本研究旨於為期超過一個學年的縱貫性追蹤研究，藉由一發展性研究計畫探討兩位個案 教師發展數學臆測探究教學歷程。研究蒐集兩位個案教師課室觀察、反思、晤談與學生 焦點團體訪談等資料，藉由持續比較分析方法與對於質性資料進行開放性譯碼及主軸譯 碼，分析兩個案教師數學臆測探究教學實務之發展脈絡。研究發現，個案教師T1 數學臆 測探究教學建立於具有良好社會性數學習常規之學生探究社群，在促進學生學習理解的 前提下以策略性佈題協助學生在特殊化、系統化及一般化的脈絡中建構數學知識。另外， 個案教師T2 以紀錄、樣式推論、論證三階段建構數學臆測探究教學模式，並在具有良好 討論的課室情境裡，協助學生在小組探究中透過特殊化、系統化、一般化、反駁等策略 培養數學思考能力。最後，本研究整合兩位個案教師數學測探究教學實務，提出以教學 實務研究為基礎之數學臆測探究教學模式。

This paper reports on a longitudinal panel study from a developmental research project aimed at investigating two junior high school mathematics teachers’ teaching practice in developing conjecturing-inquiry teaching over an entire academic year. This study collected qualitative data through classroom observation, in-depth interviews, teachers’ reflections, and students’ focus group interviews. In addition, the data were analyzed by means of open coding, axial coding, and the constant comparative method of analysis. The results revealed that case teacher T1 based his conjecturing-inquiry teaching on the well-established socio-mathematical norms within students’ inquiry community. Furthermore, with the improvement of students’ conceptualization in mind, the teacher used a strategic problem-posing approach to help students construct mathematical knowledge in specialized, systemized and generalized contexts. On the other hand, case teacher T2 built a conjecturing-inquiry teaching model consisting of three phases: keeping records, inferring patterns, and argumentation. In addition, the teacher also maintained a favorable classroom environment for discussion and helped students to develop their mathematical thinking skills in small group inquiry activities, by using strategies such as specialization, systematization, generalization and refutation. Finally, this study integrated the teaching practice of the two case teachers, and put forward a research-based mathematical conjecturing-inquiry teaching model.