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Investigations into the Growth of Elementary School Teacher’s Mathematics Teaching Competence and Reflection under the Operation of Co-Development Group
analysis of teacher interactions
mathematical teacher learning model
co-development group of mathematics teaching
mathematics teaching competence
本研究蒐集的資料包括教師教學錄影與錄音、合作成長小組教學研討錄音、教師設計的學習單、反思札記、e-mail、教學研討文件、對學生的解題類型分析、教學計畫、行動研究報告、學生的學習單、學生的施測結果、研究者的札記等。訪談對象包括參與教師、兩位實習教師、學生、行政人員等。所有錄音和錄影資料皆轉錄成逐字稿。本研究遵循Cobb and Whitenack(1996)分析大量質性資料之方法學分析資料。就合作成長小組的互動分析而言，本研究由量的分析瞭解教師互動的概況，由質的分析深入探討教師互動的內涵。研究者選出明顯反應心理和社會互動關係的非等價事件，據此統計合作成長小組互動的交互影響次數及百分比，並將之視覺化。就數學教學知能與反思能力成長的分析而言，本研究分別依據Franke, Carpenter, Levi, and Fennema (2001)的教師發展層次架構及Ward and McCotter (2004)的反思等級架構分析。本研究採多重資料來源、多重資料蒐集程序、多重時間及不同分析者的三角校正，以確保資料的信效度。
The strategy to promote participant teachers’ professional development of mathematics teaching was through the interactions of the co-development group. The purpose of this study was to explore how and why participant teachers’ mathematics teaching competence and reflection grew as a result of his interactions with the co-development group. In the end, we were finally able to create a mathematical teacher learning model. This is an interpretive study. The co-development group consisted of an investigator and three grade 1 teachers of a public elementary school in Taipei city. This co-operative intervention research lasted for one academic year. There were two reasons for choosing these three teachers as our subjects. The first reason was that these teachers were motivated to learn and taught the same grade in the same school. The second reason was that they had different teaching beliefs, experiences and personalities. The researcher played three roles: participant observer, facilitator and investigator in the process of this study. The group had regular weekly meetings to discuss their teaching. The activities that were adjusted were based on participants’ willingness, needs and collective goals. The main activities engaged in the study were analyzing patterns of students’ solutions and discussing cases of mathematics teaching, individual problems while teaching and literature. The data collected for this study included classroom observations video-taped and audio-taped, group discussions audio-taped, teachers’ worksheets, teachers’ reflective journals, e-mail, documents of group discussions, analyzing patterns of students’ solutions, lesson plans, action research reports, students’ worksheets, the results of students’ tests and research journals. Participant teachers, two intern teachers, students and administrators were interviewed. All video-taped and audio-taped data were transcribed verbatim. The data were analyzed by using Cobb and Whitenack’s (1996) methodological approach which can be used to analyze large sets of qualitative data. The interactions of the group were analyzed quantitatively and qualitatively. The number of interactions and its percentage were calculated and visualized according to the non-equivalent events apparently reflecting the relationship between psychological processes and social processes. The teachers’ mathematics teaching competence and reflection were respectively analyzed according to Franke, Carpenter, Levi, and Fennema’s (2001) ‘Levels of Engagement with Children’s Mathematical Thinking’ and Ward and McCotter’s (2004) ‘Reflection rubric’. Multiple triangulation on the source, method, time and analyst were used to validate the data. Five categories that distinguish the learning types of teachers stemmed from empirical data. Those categories were knowledge type, thinking model of learning to teach, the relationship between knowledge and action, teaching approach and belief about mathematics teaching. Four kinds of teacher’s learning types are distinguished by the categories and the frameworks. Those types are nave type, theoretical type, empirical type and practical type. The ultimate goal of a teacher is to become practical type. Two models were induced from empirical data based on activity theory and cognitive theory of practice. The first model is called the Model of Interactions Between Individual Mathematics Teacher and Co-development Group. Making conflicts of cognition and encouraging experiments are the important mechanisms to facilitate the growth of a teacher. Co-development group facilitates individual teacher’s social reflection and instruction experiment. This is a cycle where an individual teacher produces new knowledge or belief by reflecting on his teaching internally or socially. Then he puts them into practice by reflecting internally or socially. As the cycle continues, his mathematics teaching competence will grow constantly. Relatively, an individual teacher’s knowledge, belief or teaching can also influence other participants in the same way . Thus, participants grow through interacting with each other. The second model is the Mathematical Teacher Learning Model. The mathematics teacher reflects his teaching internally or socially according to his knowledge or belief as a result of forming his teaching goal. His rules of action emerge based on his teaching goal. Concepts-in-action are mainly from his knowledge or belief. He categorizes and selects information about teaching by his concepts-in-action. He infers, from the available and relevant information about teaching, appropriate teaching goals and rules according to theorems-in-action. As his knowledge or belief changes,cognition of teaching practice changes via reflection, and vice versa. Different interactions between knowledge, reflection and action of different learning types result in different growth of mathematics teaching competence. The more knowledge, reflection and action interact, the greater the mathematics teaching competence. As for contributions in theory, we can understand various learning models of different types and the use of different strategies to promote them to grow via the first model. We can understand the mechanisms and the viable ways to facilitate group development via the second model. As for teacher education implications, the models contribute to the plan and implementation of inservice professional development activities for teachers as it is designed to fit participants’ different learning types. As for methodology, a valid tool for analyzing teachers’ interactions is lacking. Therefore, the innovative method of this study can be a valid one.
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