Theory of Didactical Situations in Mathematics

2002 ◽  
Keyword(s):  
Didactical Situations ◽  
Theory Of Didactical Situations

scholarly journals Opportunities for language enhancement in a learning environment designed on the basis of the theory of didactical situations

ZDM ◽  
2020 ◽  
Author(s):  
Frode Rønning
Keyword(s):  
Primary School ◽  
Research Question ◽  
Combinatorial Problems ◽  
Learning Goals ◽  
Scientific Language ◽  
Teaching Sequence ◽  
Geometrical Shapes ◽  
Didactical Situations ◽  
Primary School Pupils ◽  
Theory Of Didactical Situations

AbstractThis paper is based on data from two teaching sequences in primary school that are designed using principles from the theory of didactical situations (TDS). The following research question is addressed: “What opportunities can a teaching design based on TDS give a teacher to gain insight into pupils’ language use, and to use this insight to establish shared, and mathematically acceptable, knowledge in a group of primary school pupils?” Empirical data from one teaching sequence on geometrical shapes and another teaching sequence on combinatorial problems are used to answer this question. The research shows that a sharp focus on well-defined learning goals does not limit the pupils’ possibilities in expressing their thoughts and ideas in their own language. The research also shows that despite clear learning goals, the teacher has rich opportunities to build on pupils’ language to connect everyday and scientific language for the purpose of developing a mathematically accepted discourse.

Towards a Problématique for Research on Mathematics Teaching

1990 ◽  
Vol 21 (4) ◽  
pp. 258-272
Author(s):  
Nicolas Balacheff
Keyword(s):  
Key Words ◽  
Mathematics Teaching ◽  
Theoretical Framework ◽  
Its Analysis ◽  
Didactique Des Mathématiques ◽  
Didactical Situation ◽  
Didactical Situations ◽  
Theory Of Didactical Situations

This article presents the main features of the theoretical framework of French research known as recherches en didactique des mathématiques. The foundation of this approach consists mainly of the relationships between two hypotheses and two constraints, which are presented together with some specific key words. Outlines are given of Brousseau's théorie des situations didactiques (theory of didactical situations). An example is given that presents in some detail the rationale for the construction of a didactical situation and its analysis. This article ends with some questions addressed to research on mathematics teaching.

scholarly journals Was Archaeopteryx able to fly? Authentic palaeontological practices in a museum programme

2019 ◽  
Vol 21 ◽  
Author(s):  
Marianne Achiam ◽  
Bent Erik Kramer Lindow
Keyword(s):  
Science Education ◽  
Reference Model ◽  
Education Programme ◽  
Authentic Science ◽  
Anthropological Theory ◽  
Didactical Situations ◽  
Point Of Departure ◽  
Theory Of Didactical Situations

Authentic science education has received increased attention in recent years, but it remains unclear what constitutes authenticity. Here, we use notions from the Anthropological Theory of the Didactic to approach authenticity. We take a point of departure in an existing education programme in a museum, and analyse it to pinpoint what constitutes its authenticity. We then use the theory of didactical situations as a way to construct a reference model; this reference model constitutes an authenticity-optimised version of the programme. We conclude by briefly discussing the implications of our findings.

Digital technologies as a means of accessing powerful mathematical ideas. A study of adults with low schooling in Mexico

2020 ◽  
Author(s):  
Santiago Palmas ◽  
Teresa Rojano ◽  
Rosamund Sutherland
Keyword(s):  
Previous Experience ◽  
Geometric Figure ◽  
Mathematical Ideas ◽  
Use Of Technology ◽  
Pick's Theorem ◽  
Area And Perimeter ◽  
Didactical Situations ◽  
Constituent Elements ◽  
Technology Resources ◽  
Theory Of Didactical Situations

