
New New MATH In FRANCE
Without Comment : Atext Isent to Paul CloptonMAthematically Correct in 1997: Brief history of the “Whole and New New Math” in France 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
hyperrationalist 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 nonnecessity 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 nonnecessity 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 ?)
Instead
of adjusting one’s sights by explaining the errors that had been made 
unthinkable , the education authority which wrote the previous
curriculum, takes halfmeasures in order to be adequate to the new low skill and so they reinforce a new fall in skills. In arithmetic, the possibility to use the pocket calculator helps to justify the drop in math
standards. and last year, during an educational conference, an expert
in education explained that asking a 6th grade pupil to divide 4374 by
532 or 2.37 by 0.564 , was a “virtuous exercise” which besides was
forbidden. The present 6th grade curriculum requires the maximum skills
to “ calculate the quotient and the remainder of a whole number by a
two digits’ whole number...... In simple cases ??? , divide a decimal
number by a whole number.... ” . That’s all : without any protest from
any teachers unions, parents association or press article : in this
case, silence is as demagogic as criminal. We could expect that the new
7th grade curriculum enable the pupils to divide 5.3 by 4.12: not at
all and silence on this subject. The required standard is going down
but Baudelot (a publicist) and the national department of statistics
for education ( DEP : “Direction de l’Evaluation et de la Perspective”)
will show , in spite of all, that the standard is going up and those
who deny it are chilly and inflexible reactionaries who are afraid of
change. The fall in math
standards would no more allow to teach arithmetic ( prime numbers) in
the 7th grade ( it was a part of curriculum for over a century). The
educrat’s solution was simple : they suppressed it in the whole
secondary school. In geometry, I will not come back to triangles
congruence postulates but for instance, calculating the area of a
circle is now part of the 7th grade curriculum when it was previously
in the 5th grade . I think that , removing any reference to this item
in comparison with older statistics series, the DEP will, one more
time, show that the standard is going up. Who will stop the crazy
machine? Generally speaking, the new
reform, which is more demagogic, does not forbid expressly anymore the
rule of three nor the triangles congruent postulates just because a
great deal of the new
teachers have not been taught and trained during their own Junior
School cursus ( only the teachers who are 35/40 and more know them and,
after 25 years of various reforms, it is not possible to decide
individually to teach them ) but the ban remains on division because
precisely all the teachers still know how to do a division.
An anecdote for the end
Yesterday,
December 3rd 1997, I took part in a pedagogic conference and, hiding
the cover of a booklet, I read the following text : “ I consider that
making mathematics is not to show calculations skills (algebraic or
arithmetic), even if, up to the last days, those know how were
indispensable for mathematics arguments. As calculus tools were not
existing, we must use mental and hand calculus ( with lost time,
origins of errors, forgetting of the aim of the problem) .....During 20
seculars, it’s that manner which had prevailed (it is normal that it
left indelible aftermath)..... I have no doubts about the fact that
“mechanization” of calculus will become an habit”. And I asked : “Who
wrote that?”. The answer of the person in charge of the meeting was
interesting . He knew that I tried to trap him and said : “I know that
you try to trap us but, perhaps an Education Secretary ...” . The
essential is that a pedagogic manager is not spontaneously able to
distinguish a pedagogic text and an advertisement for the Casio pocket
calculators. It’s funnier in France
than in the USA : teachers  and in particular this manager  are
politically left and their credo is to protect the state school 
“L’Ecole Laïque” against capitalism, market and economic liberalism.
This shows the standard level of the pedagogic speech after 25 years of
Whole and New New math.
Note on TIMMS
Mr.
Roger Fauroux, chairman of Saint Gobain, says in the October 1997 issue
of “Capital”: “ Recently a mathematics test had shown that France
was 13th, behind Singapore and the South Korea. The Senior Civil
Servants of the DEP are not speaking about this result: in 1994, after
they had accepted to take part in an OCDE international test, they
silently left after having seen the first results”. And if you look at
the TIMMS results , you can see that there is no French results for the
4th grade test. Mr. Fauroux in the “ Rapport Fauroux ” proposed last
year a reform which put forward the basic skills : for many reasons,
saying that it is insufficient  the school needs first “democracy” or
“culture”....  all the French educrats and experts in pedagogy avoid
the subject : it’s important to notice that in France
all those experts are paid and employed by French Department of
Education and that Mr. Fauroux in his report asks for an independent
and international control of the pupils skills.  Michel DELORD
This commentary is the opinion of the author and does not reflect the views of the columnist, Denver Rocky Mountain News or RockyMountainNews.com.
