Training of Mathematics Teachers

TRAINING OF MATHEMATICS TEACHERS: FUTURE PERSPECTIVES

Department of Mathematics - University of Coimbra, Portugal

Proceedings of the Conference The Future of Mathematics Education in Europe, Lisbon, December 2007
(to appear)

What?

In this text I shall be concerned with the training of Mathematics teachers for pupils in the 12-18 age group, the main point of the distinction being that, for younger pupils, not only the scientific level is less demanding but also other subjects may be combined in the teaching, and therefore in teacher training too.

I shall use the phrase “teacher training” instead of “teacher education”, not because I ascribe some particular meaning to the distinction but because that was the the wording proposed to me by the organizers of the Meeting. In Portuguese we do not have to solve this particular type of word problem, as everyone uses the phrase “formação de professores”.

Why?

There appears to be a universal consensus concerning the centrality of teacher quality in education, as compared to textbooks or curricula. Accordingly, more attention should be paid to teacher training policies. This has not always been the case, and Portugal in particular has some horror stories concerning the absence of quality assurance mechanisms of any kind, leading to the official recognition of low quality degrees, and the massive hiring by the Education Ministry of teachers with very insufficient training, often disregarding more qualified ones.

Traditionally there has been a great diversity of teacher training models throughout Europe, even inside individual countries (think of the German Länder, the Spanish Autonomous Communities, the United Kingdom), reflecting the fact that education is very much a country-reserved subject. The Green Paper on Teacher Education in Europe, published by the Umeå University in 2000, carries out a comparative description and finds widely differing systems and situations, with varying degrees of informality, concerning all aspects of teacher training: types of teachers and training institutions, admission requirements, degree and course contents and structure, qualifications and hiring policies.

In recent years, an European trend towards increasing formalization of teacher training degrees can be detected. It is now generally accepted that teacher training should be carried out in Higher Education Institutions. It is also generally accepted that three components must be present in any initial teacher degree: subject/scientific, didactic/educational, and some teaching practice.

The so-called Bologna process and the widespread attention given to the two-cycle Bachelor-Master degree structure appear to have obvious implications for teacher training models and organization. It seems natural, well adapted to the Bologna two-cycle spirit, and in my view quite correct, to separate the strictly academic or scientific subject courses ― which should find their place in a generalistic 3-year Bachelor degree in Mathematics ― from the more professionally oriented components (including the teaching practice) ― which should make up the content of a 2-year Master degree, specifically designed for teacher training.

As a possible indication of things to come, there has been movement at the European Union level on teacher training policies. Recent initiatives, apart from two meetings in Lisbon organized by the current Portuguese presidency, include the August 2007 Communication from the European Commission on improving the quality of teacher education, and the October 2007 European Council draft conclusions on the same subject. We also see change happening at this moment all over Europe (often in coordination with the Bologna reforms).

How?

What should a good model be for the training of teachers at the level we are concerned with?

The Bachelor should be a generalist undergraduate degree in Mathematics, not directed profession-wise, and therefore attended by students who do not necessarily wish to go into teacher training. This emphasizes the clear distinction between the purely scientific component and the more professional components, which are left to the Master. The Mathematics student needs an extended period for his intellectual maturing, to acquire the mathematical skills which will allow him to face his future job with ease and without fear of new and unexpected situations.

There must be minimum subject requisites in the Bachelor to make it acceptable as a basis for a teacher training Master. In the new Portuguese teacher training law of 2007, these requisites are 120 ECTS of Mathematics courses (equivalent to two years).

When?

The actual professional training of teachers should be left for the Master. This degree should clearly be profession-oriented, but keeping Mathematics and the teaching of Mathematics at the centre. Its main goal should be integration of subject knowledge and its linking to school Mathematics. Accordingly, the heaviest emphasis should be placed on courses concerned with the teaching of Mathematics at school level, underlining connections with previous Mathematics learning, revisiting the corresponding topics from a higher point of view, studying curricula and analysing textbooks, discussing teaching strategies, and so on.

Apart from these and other special courses on Mathematics ― e.g. on History, applications and special activities, and the use of technology ― the Master should contain courses covering age-group psychology, and sociological and legal issues in schools, so that the students can get an introduction to school reality well before they actually start teaching. There should be cooperation with experts on non-subject areas, and also with practicing teachers, if possible in contact with actual school teaching and observation of teaching experiences.

Finally, some supervised teaching practice must be an integral part of the Master. Coordination and partnerships with secondary schools are essential, e.g. for contact with teaching challenges and problems, and for professional practice of finishing students.

Throughout, the approach should be empirical, pragmatic and oriented to actual school and teaching issues. Also, too much “transversality” should be avoided: as it was once famously said, if the word “Mathematics” can be replaced everywhere (or in most courses) by e.g. “Geography” then the model is probably not appropriate.

Who?

The organization of such a Master course and its subject requirements raises the question of the institutional framework for it. In my view, the process should be organized and led by mathematicians, by which I mean people with a PhD in Mathematics, i.e. people who know what Mathematics is, its place and importance, how it works, how it is done and applied.

The main reason in favour of this is the priority given to Mathematics in the training of teachers for the levels described. Even in a Master degree specifically designed for teacher training, and thus profession-oriented, Mathematics must remain at the core: in discussing strategies for introducing and teaching special topics, in analysing curricula and textbooks, in experimenting with technology, it is better to keep Mathematics front and centre, with the aim of training mathematically strong teachers.

Keeping Mathematics at the centre in a teacher training Master degree is best done by mathematicians, people with a research record in Mathematics who develop a serious interest in education issues. This appears to be the best way to avoid imbalances in the classical Mathematics vs. educational science opposition. In particular, the farther you go from real Mathematics and its practice, the more vulnerable you are to abstract, radical views of Mathematics as a subjective construct, leading to pedagogical approaches ― full of “meaningful mathematical experiments”, “learning by discovery”, “student explorations”, and questioning of basic Mathematics learning as supposedly opposed to understanding ― which may look plausible on paper but can prove disastrous in practice. The view I espouse states that knowledge exists, that there is a cultural, scientific and civilizational heritage whose acquisition by the young is the primary mission of schools.

Where?

The above ideas may mean that the training programmes of Mathematics teachers for the levels I mentioned are carried out in University Mathematics Departments. Of course, this depends on individual countries, and should take into consideration in which institutions in each country the appropriate people are located. In Portugal, it certainly means that such programmes should be the responsibility of Mathematics Departments, the only places in the country where you find people with the profiles indicated above.

To qualify, a Mathematics Department should be willing to take very seriously the organization of such a degree. Some Departments may be overstretched with service courses, and others may consider this as outside their strategic agenda. I would find it a mistake that good Mathematics Departments in Portugal don't take part in this effort, and leave the training of Mathematics teachers to the wrong approaches, at the wrong type of institutions. But, again, this may be different in other countries.