Context Design for Analyzing Students' Abstraction with Different Cognitive Styles in Learning Tangent Lines of Circles

摘要

Mathematical abstraction is one of the most important process in learning mathematics concepts. Unfortunately it is difficult to be expected naturally happen in the instructional process. A context need to be designed so that it can trigger the process. This paper aims to design a context for analyzing students' abstraction with different cognitive style in learning tangent lines of circles. The design will be used for analyzing mathematical abstraction of junior high school student with field dependent and field independent cognitive style in learning topic of tangent lines of circles. Abstraction in Context (AiC) is used as theoretical and methodological framework for this study. This study was conducted in a government junior high school in grade 8 with 32 students as the participants. Based on the questioner result, there are 14 students with field independent cognitive style and 18 students with field dependent cognitive style. There were four learning tasks proposed in a priori analysis to trigger the construction of four main knowledge elements. After the a priori analysis of the design, some adjustments need to be made related to the complexity of the problems, knowledge elements that need to be constructed, and the social context for classroom setting. The final design consists of six knowledge elements as the prior knowledge, four main knowledge elements with five sub-knowledge elements, four learning tasks, and thirteen groups of students consist of two and three members based on their cognitive style.