Didactic Situations and Didactical Engineering in university mathematics: cases from the study of Calculus and proof

Abstract

This paper discusses the use of the Theory of Didactic Situations (TDS) at university level, paying special attention to the constraints and specificities of its use at this level. We begin by presenting the origins and main tenets of this approach, and discuss how these tenets are used towards the design of Didactical Engineering (DE), particularly adapted at the tertiary level. We then illustrate the potency of the TDS-DE approach in three university level Research Cases, two related to Calculus, and one related to proof. These studies deploy constructs such as didactic contract, milieu, didactic variables, and epistemological analyses, among others, to design Situations at university level. We conclude with a few thoughts on how the TDS-DE approach relates to other approaches, most notably the Anthropological Theory of the Didactic.

Situaciones Didácticas en Educación Matemática

“…Por otra parte, se ha reconocido la dificultad para encontrar situaciones a-didácticas apropiadas para el aprendizaje de diversos conceptos sobre todo los que se abordan en el nivel superior (Grønbaek et al, 2009). Esta dificultad se debe, principalmente, al nivel de abstracción de los conceptos que se revisan en el nivel universitario, así como al nivel de organización y las interrelaciones entre estos, además de la cantidad de conocimientos previos necesarios para abordarlos y entenderlos (González-Martín, et al, 2014).…”

The investigation of process of teaching function concept in an Adidactic learning environment

“…Adidaktik ortamlarla ilgili yapılan çalışmalar incelendiğinde; bu ihtiyacın milieudan alınan dönütlerle karşılandığı ve milieu ile etkileşimin ilgi ve motivasyonu arttırarak öğrenmeyi olumlu yönde etkilediği görülmüştür (Altundağ, 2010;Brousseau, 2002;Hersant & PerrinGlorian, 2005;Sensevy et al 2005;Vankúš, 2005). Öğrencinin müdahale olmaksızın kendisini öğrenmeye güdülendiği adidaktik öğrenme ortamlarında didaktik mühendisliği (Artigue, 2009;González-Martín et al 2014) ve didaktik antlaşması (Laborde & Perrin-Glorian, 2005;Putra, 2016;Sarrazy, 2002;Yavuz & Kepceoğlu, 2016) gibi sistemden kaynaklanan kısıtları ortadan kaldırarak öğrenme sürecine esneklik katmaktadır. Öğrenme sorumluluğun öğrencide olduğu böyle bir ortamda öğrencinin kendi öğrenme faaliyetlerini kontrol etmesi beklenir.…”

“…In the adidactic learning environments, learner motivates himself/herself to learn without intervention. Thus, it adds flexibility to the learning process by eliminating systematic constraints such as didactic engineering (Artigue, 2009;González-Martín, Bloch, Durand-Guerrier & Maschietto, 2014) and didactic contract (Laborde & Perrin-Glorian, 2005;Putra, 2016;Sarrazy, 2002;Yavuz & Kepceoglu, 2016). It is expected that in such an environment where the student has responsibility of learning, the student should control their own learning activities.…”

Research on Teaching and Learning Mathematics at the Tertiary Level: State-of-the-Art and Looking Ahead

“…Additionally, Anthropological Theory of Didactic (ATD, Chevallard 2003;Winsløw et al 2014) that analyze institutionally conditioned relationships in knowledge and practice and the Theory of Didactic Situations (TDS, Brousseau 1996;González-Martín et al 2014) that consider the implicit or explicit rules of the interactions taking place within a system formed by the teacher, the students and the milieu, have been the frame of studies in tertiary mathematics education.…”