Examining the Effectiveness of Teaching Through Definitions in the Definition and Conceptualisation of Number Sets by Pre-Service Mathematics Teachers

Examining the Effectiveness of Teaching Through Definitions in the Definition and Conceptualisation of Number Sets by Pre-Service Mathematics Teachers

Ceylan ŞEN & Gürsel GÜLER

ABSTRACT
The purpose of the present study is to identify the effectiveness of the teaching process undertaken by means of definitions on the definition of the mathematical concepts included in number sets by pre-service mathematics teachers as well as their conceptualisation concerning the operations performed. The study is designed as a case study, a qualitative research method, and conducted with the participation of 68 pre-service middle-school mathematics teachers selected through purposeful sampling. It makes use of individual interviews, worksheets and teaching process videos as data collection tools. The study is conducted in two stages: The first stage involves revealing the definitions by pre-service teachers of the mathematical concepts included in number sets prior to teaching through definitions during individual interviews. As for the second stage, the definitions and conceptualisation by the pre-service teachers were examined within the framework of worksheets and teaching process videos during the course titled "Fundamentals of Mathematics I" taught through definitions. This allows the researcher to identify the effectiveness of definitions on the processes of definition and conceptualisation among pre-service teachers. The findings of the present study lead to the conclusion that teaching through definitions is effective in the definition and conceptualisation of the concepts included in number sets by pre-service teachers. Furthermore, pre-service teachers are also seen to make definition-based explanations during persuasion, generalisation, and proving. Definitions are found to be effective in the use of mathematical language and representation by pre-service teachers.

KEYWORDS: Teaching through definitions, definition, conceptualisation, pre-service middle-school mathematics teacher

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