Abstract
The implementation of modern mathematics in Morocco occurred in three main phases, from the early 1960s through the mid-1970s. In the first phase, the implementation mainly concerned the introduction of new vocabulary and symbols of set theory and algebraic structures into upper secondary education. In the second phase, which began in 1968, the latter notions were introduced in lower secondary education and were reinforced in upper secondary education by vector, affine, and analytical geometries. In the third phase, which began in 1971, there was a strengthening of modern mathematics by a restructuring of the content of the programs and by removing classical concepts of geometry from them. But, in 1975, the teaching of mathematics—which elicited a negative reaction from users of mathematics—was the subject of a national conference whose recommendations advocated changes in the mathematics programs taught in secondary schools so that they would be beneficial to the majority of students. Then, in 1978, the Minister of Education created a commission to discuss mathematics programs and made the necessary changes. Modern mathematics was abandoned gradually from 1983 to 1989. In this chapter, we describe the different stages and the peculiarities of implementation of modern mathematics in Morocco.
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Notes
- 1.
We refer hereinafter to this document by MEN, an acronym for Ministère de l’Éducation Nationale [Ministry of National Education]. We use the second edition of 1973. The first edition was published in 1969; there were other editions in 1976 and 1979. There are no notable differences between these editions.
- 2.
In fact, according to some oral testimonies, modern mathematics was indeed introduced into the second cycle well before 1962. The latter was said to be the year of the official introduction of modern mathematics into the curricula.
- 3.
This exam is the highest level competitive exam for teachers in France.
- 4.
See http://rhe.ish-lyon.cnrs.fr/?q=agregsecondaire_laureats & nom= & annee_op =%3 D & annee%5Bvalue%5D= & annee%5 Bmin%5D= & annee%5Bmax%5D= & periode=4 & concours=13 & items_per_page=100 & page=12 (retrieved February 15, 2021).
- 5.
According to some sources, Nuss also gave courses at the Faculty of Science of the University of Rabat. More precisely, this course concerned: Mathematics course of Propaedeutics General Mathematics and Physics MGP (M. Akkar, personal communication). He was the one who developed the first Moroccan mathematics programs for the second cycle of secondary education (El Mossadeq 2007). Nuss was credited with the first Moroccan textbooks containing elements of modern mathematics (Moatassime 1978). It seems, however, that these books, which were not marketed, were intended primarily for teachers (M. Akkar, personal communication). When he returned to France, he wrote a textbook for the third year of secondary education in the Queysanne collection (Nuss 1968). Note that we have not yet managed to find copies of Moroccan textbooks by Nuss.
- 6.
Initially, Yves Peureux was a technical college teacher seconded to Morocco in 1950 (Bulletin Officiel de la République Française [Official Bulletin of the French Republic], September 1951, p. 9575). Probably when he returned to France, Yves Peureux was appointed inspector of mathematics for technical education in 1979, at the Academy of Dijon (Bottin administratif et documentaire [Administrative and documentary directory], 1979, p. 436).
- 7.
At the time, there were two types of secondary education in Morocco. A short one that ended at the end of first cycle of secondary education and led to the certificate of secondary education, and a long one that led to the baccalaureate.
- 8.
Primary education was influenced by the wave of modern mathematics in an indirect way during the 1970s. This influence was manifested by the introduction of set language: Teaching numbers from a collection of objects and emphasizing educational intent on understanding concepts and corresponding properties instead of focusing on numeracy skills (Lakramti 2001, p. 3).
- 9.
The 1962 reform was carried out all at once, i.e., the programs of the three levels were changed in the same year. But for the other reforms, content was changed gradually, from year to year (Aboutir 1994, p. 12).
- 10.
During the period covered by this study (1962–1989), secondary education (first and second cycles) was generally made up of seven levels (four in the first cycle and three in the second cycle). Note, however, that the names given to these levels were not the same throughout this period. Between 1963 and 1972, these were for the 1st cycle (observation class, 1st year, 2nd year, and 3rd year) and for the second cycle (4th year, 5th year, and 6th year). Between 1973 and 1989, the names of the levels were: 1st year, 2nd year, 3rd year, and 4th year (for the first cycle) and 5th year, 6th year, and 7th year (for the second cycle). In this chapter we refer to these levels by the latter names. Moreover, students who entered to the second cycle were directed to one of the sections: Science, letters, or techniques. Each of these sections was divided, in the last two years of the lycée, into subsections. For example, for the science section, the subsections were as follows: Mathematics, mathematics and technics, experimental sciences, and economics.