Abstract This paper derives from a study which main purpose was to investigate how a group of adults with low schooling can have access to powerful mathematical ideas when working with activities that involve the use of technology resources and that take into account the adults’ previous experience with mathematics. Specifically, adults’ previous experience with area calculation was considered. Principles of the Theory of Didactical Situations (TDS) formulated by Brousseau guided the study design, and Pick’s theorem was recreated in a dynamic digital setting, with which it is possible to calculate the area of regular and irregular polygons. In this approach, intuitive notions of area and perimeter are resorted to, seeking to promote the experience with powerful ideas such as ‘the generality of a method’, ‘realizing the existence of different methods used for one and the same end’ and ‘realizing that each method possesses advantages and limitations’. Analysis of interview protocols from three noteworthy cases (which include both adults’ work in the digital setting and their discussions with the researcher) suggests the presence of powerful underlying mathematical ideas, such as the idea of generality and the power of a method and the features of the constituent elements of a geometric figure that are involved in calculating its attributes, attributes such as area.

scholarly journals Unfolding the Educational and Practical Resources Inherent in Mathematics for Teaching Mathematics

2020 ◽  
pp. 1-24
Author(s):  
Erich Christian Wittmann
Keyword(s):  
Learning Environments ◽  
Mathematics Teaching ◽  
Teaching Model ◽  
Main Role ◽  
The Common ◽  
Mathematics For Teaching ◽  
Didactical Situations ◽  
Natural Way ◽  
Theory Of Didactical Situations

AbstractThe objective of this introductory chapter is to explain the common rationale behind the papers of this volume. The structure is as follows. The first section shows that learning environments are a natural way to address teachers in their main role, teaching, and that therefore this approach is promising for improving mathematics teaching in an effective way. The section ends with a teaching model based on Guy Brousseau’s theory of didactical situations.

scholarly journals ENGENHARIA DIDÁTICA: IMPLICAÇÕES PARA A PESQUISA NO ÂMBITO DO ENSINO EM ANÁLISE COMPLEXA - AC

2016 ◽  
Vol 38 (2) ◽  
pp. 694
Author(s):  
Francisco Regis Vieira Alves
Keyword(s):  
Conceptual Framework ◽  
Research Design ◽  
Complex Analysis ◽  
A Priori ◽  
Didactical Engineering ◽  
Didactical Situations ◽  
A Priori Analysis ◽  
French Tradition ◽  
Didactics Of Mathematics ◽  
Theory Of Didactical Situations

This article discusses and describes the two initial phases provided by a nominated research design of Didactical Engineering – DE. Thus, in view of an interest declared by the teachhing of Complex Analysis – CA, the work emphasizes the elements that hold the potential to constitute the two initial stages of an DE, nomitaded by preliminary and a priori analysis, with emphasis on description and conception of only two problems situations. So, in view of the long heritage of the French tradition in Didactics of Mathematics, also elects the Theory of Didactical Situations – TSD, in complementary character in other to ensure the reasonable control of the didactic mediation, as well as the predictive character of a theorical and conceptual framework for the research, structured for teaching of CA, reproductible and repeatable in any empirical situation of application in academic locus.

scholarly journals Types of Generalization Made by Pupils Aged 12–13 and by Their Future Mathematics Teachers

2021 ◽  
Vol 11 (2) ◽  
pp. 40-52
Author(s):  
Mária Slavíčková
Keyword(s):  
Cognitive Development ◽  
University Students ◽  
Mathematics Teachers ◽  
Research Data ◽  
Algebraic Reasoning ◽  
First Year ◽  
Research Questions ◽  
Didactical Situations ◽  
Limited Scope ◽  
Theory Of Didactical Situations

This paper seeks to establish what kind of arguments pupils (aged 12–13) use and how they make their assumptions and generalizations. Our research also explored the same phenomenon in the case of graduate mathematics teachers studying for their masters’ degrees in our faculty at that time. The main focus was on algebraic reasoning, in particular pattern exploring and expressing regularities in numbers. In this paper, we introduce the necessary concepts and notations used in the study, briefly characterize the theoretical levels of cognitive development and terms from the Theory of Didactical Situations. We set out to answer three research questions. To collect the research data, we worked with a group of 32 pupils aged 12–13 and 19 university students (all prospective mathematics teachers in the first year of their master’s). We assigned them two flexible tasks to and asked them to explain their findings/formulas. Besides that, we collected additional (supportive) data using a short questionnaire. The supporting data concerned their opinions on the tasks and the explanations. The results and limited scope of the research indicated what should be changed in preparing future mathematics teachers. These changes could positively influence the pupils’ strategies of solving not only flexible tasks but also their ability to  generalize.

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