許多國家之課程對國小學童推理能力之發展均相當重視，推理不僅能促進數學概念的理解，亦可以藉此去探索發現數學新知識（Ball & Bass,2003）。然而，目前較少研究探討關於教師如何使用策略去支撐學生推理歷程的發展。本文延伸Cobb 與Yackel（1996）社會數學規範之理論，去探討課室討論文化中，教師如何發展推理規範之情形，以及推理規範對學生課室數學討論實踐的影響為何。
本研究採用質性研究法，研究者實際參與觀察數學課室之運作，記錄課室中自然的樣貌，也將上課情形錄影下來，並蒐集學生解題紀錄及數學日誌等作為分析資料之依據。研究對象是一位新竹市某國小六年級教師，此教師曾參加一個發展課室討論文化教師成長團體達六年之久，其對課室討論之社會規範和社會數學規範之發展有相當多的經驗，因此本研究選擇此位教師作為觀察對象，觀察其六年級之數學教學，探討其如何促進學生之推理歷程的發展。
從研究結果中發現，教師使用各種策略去引出學生原來的數學經驗，支撐學生對數學的理解，並擴張學生的數學思考。在教師引出、支撐、和擴張的數學活動中，逐漸發展出課室社群共同可接受的推理規範。研究結果中發現，在此課室中共形成四個規範：一、說明須回到題目並說明使用哪些學過的數學知識；二、學童所使用的方法，須說服別人方可使用；三、已證明過的數學事實在情境改變時須重新證明；四、演繹推理證明。在教師引出、支撐、擴張的活動和推理規範的發展下，亦逐漸發展出此課室社群的數學討論之實踐。

Many countries＇ curriculum very emphasize how to develop children＇ reasoning ability. The processes of reasoning can help children to understand the concepts of mathematics and also to explore the new mathematical knowledge.However, few researches study what the strategies elementary school teacher used to support the development of children＇s reasoning process. This paper extends Cobb and Yackel＇s(1996) theory of sociomathematical norms to study how an elementary school teacher to develop reasoning norms and how those norms affect this classroom＇s discourse
mathematical practice.
This study uses the qualitative methodology to collect data: taking video record about classroom activities, collecting students＇ work, and also taking field notes. This teacher participated the research project of classroom discourse almost six years. She has more experiences to develop social norms and sociomathematical norms before teaching the sixth grade.
The results of this study showed how this teacher use several strategies to initiate children＇s mathematical experiences, support children＇s mathematical understanding
and extending children＇s mathematical thinking. Behind those initiating, supporting, extending activities, some reasoning norms were developed and accepted by that classroom community. Four reasoning norms were found in this study as follows: explaining the processes need based on the situation of problem and what they already learned
mathematics before, your solution method need to convince all classmate then you can use it otherwise you can＇t, mathematical truth need to be reproved if the condition was
changed. proof of induction reasoning. Under teacher＇s initiating, supporting, and extending activities and the development of those reasoning norms, this classroom community develops a real discourse mathematical practice.

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