比與比例的教學實務中教師的MCK與MPCK之關連性：以印尼(東爪哇)小學教師為例

Abstract

略This dissertation investigates the relationship between teachers’ Mathematics Content Knowledge (MCK) and Mathematics Pedagogical Content Knowledge (MPCK) that captured within teaching practice. Both Quantitative and Qualitative method of data collections including paper and pencil test assessment, statistical analysis, interviews and natural classroom teaching observation were applied in this study. MCK and MPCK instrument for paper and pencil test on ratio and proportion were developed and administered to 271 Indonesian in-service primary teachers’ with a variety of educational backgrounds and teaching experiences. For quantitative part of this study, The MCK and MPCK instruments which found to have good acceptability in the reliability analysis resulted 3 factors for MCK (meaning of proportional and non-proportional situations, number structures in situation, and figural representation) and 3 factors for MPCK (Knowing student’ conceptual understanding, ratio and proportion task level feature and Teaching problem solving strategy). Besides, another quantitative part of the study, cluster analysis was done to assign teachers into three categories (“Good”, “Middle”, or “Low”) for MCK and MPCK respectively. In particular for MCK, Indonesian primary teachers had difficulty with the factor on figural representation, but they performed best on number structures in situation representing products of proportional reasoning. In terms of MPCK, Good and Middle MPCK teachers have challenges on knowing students’ conceptual understanding and Low MPCK teachers have challenges on Teaching problem solving strategy. In addition, teachers’ beliefs about teaching mathematics and problem solving strategy were also included in some analysis. Qualitatively, teachers’ belief could be interpreted influence teachers’ teaching practice and teachers’ presentation of task and its strategy solution. Of the 271 teachers, 4 teachers with different assigned categories (GG, LG, MM, LL) were chosen for additional natural classroom teaching observation. Framework for teaching observation regarded MCK, MPCK and its relationship were developed to investigate clear captured moment in teaching practice. The overall teaching observation result indicated that teacher with Good MCK and Good MPCK (GG teacher) performed differently with the other three teachers. Qualitative analysis revealed the intertwinement relation of MCK and MPCK that could only be captured in GG teacher. However, though other three teachers could show potential MCK and MPCK components in their teaching, there was no relation of that knowledge elaborated. There was a tendency of presenting superficial teaching with textbook oriented except for GG teacher.