本研究採用個案研究法和教室觀察法描述兩位國中數學教師幾何單元的數學教學概念。依據七年級數學課程的內容，將研究過程分為以數型關係為主題的前導研究以及平面幾何圖形與幾何圖形轉變的第一和第二階段研究。個人透過問卷調查、個案晤談和教室觀察蒐集各類實徵資料，據此分析與詮釋兩位個案教師在不同類型班級中的幾何教學構思和教學實作。

研究結果顯示，兩位教師分別呈現出相似和不同的幾何教學概念，而且對於不同類型的班級也會有不同的教學構思與實作方式。其中，教師個人之前的數學學習經驗、對學生學習的掌握和課程教材內容的理解是影響教學構思的主要因素。雖然，個別教師教學前的構思和實際的教學活動具有相當程度的一致性，但是，學生的學習成效不佳和教材內容不易理解會使得教師的構思與實作有些微的落差。兩位教師的幾何教學實作最大的差異在於操作取向的教學活動
。其中一位認為操作和幾何概念應該並重，因而利用具體物來協助學生建立幾何圖形的視覺心像。另一位則採用生活實例或自製教具來講述抽象幾何概念的內容，以幫助學生建立相同的視覺心像。另外，兩位教師也會藉由反思自己的教學和學生的學習情況，以及透過與同事互動討論來學習如何教授幾何概念，以提升教學的品質。

最後，本研究的結果應能協助國中在職數學教師瞭解幾何單元教學構思與實作的內涵、差異及影響因素，以設計出更適合國中生幾何學習的活動；更希望有助於國中數學教師瞭解自己的幾何教學概念，進而引動數學教學專業的成長。

Case study and classroom observation were adopted in this study which described the pedagogical conception of two junior high school mathematics teachers when they taught geometry. According to the content of 7 grade’s mathematics curriculum, this research process was divided into the pilot study which took the relations of numbers and patterns as the theme, and first and second stage studies took geometric plane figures and transformation of geometric figures as the themes respectively. The author used questionnaires, interviews and classroom observations to collect the empirical data, to analyze and interpret the pedagogical thinking and teaching practices when they taught different kinds of classes.

The results revealed that two teachers displayed similar and different pedagogical conceptions of geometry, and they had different pedagogical thinking and teaching practices in different kinds of classes. Among them, teachers’ former learning experience, grips of students learning conditions and understanding of curriculum materials were the main factors that influenced teachers’ pedagogical thinking. Although the teacher’s pedagogical thinking and classroom activities were fair coincidence, but the low efforts of students’ learning and the indigestibility of materials would make her pedagogical thinking and teaching practices slightly disagree. The main difference between two teachers’ teaching practices in geometric units was the manipulative activities. One of them considered manipulative activities and geometric concepts should be equally emphasized, therefore she used the concrete objects to help students to construct visual imagery of geometric figures. Another used the examples of live or handmade instructional aids to discourse the abstract geometric concepts to help students to construct the same visual imagery. In addition, they would also reflect their classroom activities and students’ learning conditions. They also discussed with colleagues about how to teach geometric concepts, so as to advance their teaching quality.

Finally, the results of this research might help junior high school in-service teachers to understand the connotations, differences and influential factors of pedagogical thinking and teaching practices. On the basis of these results the junior high school mathematics teachers could design more proper geometric learning activities to students, and helped them to figure out their own pedagogical conceptions of geometry, furthermore to facilitate their professional development of teaching.

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