#### Table of contents

#### Opinion on the proposals for the readjustment of mathematics syllabuses, DES

*Coordinating Committee of the Mathematics and Education Section of the SPA*

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We will divide this technical opinion into five areas.

##### 1. Preliminary issues

We note positively, first of all, the willingness expressed by the authors of the programmes to discuss the curricular changes. It is a cut, which we view with pleasure, with an authoritarian (and autistic) past. However, the urgency of issuing a technical opinion, as well as the ignorance of the authors’ intentions in relation to 11 and 12 grades, severely limits the possibilities for further discussion.

##### 2. About the orientation module

We disagree with the introduction of the guidance module at the start of the tenth grade. It is apparently intended to give “a chance to correct educational paths”. However, the proposed solution is much worse than the current situation. We criticise the form, content and feasibility of this proposal.

2.1. As for form, we think the year is starting in the worst way. Starting the new cycle with a module that will have decisive consequences for the continuation of studies is extremely demotivating for both students and teachers.

2.2. As for the content, we do not understand the reason for the choice of geometry. Geometry has no predictive virtues for performance in mathematics. No research shows (or even suggests) that students with difficulties in geometry should not pursue studies involving mathematics. This objection of ours is, however, more general, and we think that no topic in mathematics has by itself such predictive virtualities.

2.3. As for feasibility, we think, on the one hand, it is impossible to form an opinion on the suitability of pupils for any subject in 9 lessons. And what will happen to the maladapted? Do they change course? After nine lessons? What if they are maladapted to various subjects? Which body is responsible for denying students continuation in their chosen courses?

Introducing or reinforcing counselling mechanisms for students at the end of 9 grade, or when they enrol in 10 grade, by making them compulsory, seems to us a much more fruitful option than the current proposal.

##### 3. About Mathematics B

We express many reservations regarding the syllabus of Mathematics B, where we think that the mistakes made with the Quantitative Methods syllabus are being repeated and others are being added.

3.1. We disagree with the process of construction of the Mathematics B syllabus. This seems to have been derived from that of Mathematics A, deleting several topics (we could not discern a criterion for the cuts). However, we think that this is not the appropriate way to design a curriculum, as this process ends up ignoring the interests of the audience. Mathematics B should be built, positively, from the needs of the students and not, negatively, through cuts. We think that an excessive concern with permeability between courses has led to a maladjusted programme.

3.2. We further disagree with the content. The needs of the courses for which Mathematics B is intended are very diverse and we see no reason for uniformity of this syllabus. Certain courses will favour certain topics to the detriment of others, less significant for the students’ training.

We think that the Mathematics B syllabus should be rewritten, taking into account essentially its suitability for the courses in which it is integrated. We propose, for example, that it be made up of several modules and that, for each course, some of them be selected.

##### 4. On the approach to Theme III throughout the year

The proposed approach to Theme III throughout the year as part of the Project seems bizarre to us.

4.1. On the one hand, we question whether it is feasible to integrate the whole of a mathematical topic into the Project. While much content that is traditionally taught in a lecture mode can be taught to advantage by involving pupils in project work, other content can only be taught in a very forced way. Even in the subject of Statistics, there are areas that should be taught formally (although not necessarily in an expository way).

4.2. On the other hand, this option raises numerous practical difficulties. What happens if the Project Area does not involve mathematics? And how will you integrate Sequences and Trigonometry and Complexes in the Projects? How do we ensure the study of all the fundamental concepts of these subjects?

We therefore recommend that this idea be abandoned.

##### 5. Amendments to the current programmes

We think that this curricular change should be taken advantage of to change some aspects of the current syllabuses that have been transferred to Mathematics A. We are thinking, for example, that both the applications of mathematics and problem solving and investigative work appear only in the methodological suggestions, but not in the contents. In curricula of other countries, these topics are viewed more strongly and are taken up as fully-fledged topics in mathematics curricula.

March 11, 2000