National Academy for Educational Research

　　本研究從「對話式形成性評量實務」（DAP）的角度探討國中數學教師教學及其與學生數學素養表現之關係，邀請兩位具有十年以上教學經驗的教師參與研究，其中一位為專家教師，兩位教師皆教授國中七年級數學。研究者進班觀察參與教師在「量與數」相關單元的教學，資料蒐集包括教學錄影、訪談逐字稿與研究日誌；為瞭解學生數學素養的表現，研究者以現有的數學素養題目編製試卷，經預試與諮詢專家意見確保信效度之後，對兩班七年級學生進行施測。研究發現專家教師較頻繁進行對話式形成性評量，師生間有比較多的互動與對話，提問較多類別的高層次問題，然而兩位教師提問的高層次問題類別有限，低層次問題大多集中在短答，有時候會提問修辭性問題，當學生正確回答時，兩位教師才會追問學生，要求他們針對答案提出解釋或說明，一旦學生回答錯誤，教師的回饋是拉高音調與重複答案來暗示學生回答錯誤，而不是追問瞭解學生錯誤回答背後的想法。兩位教師皆指出以“個案研究”的方式進行DAP，對他們的幫助最大。針對學生數學素養表現的分析發現，兩位教師的任教班級在前、後測得分並沒有顯著的差異，雖然許多證據顯示教師進行形成性評量對於學生的學習表現有所助益，然而，在本研究中教師的DAP與學生的表現的聯繫仍不明顯，建議後續的研究探究教師的DAP對於學生學習表現的影響。

　　This study attempted to differentiate discourse-based formative assessment practice (DAP) between an expert and a mathematics teacher, to form educational implications on teachers’ professional development, and to investigate the relationship between teachers’ DAP and their students’ performance in mathematics literacy. Two key critical stages of formative assessment, evidence elicitation and informed action suggested by Popham (2008), were respectively carried out in terms of questioning and oral feedback (Tunstall & Gipps, 1996) either in a convergent or a divergent way (Pryor & Crossouard, 2008). Crockett, Chen, Lee & Zilimu‘s (2012) framework to analyze mathematics discourse were adapted for the data analysis in the current study. Transcripts were organized into initial exchange, move, the type of teacher utterance, the type of questioning, and the kind of feedback so that the teachers‘ DAP and the similarities and differences were characterized. It’s found that the expert mathematics teacher tend to conduct divergent DAP while the other teacher conducted convergent DAP. Also, more extended sequences and teacher-student interchanges were observed in the expert teacher’s classroom. In addition, the expert teacher asked more categroies of high-level questions than her counterpart. However, the categroies of high-level questions initiated by the two teachers were limited. The majority of low-level question asked by the two teachers was short anwer. When stundents’ answers were corret, the two teachers posed the “Why” question to ask the students to explain their answers. Once stundents’ answers were incorret, instead of posing questions to probe the students’ ideas, the two teachers’ feedback was to raise pitch and to repeat the answers to hint that stundents’ answers were wrong. It is suggested that mathematics teachers need assistance to shift teaching practice from convergent DAP to divergent to fulfill student-centered education. Case study on discourse between teachers and students may be a promising way to improve teachers’ DAP. Although conving evidence suggets that students’ learning achievement benefits from their teahcers’ formative assessment practice, the relationship between the two teachers’ DAP and their students’ performance in mathematics literacy is unclear. It is suggested that the future study investigates the impact of teachers’ DAP on students’ learning performace.