- 11.
The other three parts are devoted respectively to Geometry of space; equations and inequalities; and functions, numerical functions, and point transformations.
- 12.
This knowledge is spread over three chapters. “General notions” are dealt with in Chapter 1 (see below); “real numbers” and “vectors” are presented in Chapters 2 and 3, respectively.
- 13.
For example, the second-year textbook gave the following definitions for a half-line and for a segment:
-
(1)
Let D be a straight line and A a point of D. A determines two half-lines d1 and d2 of common origin A such that d1⊂D and d2⊂D; d1∩d2 = {A} and d1∪d2 = D.
-
(2)
We call a line segment, with ends A, B, noted [A, B], the non-empty intersection of the two half-lines d1 (of origin A) and d2 of origin B); d1∩d2 = [A, B] (Aiouch et al. 1969, pp. 227, 229).
-
(1)
- 14.
One can read in the instructions for the third year in a passage entitled “commentary on geometry”: A parallelogram whose vertices are A, B, C, D is the quadruplet (A, B, C, D) (MEN 1973, p. 60).
- 15.
This general introduction is followed by the following sections: II. First-degree equations and systems of equations; III. First-degree inequalities and systems of inequalities.
- 16.
The instructions appeared with the 1968 programs.
- 17.
The document adds in parentheses: “This last point should retain all the attention of the teacher.” It is probably to justify the importance of this theme that an exercise textbook (with solutions) was compiled on the internal laws of composition. This textbook, consisting of two booklets, one of which contains the statements of the exercises and the other is devoted to solutions and indications, contains more than 500 exercises spread over 8 chapters (I to VIII). The distribution is as follows: I. Internal composition laws (133 exercises); II. Associativity (78 exercises); III. Neutral element (42 exercises); VI. Symmetrical elements (66 exercises); V. Regular elements (29 exercises); VI. Commutativity (59 exercises); VII. Distributivity (19 exercises); VIII. Group concept (75 exercises) (El Mossadeq and Peureux 1971, see Figure 23.2).
- 18.
In fact, this quote is made up of two passages appearing in different pages of Choquet’s book (1964). The first passage “It is well established ... in textbooks” appears on page 10 (in the introduction). The second passage “some teachers ... with metrics” appears on page 153 (in Appendix 1).
- 19.
- 20.
The names of the secondary levels are not the same in France and in Morocco. In France, the secondary levels are designed as follows: 6th, 5th, 4th, 3rd, 2nd, 1st, and terminale, but in Morocco these levels are named as follows: 1st, 2nd, 3rd, 4th, 5th, 6th, and 7th.
- 21.
For example, the congress of African mathematicians in Rabat in 1976 made a recommendation that “we do not accept programs used in foreign countries, but we must design programs suitable for our development problems,” which in a way contradicted the recommendation made in Cairo in 1969, which advocated the introduction of modern mathematics as in developed countries (El Mossadeq 1989).
- 22.
The programs do not meet the needs of the majority of students, but only those who will be oriented in mathematical sciences. This has led some teachers who use mathematics to remark: The programs work as if all students would become mathematicians in the future (Aboutir 1994).
- 23.
The main remarks and recommendations resulting from this conference are reported in MEN (1983).
- 24.
Often at the level of high school, the exercises given to the students were superficial and concerned properties that the majority of students already knew in other forms, which made them unable to see the point of such exercises.
- 25.
From this perspective, some researchers believe that the 1968 programs were of an experimental nature. They even add that “Inspector J. P. Nuss, who was among those responsible for the preparation of school programs and textbooks, considered Morocco as a space for experimentation with these programs before their application in France” (Mawfik 2001, p. 2).
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Acknowledgments
I thank Mohamed Akkar, Pierre Ageron, Abdellatif Sghir, and Dirk De Bock for their remarks, comments, and suggestions which helped me to improve the content of the chapter. Also, I thank Nada Laabid for her help with the English of the present chapter.
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Laabid, E. (2023). Modern Mathematics: An International Movement, the Experience of Morocco. In: De Bock, D. (eds) Modern Mathematics. History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-11166-2_23
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