Mathematics and Science: The relationships and disconnections between research and education

 

As a result of attending the course, you will:

• Acquire a solid foundation in the recent advances in the theoretical framework of didactic transposition and its related notions.
• Develop the ability to recognize and validate problems within this domain.
• Acquire an understanding of relevant research methodologies and techniques and their application within this domain.
• Gain experience writing scientific, peer-reviewed manuscripts (that can be developed further into publications at the participants’ own initiative).

Requirements

By July 1, participants must submit a 5-page outline of a selected problem from their current work and how they propose to use the theoretical framework in their work (based on their own readings of the course texts, which will be distributed upon acceptance).

During the course, participants must actively participate to develop their ideas under the supervision of the course teachers and guest lecturers. This includes giving a 20 min presentation of their 5-page synopsis.

By October 31, participants must submit a 10-page paper on the use of the theoretical framework in their own research.

Background

The teaching and dissemination of mathematics, physics, biology, chemistry and other sciences (designated in the following as ‘science’) in schools and other educational institutions is fundamentally based on the research disciplines that give them their name. Through a process of didactic transposition, science knowledge, values and practices are apprehended from their place of production – the domain of scientific research – and deconstructed and reconstructed in order to become teachable in the domain of science education. This process is inevitable and indeed, necessary; however, it is regulated by a number of factors, not all of which correspond to didactic intents. On the one hand, the role of the school is not simply to transmit as much of science disciplines as accurately as possible, but to form citizens who can function in today’s and not least tomorrow’s societies; on the other hand, the distance between ‘living science’ and ‘school science’ is not always justified by this basic role, but simply by the distance among research institutions and schools, as when the school discipline perpetuates the teaching of knowledge which has become more or less obsolete in scientific research and, eventually (sometimes even quicker!) also in society. Thus, didactic transposition carries with it the risk of delay (Quessada & Clément, 2007), the introduction of notions in isolation from their origin and thus concealment of the ‘true’ functioning of science (Brousseau, 2002), or ultimately, pathological substitutions (Chevallard, 1991). These phenomena have implications for variety of educational contexts; from teacher professional development (Winsløw to appear) to the design of teaching-learning sequences (Levrini & Fantini, 2013), quality of textbooks (Quessada & Clément, 2007) and development of museum exhibits (Mortensen, 2010). In brief, didactic transposition must remain ‘alive’ and alert to new potentials of interactions between ‘science in the making’ and, more broadly, ‘science in society’ on the one hand, and the teaching and dissemination of science in schools and museums on the other. The societal and institutional conditions for maintaining these links differ from one society to another, and so an international perspective can also help to identify possibilities and obstacles in a particular society.

Literature

Brousseau, G. (2002). Theory of didactical situations in mathematics. New York: Kluwer Academic Publishers.

Chevallard, Y. (1991). La transposition didactique: Du savoir savant au savoir enseigné. Grenoble: La Pensée Sauvage, Editions.

Levrini, O., & Fantini, P. (2013). Encountering productive forms of complexity in learning modern physics. Science & Education, 22(8), 1895-1910.

Mortensen, M. F. (2010). Museographic transposition: The development of a museum exhibit on animal adaptations to darkness. Éducation & Didactique, 4(1), 119-137.

Quessada, M. P., & Clément, P. (2007). An epistemological approach to French syllabi on human origins during the 19th and 20th centuries. Science & Education, 16(9-10), 991-1006.

Winsløw C (to appear). The transition from university to high school and the case of exponential functions. Proceedings of the 8th Congress of the European Society for Research in Mathematics Education.

Intro: Presentation of course and participants.

Lectures: Presentation of coherent research area/problem, with overview of methods and results.

Group work: Participants discuss one of the papers in the course compendium (related to one of the day’s lectures) in order to raise questions for the seminar.

Seminar: Two parallel sessions, led by lecturers of the day, taking up questions formulated in group work.

Presentation + Supervision: Five parallel sessions with 20 min paper presentations by two participants in each session, followed by discussion led by one designated supervisor.

Outing: Social arrangement, followed by festive dinner.