TEACHING GEOMETRY THROUGH DIDACTICAL SITUATIONS - THE CASE OF THE TRIANGLE INEQUALITY

Oct 15, 2026

Uploaded by Aditya

This paper examines how Brousseau’s Theory of Didactical Situations (TDS) can support eighth-graders in learning the triangle inequality in Euclidean geometry. Evidence is drawn from observation notes, video recordings of lessons, and students’ written work. Analysis applies deductive content analysis using a conceptual framework grounded in TDS. Results show expected student behaviors across phases, with new mathematical ideas gradually formulated and justified. Students also devise and defend strategies for an open-ended task, developing informal knowledge through peer-driven situations.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages19

Reading Time48 min

AccessFree to download

Introduction

Teaching Geometry with TDS

Triangle Inequality in Euclidean Geometry

Rationale for the Study

Study Context and Data Sources

TEACHING GEOMETRY THROUGH DIDACTICAL SITUATIONS: THE CASE OF THE TRIANGLE INEQUALITY Murat GENC, Semra ERGAN Abstract: This paper aims to discuss the use of Brousseau’s Theory of Didactical Situations in mathematics (TDS) for eighth-graders to explore the concept of triangle inequality in Euclidean geometry. Data sources included observation notes, video recordings of lessons, and students’written work. Data analysis was done through a deductive content analysis approach that utilized the conceptual framework based on Brousseau’s notion of didactical situations. Findings revealed that student behaviors that were expected to take place through situations occurred at every phase as stated in the theory. Mathematical ideas leading up to the construction of new knowledge were gradually formulated and justified as stages progress. Students worked out different methods of evaluation to solve an open-ended exploratory task and defended them in a way that invited other students to implement their chosen strategies. They developed their implicit informal knowledge by building on their thinking and the thinking of others through situations. All these results highlight how important it is to use didactical situations to pave the way for learning to learn, as it not only facilitates the purposeful exchange of ideas through whole-class discussion that ensures a common understanding of mathematical ideas but also allows students to create their own learning adventures. Keywords: theory of didactical situations in mathematics, a-didactical situations, triangle inequality 1. Introduction The issue of creating appropriate learning environments in which students have a leading role in their own learning becomes more and more important in today’s education. Since learning mathematics is considered both a process of active individual construction of knowledge and a process of acculturation (Cobb, Wood & Yackel, 1991; Cobb, 1999), modern approaches to mathematics teaching have drawn attention to social constructivist paradigms that allow meaningful learning in the planned teaching environments. A social constructivist orientation requires learners to share and develop mathematical meaning by taking into account their existing knowledge, abilities, and feelings (Bishop, 1985; Ernest, 1994). With the social constructivist approach to teaching, the expectations from all major stakeholders that make up the education system have also been rearranged. While the student becomes the main actor in her learning process, the teacher is expected to be the moderator who guides this process. In this sense, much more emphasis is placed on learners taking responsibility for socially constructing knowledge through discourse and interaction related to challenging problems (National Council of Teachers of Mathematics, 2014) . The trend towards constructivism has also led to a new research focus in mathematics education that brings with it various educational theories. One of these theories is the Theory of Didactical Situations in mathematics (hereafter denoted as TDS) (Brousseau, 1997), which ensures the rigorous construction of mathematical knowledge in a particular teaching and learning situation designed and utilized to provide students with opportunities to achieve a better understanding of mathematical concepts. TDS is mainly influenced by Piaget’s theorization of cognitive development as a constructive adaptation process (Brousseau & Warfield, 1999) . Constructivism underlines that knowledge is not transferred from one person to another but is actively constructed by the learner (Kilpatrick, 1987) . It is the person herself who has all power and authority over the process of constructing knowledge (Lerman, 1989) . Like the constructivist approach, the theory of didactical situations also involves the construction of knowledge by the learner rather than just passively receiving and memorizing it in the learning context what is called the milieu,

FAQs

What teaching approach does the paper focus on?

The paper focuses on Brousseau’s Theory of Didactical Situations (TDS) to design learning situations for mathematics students.

How is student learning of triangle inequality supported?

It uses didactical situations where learners work autonomously with a constructed milieu, allowing knowledge to emerge from problem situations.

What evidence and analysis methods are used in the study?

The study uses observation notes, lesson video recordings, and students’ written work, analyzed through deductive content analysis based on TDS’s conceptual framework.

Oct 15, 2026

Uploaded by Aditya