Investigating mathematics teachers' covariational reasoning and its relation to their knowledge of and teaching quadratic functions

Date

2024-8-28

Author

Belin, Mervenur

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

371
views

114
downloads

Cite This

This multi-case study investigates two high school mathematics teachers’ covariational reasoning and its relation to their knowledge and teaching practices of quadratic functions, considering the emphasis on correspondence and covariation approaches. Semi-structured interviews on covariational reasoning, the rate of change, and quadratic functions were conducted to reveal teachers’ specific ways of thinking and understanding. Additionally, twenty-four hours of teaching were observed, and interviews were conducted before and after the teachings to characterize teaching actions and behaviors. Findings regarding covariational reasoning pointed to teachers’ different reasoning patterns. Furthermore, the teacher who reasoned covariationally up to direct coordination and gross quantification, showed only the correspondence approach in his explanations of quadratic functions. The teacher who reasoned covariationally up to direct and systematic coordination and extensive and intensive quantification, used both correspondence and covariation approaches in her explanations of quadratic functions. There were also sharp differences in their teachings of quadratic functions. One teacher taught the topic from a correspondence approach, and he depicted decentering levels 1-Interest and 0-No interest in student thinking. The other teacher used correspondence and covariation approaches at four levels of decentering. However, at decentering levels 2-Make sense and 3-Use of student thinking, she focused on covariation approach. Therefore, a relationship was observed between teachers’ emphasis on functional approaches and teachers’ quality of interaction with students. This study provided evidence for considering covariational reasoning as an essential component of teachers’ mathematics knowledge of quadratic functions.

Subject Keywords

Covariational Reasoning, Quadratic Functions, Teacher Knowledge, Decentering, Teaching Practice

URI

https://hdl.handle.net/11511/111274

Collections

Graduate School of Natural and Applied Sciences, Thesis