為了觀察並分析師培者的專業覺察力，並比較兩岸師培者在覺察什麼與如何覺察的差異，本研究採個案研究法，選擇在科技部計畫下的兩岸學術論壇活動為背景，觀察參與活動的兩岸師培者們在臆測教學課堂覺察力的比較。
研究結果發現，兩岸師培者在覺察對象的部分，會同時關注學生和老師，偶而會以師培者本身的經驗或歷程做說明；在覺察主題的部分，兩岸師培者會同時關注數學思考，其次，台灣師培者聚焦數學內容，中國師培者聚焦老師的教學法；在覺察論證的方面，兩岸的師培者都傾向聚焦覺察猜想與支持例。
而兩岸師培者在如何覺察的部分，都關注發展證明、學生觀察的層次以及猜想品質，也都相當讚賞臆測教學的成效，以及臆測教學跟一般課堂教學活動的差異性。差異的部分，臺灣的學者比較重視學生數學概念的釐清、證明的層次、如何提昇學生的數學認知發展、老師在臆測教學各個階段的教學規劃以及教學細節，也比較強調教師如何提供學生鷹架。而中國學者則會比較重視課程的效率、學生思維的發展、文化規範層次、老師如何去發展設計出臆測教學任務、教師角色、數學術語化，以及教師介入的時機與方法。此外，臺灣老師提到了反例的例子，中國的學者關注教學計畫，同時重視回應其他評述者以進行交流，並覺察到台灣包班制和中國分科制教學形態的差異。
本研究顯示，兩岸的師培者在覺察臆測教學關注的重點有差異，但都能聚焦於學生數學思考，善用各種例子解釋學生的猜想，並針對證明的層次進行舉例說明，以及提供老師教學策略的建議。

In order to observe and analyze the professional noticing of the analysts, and to compare the differences between what the cross-strait educators notice and how they notice. This study uses a case study method. The background of the cross-strait academic forum activities was sponsored by the Ministry of Science and Technology. Observing the cross-strait teachers who participated in the activities, they were comparing the perceptions of teaching classrooms.
The study found that regarding the actors, the teacher educators on both sides of the strait notice on students and teachers at the same time. The teacher educators will occasionally explain the experience or resume of themselves. When regarding the topics, cross-strait teacher educators both noticed mathematics thinking. Secondly, Taiwanese teacher educators notice mathematics content, while Chinese teacher educators notice teacher's teaching method. In terms of argumentation, the teachers of both sides of the strait are inclined to notice conjectures and supporting cases.
About how teacher educators notice, the cross-strait teacher educators who notice the development is concerned with the development of proof, the level of student observation and the quality of conjectures. They also appreciate the effectiveness of speculative teaching and the difference between speculative teaching and general classroom teaching activities. In the difference, Taiwanese scholars pay more attention to the clarification of the mathematical concept of students, the level of proof, how to improve the development of students' mathematical cognition, the teaching planning and teaching details of teachers at all stages of speculative teaching, and also emphasize how teachers provide students with scaffolding. Chinese scholars will pay more attention to the efficiency of the curriculum, the development of students' thinking, the level of cultural norms, how teachers develop and design the teaching tasks, the role of teachers, the terminology of mathematics, and the timing and methods of teacher involvement. In addition, the Taiwan teacher mentioned examples of counterexamples. Chinese scholars pay attention to teaching plans and attach importance to responding to other commenters for communication. I also noticed the difference between the Taiwanese shift system and the Chinese sub-system teaching style.
This study shows that the teacher educators on both sides of the strait are different in their noticing of the focus of conjecturing. But they all notice students' mathematical thinking and use various examples to explain students' conjecturs. And give examples of the level of proof, and provide advice on the teacher's teaching strategy.

中文摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 V
表目錄 VI
第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的與問題 3
第三節 名詞釋義 3
第四節 研究範圍與限制 4
第二章 文獻探討 6
第一節 教師覺察力 6
第二節 數學臆測教學課堂 20
第三節 師培者的覺察力 29
第三章 研究方法與設計 32
第一節 研究方法 32
第二節 研究情境與對象 33
第三節 資料蒐集與分析 37
第四節 研究架構 47
第五節 研究流程 49
第四章 研究結果與討論 51
第一節 台灣師培者觀察臆測教學覺察什麼 51
第二節 中國師培者在觀察臆測教學覺察什麼 60
第三節 兩岸師培者如何覺察臆測教學之比較 69
第五章 結論與建議 132
第一節 研究結論 132
第二節 研究建議 136
參考文獻 138
中文參考文獻 138
英文參考文獻 140

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