資深高中數學教師教學知識與教學構思的個案研究

• Main Author: 陳亭瑋
• Other Authors: 金鈐
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/56168730410843688154

碩士 === 國立臺灣師範大學 === 數學系 === 99 === This study applies qualitative case study, which explores the professional knowledge and thinking of an experienced high school mathematics teacher. The study is structured into three research stages including the pilot, initial, and second stage. The teaching units include「plane and line in space」、「combination with repetition」and「mathematical expectation」. The study material comes from videotaped lessons, interviews, and class handouts provided by the participant teacher. The observation system is adapted from coding system of the Mathematical Quality of Instruction (MQI) developed by Learning Mathematics for Teaching (2006). First of all, I modified the system codes to adapt to the actual quality of the teacher’s classroom teaching. Second, I analyzed the video tapes. Last, the coding results were mostly supported from another independent coder to establish the acceptable inter-coder reliability. Using three different observed teaching units within an academic year, I describe the participant teacher’s knowledge and thinking of/about mathematics teaching in terms of both MKT (Mathematical Knowledge for Teaching) (Ball et al., 2008) and PUFM (Profound Understanding of Fundamental Mathematics, Ma, 1996) theoretical frameworks. The results reveal that, the teaching of the teacher mostly presented PUFM qualities of connectedness, multiple perspectives, unity, and the basics. However, considering of emphasis on subject matter knowledge of PUFM, I took the aid of MKT structure to further analyze some teaching clips which PUFM is unable to cover. According to the instruction above, I brought up some mathematical teaching cases which highlight MKT characteristics, which also indicates that MKT and PUFM seem to have some parts overlapped, but some not neither. The study result in addition presents the teaching tendency of the teacher was much alike PUFM as a whole, yet also reflecting some MKT elements inside. Furthermore, the teacher also showed sort of spiral features of mathematics teaching. Finally, the present study described the possible relationship between PUFM and MKT, which may provide some insights into the future study of both the tension and relationship between high school mathematics teacher’s PUFM and MKT. Hopefully, my study results may be used to increase the quality and usefulness of the MKT observational system at high school level, as well as to examine and develop professional knowledge of high school mathematics teachers.