A design-based investigation on advanced mathematical knowledge for mathematics teachers in the context of limit

Date

2024-9-06

Author

Toker Kekik, Habibe

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The study had two principal aims. The first was to explore the essential advanced mathematical knowledge of limits for mathematics teachers from the perspective of experts. The second was to document the characteristics of the difficulties experienced by mathematics teachers in a teaching sequence designed to promote their advanced mathematical knowledge of the concept of limit. A design-based research approach was adopted to fulfil the objectives of the study. In this context, a need analysis phase of the design-based research comprised an interview study, conducted with five mathematicians and mathematics educators. Subsequently, the main study was held with six secondary school mathematics teachers in Alanya as an exploration phase. A variety of data collection instruments were employed, including interviews, pre- and post-tests, questionnaires, observations, written in-class works, and video data. These data were analyzed using qualitative methods. The results of the interview study demonstrated how the concept of equality is interpreted differently in the context of limits, as opposed to other mathematical contexts and revealed essential advanced mathematical knowledge for limit. Furthermore, the findings explicitly revealed covariational relationships in the definition of limit. The data from the main study indicated that despite the presentation of a variety of arguments and approaches throughout the teaching sequence, the teachers demonstrated a certain degree of difficulty in comprehensively understanding the concept of limit, constructing covariational relationships among variables within limit, and employing equality and symbols appropriately. In light of these results, the study offered several key implications, limitations and suggestions for further research.

Subject Keywords

Advanced mathematical knowledge, Limit, Design-based research, Teaching sequence, Need analysis phase

URI

https://hdl.handle.net/11511/112264

Collections

Graduate School of Natural and Applied Sciences, Thesis