教師建構等值分數教學知識的歷程

The Process of a Case Teacher Constructing Pedagogical Knowledge of Equivalent Fraction

本研究的目的是分析一位個案教師在數學專業成長團體下建構等值分數教學知識的歷程。資料包括個案教師對等值分數教材的分析、教學及專業成長團體討論會逐字稿、數學日誌及個案教師為學生進行等值分數教學前和教學後的評量。本研究發現在準備階段，個案教師分析各版本教材構思了假設性等值分數教學的雛形。在進入階段，個案教師對使用的版本教材提出了質疑，團體成員的專業對話、閱讀國內外等值分數的相關文獻、分析並比較各版本在等值分數教材的處理、學生在教學前的診斷性評量是個案教師對教材提出質疑的主要來源。在進攻階段，個案教師提出了假設性等值分數教學活動，並且對教學活動設計提出了七個論述。在回顧階段，個案教師針對學生的學習成效進行評估；本研究並提出了個案教師建構等值分數教學的知識套件。

The study was designed to explore how a case teacher participating in a professional team constructed her knowledge of teaching equivalent fraction. The data collected in the study included: The analyses of textbook used by the teacher， the transcription of teaching， the pretest， posttest and follow-up interview of students conducted by the teacher. The process of the case teacher constructed the pedagogical knowledge of equivalent fractions was characterized as four stages: preparing， entry， attacking， and reviewing. In preparation stage， the case teacher initiated the hypothetical structure of teaching equivalent fraction on the basis of analyzing various versions of textbooks. In entry， the teacher criticized the textbook. The professional dialogues of the team， reading the literature of equivalent fraction， comparing and analyzing teaching activities arranged by the different textbooks， students’ performing in the pretest and their responses to interview were the resources of the teacher’s critiques. In the attack stage， the teacher conjectured alternative teaching activities and justified the activities. In the reviewing stage， the teacher evaluated students’ performance of the equivalent fraction based on students’ posttest.