DS0701 -

Didactics and Epistemology of the interactions between Mathematics and Informatics – DEMaIn

Submission summary

This project addresses the study of the epistemology and the didactics of the relations between mathematics and informatics. The project aims at a better understanding of the relations between mathematics and informatics by studying the foundations, the objects, the methods, the questions and the thinking, shared or specific, and by addressing the questions that each field asks to the other and the place that they occupy one in each other (as tool and as object).
The work will be led according to a classical methodology in didactics of sciences that consist in linking together epistemological and didactical studies in order to build and analyse learning situations that allow a suitable appropriation of the targeted concepts. This work of didactical engineering will be set up by developing observations and analysis of students' productions and by experimenting in a laboratory setting and then in classrooms, learning situations in link with the concepts from mathematics and informatics involved. Those works will be experimented and developed in a close collaboration with teachers from secondary school and university who will be involved in the project.
The epistemological analysis aims at deeply study how mathematics and informatics interplay, and particularly how the development of the field informatics impacts mathematics and its practice, how mathematics take part in informatics, and how mathematics and informatics interact in the fields at their interface. Indeed, informatics has a great part of its theoretical and practical foundations in mathematics and has been partly built up as a branch of mathematics and logic before getting independent. In return, Informatics asks new questions to mathematics, opens new research fields and enhances some traditional fields of mathematics. Moreover, computer science's tools deeply modify some of the mathematicians' practices. Particularly, informatics questions mathematics about validation (through proofs like the one of the four colours theorem), the value of its results (through the question of the place of constructive mathematics) and their methods (experimental dimension of mathematical activity).
The study is organised according to two aspects: (1) Scientific foundations (logic, algorithmics, language, proof), and (2) Concepts and objects (mathematics of computer science, discrete mathematics, representation of objects). For each aspect, we will study how the two disciplines interplay (through the analysis of the knowledge and of the main questions structuring each one) and we will investigate researchers' and experts' practices.
This epistemological study will provide elements that permit to analyse and enlighten the didactical choices made in secondary and university teaching and to produce answers to difficulties regarding the introduction of computer science's tools in mathematics, the mathematical issues in informatics, the place of proof, logic and algorithmics in mathematics and informatics, and regarding also the introduction of mathematical contents fitting better with contemporary issues.
The main application will be the conception and proposition, on the base of the developed research, of resources and in-service and pre-service training for teachers and trainers. The aim is to take into account informatics in the teaching of mathematics to motivate taught mathematics contents, to better grasp the mathematical issues in the teaching of informatics, and to anticipate the interactions between the teaching of mathematics and a generalised teaching of informatics. It is also about understanding how students from secondary school can be better prepared and how university teaching can be adapted to foster the transition between secondary school and university in mathematics and informatics.

Project coordination

Simon MODESTE (Université de Montpellier)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

UM Université de Montpellier

Help of the ANR 268,955 euros
Beginning and duration of the scientific project: October 2016 - 48 Months

Useful links

Explorez notre base de projets financés

 

 

ANR makes available its datasets on funded projects, click here to find more.

Sign up for the latest news:
Subscribe to our newsletter