Josep Gascón

Didactic restrictions on the teacher's practice: The case of limits of functions in Spanish high schools

The Anthropological Theory of Didactics describes mathematical activity in terms of mathematical organisations or praxeologies and considers the teacher as the director of the didactic process the students carry out, a process that is structured along six dimensions or didactic moments. This paper begins with an outline of this epistemological and didactic model, which appears as a useful tool for the analysis of mathematical and teaching practices. It is used to identify the main characteristics of the mathematical organisation around the limits of functions as it is proposed to be taught at high school level. The observation of an empirical didactic process will finally show how the internal dynamics of the didactic process is affected by certain mathematical and didactic constraints that significantly determine the teacher’s practice and ultimately the mathematical organisation actually taught.

Introduction to the Anthropological Theory of the Didactic (ATD)

The chapter briefly introduces the Anthropological Theory of the Didactic (ATD) by referring to the data from Chap. 2. ATD provides a frame for investigating mathematical and didactic activities in terms of praxeologies, focusing on their components, dynamics, and the conditions that enable their existence and development in a given institutional setting. The main idea of the concept of praxeologies is that all human activities comprise and link two parts, a practice and a theory one.

Starting Points for Dealing with the Diversity of Theories

This chapter presents the main ideas and constructs of the book and uses the triplet (system of principles, methodologies, set of paradigmatic questions) for describing the theories involved. In Part II (Chaps. 3, 4, 5, 6, and 7), the diversity of five theoretical approaches is presented; these approaches are compared and systematically put into a dialogue throughout the book. In Part III (Chaps. 9, 10, 11, and 12), four case studies of networking practices between these approaches show how this dialogue can take place. Chapter 8 and Part IV (Chaps. 13, 14, 15, 16, and 17) provide methodological discussions and reflections on the presented networking practices.

A ‘study and research path’ enriching the learning of mechanical engineering

ABSTRACT Study and research path (SRP) is an inquiry-based teaching format grounded in the Anthropological Theory of the Didactic. One of the specific characteristics of SRP is its task-design basis, which includes explicitly questioning the knowledge at stake in study processes. In this work, we propose general guidelines for the design of SRPs for Engineering courses. We have explored the validity of the SRP methodology for learning Strength of Materials, a key subject in Mechanical Engineering. The use of question–answer maps and the media–milieu dialectics throughout the development of the SRP are discussed, together with the student’s perceptions on the new learning process.