Students’ Mathematical Ideas in Problem-Solving Mathematics Classrooms: A Case Study of Circle Area Application
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Abstract
This study employed a case study design and a qualitative research methodology. Data were analyzed using deductive content analysis. The objective was to identify the characteristics of sixth-grade students’ mathematical ideas that emerged during problem-solving tasks related to the application of circle area. The target group consisted of 64 sixth-grade students from a national university-affiliated elementary school in Japan, selected through purposive sampling. The primary data source was a lesson plan from the unit on the area of a circle, specifically the fourth lesson in a five-lesson sequence. Data were collected from students’ written work, and the analysis was guided by the framework of mathematical thinking developed by Isoda & Katagiri (2012).
The findings revealed eight core mathematical ideas demonstrated by students: the idea of sets, the idea of units, the idea of representations, the idea of operations, the idea of algorithms, the idea of approximations, the idea of fundamental properties, and the idea of expression. Examples of student thinking included the use of images and symbols to explain calculation methods and solutions, execution of mathematical operations to determine area, and application of fundamental properties to construct and interpret mathematical expressions.
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References
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