The Image of Mathematics in Society
2006-2013
This project, which began in October 2006, was undertaken locally within the DiMaGe team and had to do with many members (Pierre-Alain Chérix, François Conne, Audrey Daina, Jean-Luc Dorier, Annick Fluckiger). It was part of a larger project endorsed by the Rhone Alpes region (Cluster 14 : Problematics and representations of science, technology and their usage’ theme 4 ‘Scientific training and didactics of science,’ Project on ‘Youth disaffection for scientific studies’).
The general question of youth disaffection for scientific studies takes a specific turnon a specific nature when it comes to mathematics. It seems to us that beyond the more or less objective indicators, different reports or studies have emphasised, particularly concerning the drop in in numbers within the top universities for mathematics courses, mathematics suffers from a negative ‘image’ in people’s minds, and in students’ minds in particular. The paradox, emphasised by many authors including Chevallard, is that mathematics have never been more present in our daily lives than today, even though they are increasingly invisible, locked in inside advance technologies’ black boxes. The result is that their impact on society as a whole is disguised and that the 21st century citizen cannot perceive its utility in her daily life.
Mathematics as a school subject have also had to suffer the negative reception of modern mathematics by the public and their use as a distinguishing subject. For some years now, the multiple changes of the curricula have tried to show how mathematics can be used in every day life, and in other subjects; recalling elements of its history has also been seen as a way of giving them some form of a human element. The impact of these modifications, their feasibility and their pertinence within the constraints of the educational system has been the focus of only a few studies. Moreover, the credibility of these changes is far from being unanimously accepted by the mathematics community (whether it be teachers or academics).
These different factors have had a significant impact, in our opinion, on the image of mathematics in society and education. In the era of supercomputers, pocket calculators, is it truly necessary to know how to do mathematics? We know that these type of ideas have been called for by a French minister of Education and that there followed a cut in the number of hours of mathematics in secondary school. What, in the end, does doing mathematics mean? Is it only a subject that helps to train the mind, which de facto would legitimise as a distinguishing subject, just like Latin before it? Is it really a way of investigating the world around us, and in this way do they contribute to the education of the human of the street? Or is it only a subject which serves other sciences and therefore to be restricted to specialists? These essential questions need to addressed, if only partially, taking into account the constraints of the modern world, the place of technology, the value of science and the tasks of education.
Teachers of course have an important role to play in the image that society has of mathematics. This part of the problem needs to be addressed in a very different way for primary school, middle school, and secondary school teachers and then university level professors, who have a specialised background. In this way, the project we are proposing looks to do a review of the image that teachers have of mathematics and of their discipline, and then to draw out hypotheses (to be checked) about the effect on their teaching.
This part of the research was undertaken on the basis of questionnaires and individual interviews. It concerned, distinguishing between approaches, the primary school teachers (experienced, beginners or in training) on the hand, and secondary school teachers on the other. Finally, we designed and transmitted a questionnaire to our first year students in educational sciences in Geneva, many of whom are to become teachers, to masters level student in mathematics and to students in economics. Globally,among non specialised populations the image of mathematics is less negative and ‘naïve’ than we could have thought. These results led to us to refining our analyses. Therefore, we then designed a more complex tool, allowing for more refined analyses, but concerning a smaller sample. We designed a mathematics questionnaire that we circulate in a written form to a duo comprising a future teacher or a part time teacher and masters student in mathematics or a secondary school mathematics teacher. These two (future) teachers are then invited, under the supervision of a member of our team, to exchange their answers during an hour long interview. Through this tool, we aim at making clear the significant differences in the image of mathematics of the two populations. The underlying hypothesis of our work is that primary school teachers play a decisive role in the interest of students (later, students) for mathematics. We aim to see if there are curcial points on which there are significant differences between primary and secondary school teachers’ influence on the motivation of young people to pursue a career in mathematics. If this is the case, our work can allow us to develop an educational tool that would allow a better managing of the primary/secondary school interface in the initial training of teachers (see below) in order to foster a better image of mathematics all along school years.