Brief history of the
“Whole and New New Math” in France

Letter addressed by Michel Delord to Paul Clopton and “2+2=4
Mathematically Correct” in 1997

Difficulties: This
text is a translation of an appropriate text (written in June 1996) which is
partial. I am writing a more general text.I give the same
meaning to two couple of notions: a) “matématiques modernes” and “Whole Math”
and b) the avatars of present (from 1980) French reform and the New New Math in
the USA: I’ll hope there will be no misunderstandings.

According to the
accounts from French teachers who taught in the US in the mid 80’s, the
American average mathematics standard was lower than the French one, but it’s
difficult to use the term “average” for the USA as standards and curriculums
are not centralized state’s obligations as in France.

About the problem of
New Math, I only know one text in English by Rene THOM: “Modern mathematics: an
educational and philosophical error?” American Scientist, 59,6 p 695. But there
are other excellent texts from the 70’s on the subject by the same in French:
I‘ll try to translate, or, better, I’ll scan them if you find a translator in
the USA.

The pupils’ math
standards, which formed the Certificate of Primary School, are going down.
Regarding the field into which we could interfere and which does not certainly
depend on families which are not to blame - those teachers’ arguments against
family’s responsibility and against the previous grade teachers’ skills are
used to justify the servile attitude of the teaching staff in relation to its authority-
this fall is essentially due to several factors:

First, the constant
change of the curriculum which, for instance, forbids generations to help each
other (but increases the market for new books in schools, for home education
products and remedial courses). Is a straight line the shortest distance
between two points or “the set of the affine bijections from R to R”? For your
information, in the 70’s, the “set theory” and the bijection were necessary to
“develop the mind” of the sixth grade pupils (and even pupils of the primary
school) but nowadays they are only partly studied in the scientific 11th and
12th grades.

This only fact shows
the inextricable situation of the French Education State Department: they
simultaneously want to suppress important parts of the curriculum and show a
rising of standard of education. In the same way, why is the rule of three
forbidden in the 70’s and why are the proportional tables imposed to deal with
the same problems? Here I stop giving examples because I am not attending a
thesis. I do not neglect the contribution of modern mathematics but, according
to me, they seem to allow solving problem, which are to be found neither in
primary school nor in junior high school. In one sense, acting with a good
intention against the previous formalism, the central aim of modern mathematics
introduction in school was hyper-rationalist philosophy: nobody can learn 2+2=4
without understanding group theory and calculus in all bases; but “ratio” is
against the instinct which is the basis of pedagogic intervention. We can find
the same rationalistic approach in the New New Math where a pupil, in one
sense, must find again by himself all the knowledge of the past.

Secondly, one of the
main factors is the very content of those curriculums. We have gone from the
period of “Whole Math” to the one of the 80’s reform.

Whole Math (70’s)

Roughly speaking, the
contents of the “mathématiques modernes” period (1970 -80), with the formal and
the structure put forward, was:

- in arithmetic, the non-necessity
to learn to calculate ( it was before the pocket calculators). It was the basis
era when we learnt that 3+2 could be 10 or 11 before knowing how to give change
and without knowing the tables of operations by heart. From which mockery about
arithmetic old fashion problems began: those problems have derisively been
called “leaking tap problems” whereas they are essential because they allow
learning the complexity of the basic mathematics tools in a simplified
situation. . The latter is introduced as artificial ( and not concrete) without
noticing that the real situation presents “physics’ rubbings” which are not
controllable in a training situation ( try to calculate the volume of my
“concrete” shoe!!). This non-necessity quickly transformed itself in a fall of
calculus skills....

- in geometry : under
the pretext that a straight line could not be straight ( also true for other
basic figures), the primary school has a bad knowledge of basic figures.. Also
under the pretext of the discovery of the invariant elements in the geometric
group theory, the teaching of what was a basis of learning of proof is
eliminated and forbidden : I mean the “ 3 cas d’égalités des triangles” - in
English, I think, SSS, SAS and ASA congruence postulates - which indeed is
unperfected in the absolute but largely adequate and very efficient for a
junior high School pupil. So this teaching is eliminated to be replaced by the
use of transformations (symmetry, rotation) which is per se more difficult to
use in many situations and that an 8th grade pupil is not able to control. They
had better made friezes that teach as much for the invariant elements..

The reform of the
reform ( 1980 up to ?)