本研究的研究目的欲探討高中數學教師對於數學推理的信念，將從數學推理的本質、教師對於數學推理的教與學的信念、以及教師對於數學推理與數學推理教學之自我效能等三個面向切入，並加以分析其中關係。
本研究採取現象圖析學，此研究法主張不同的個體對於類似的經驗都有不同的體會與理解，故本研究以立意取樣選取六位經驗豐富的高中數學教師為研究對象。再利用半結構式的訪談，蒐集六位教師在數學推理的本質、數學推理的教與學的信念、以及數學推理與數學推理教學之自我效能三個面向上的論述，並透過既有文獻對數學推理的分類加以分析歸納，亦使用紮根理論進行編碼分析。第一個面向，將數學推理的本質分成三個部份加以探討，分別是四種脈絡下的類別、四種方法與兩種目標，並探討其中之交互關係。第二個面向，將數學推理教與學的信念分成兩種向度，分別是「傳遞－接受」的教學與學習觀、以及「建構－發展」的教學與學習觀。第三個面向，將數學推理與數學推理教學之自我效能分成三個層次，分別是高自我效能、中自我效能和低自我效能。
資料分析結果顯示，第一個面向，六位教師在不同脈絡下的類別、方法、與目標中，以教師對於概念性質定義或公式的理解上之信念有較大之差異，亦容易造成教師對於數學推理原本的認知有所衝突。第二個面向，六位教師在教學與學習的信念中，有三位教師偏向單一向度的信念，另外三位教師呈現兩種向度混合的信念，並呈現不同信念的教學模式與學習特點。第三個面向，六位教師數學推理及其教學的自我效能皆呈現兩種不同的依據。就各面向之間的交互關係，研究者依據分析結果合理猜測，教師對於數學推理本質的信念越廣，其教與學信念偏向混合觀；教師對於數學推理教與學的信念也與其數學推理與數學推理教學時的自我效能有關。但是，教師對於數學推理的本質與其進行數學推理與數學推理教學的自我效能間較無明顯的關係。

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