of the three sections of this seminar, made his famous declaration
that “Euclid must go” (see Dieudonné 1961). The subsequent report released
in 1961 led to the systematic disappearance of Euclidean geometry from the curricula
of most participating countries. In fact the original SMSG materials included
Euclidean geometry. Thus, the influence of prominent Bourbakists on New Math in
Europe was instrumental in changing the face of mathematics education completely.
In spite of the history presented in the previous section, not every prominent
French mathematician was enamored by New Math’s promise of modernizing mathematics.
In his address to the 2nd International Congress of Mathematics Education,
René Thom (1923–2002) was unsparing in his criticism:
Mathematics having progressed, so we are told, considerably since Cauchy, it is strange
that in many countries the syllabuses have not done likewise. In particular, it is argued that
the introduction into teaching of the great mathematical ‘structures’ will in a natural way
simplify this teaching, for by doing so, one offers the universal schemata which govern
mathematical thought. One will observe that neither of these two objectives is, to be precise
‘modern’ nor even recent. The anxiety about teaching mathematics in a heuristic or