The Analysis of the Algebraic Proving Process Based on Habermas’ Construct of Rationality

The Analysis of the Algebraic Proving Process Based on Habermas’ Construct of Rationality

Selin URHAN & Ali BÜLBÜL

ÖZET
Proving is considered to be one of the most important activities in mathematics. Some of the studies on mathematical proof provide various useful tools, which enable us to analyze the proving processes of students. Recent studies have shown that the proving process of students needs to be evaluated comprehensively and coherently considering the proving strategies students use and the mathematics level of the community students are in and they communicate with. To this end, Habermas’ construct of rationality has been used by the researchers to analyze some mathematical activities, such as problem solving, proving and modeling. Habermas’ construct of rationality is composed of three integrated components which are epistemic, teleological, and communicative rationality. This study is a qualitative case study, which aims to analyze the proving processes of university students in the field of algebra within the context of these rationality components. The results of the study revealed that the algebraic proving process of the students has substantially been affected by the interaction between the rationality components. Furthermore, based on the needs that arose during the analyses, it is recommended to add new sub-components to the modeling requirements of the epistemic rationality and the communicative rationality components of Habermas’ construct of rationality.

ABSTRACT
Proving is considered to be one of the most important activities in mathematics. Some of the studies on mathematical proof provide various useful tools, which enable us to analyze the proving processes of students. Recent studies have shown that the proving process of students needs to be evaluated comprehensively and coherently considering the proving strategies students use and the mathematics level of the community students are in and they communicate with. To this end, Habermas’ construct of rationality has been used by the researchers to analyze some mathematical activities, such as problem solving, proving and modeling. Habermas’ construct of rationality is composed of three integrated components which are epistemic, teleological, and communicative rationality. This study is a qualitative case study, which aims to analyze the proving processes of university students in the field of algebra within the context of these rationality components. The results of the study revealed that the algebraic proving process of the students has substantially been affected by the interaction between the rationality components. Furthermore, based on the needs that arose during the analyses, it is recommended to add new sub-components to the modeling requirements of the epistemic rationality and the communicative rationality components of Habermas’ construct of rationality.

ANAHTAR KELİMELER: Algebraic proof, proving process, Habermas’ construct of rationality, algebra

KEYWORDS: Algebraic proof, proving process, Habermas’ construct of rationality, algebra

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