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 ?)

 Instead of adjusting one’s sights by explaining the errors that had been made - unthinkable- , the education authority which wrote the previous curriculum, takes half-measures 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.


Michel Delord

 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.