本研究是描述研究者以設計臆測任務融入國小三年級數學教學的行動研究歷程，說明研究者在設計數學臆測任務及進行數學臆測教學時所遭遇到的問題及因應策略，進而從中了解教學問題及學生的學習情形，透過因應的解決策略來增進自己的數學教學知識及數學教學專業知能。
研究者以自己任教的三年級班級為研究場域，並在數理研究所進修時加入跨校教師數學專業成長團學習數學臆測教學。研究者以學生現有的數學教科書教材(三上「圓」及三下「面積」兩個單元)進行教材分析及前測分析，發現教材的不足及學生的迷思，進而設計數學臆測任務，並以數學臆測教學模式的五個階段(造例組織觀察、發現關係並提出猜想、驗證猜想、猜想一般化、證明一般化)來融入數學教學活動以達到教學目標。研究期間，研究者透過教材分析、前測分析、教學實踐錄影錄音、學生解題工作單記錄、成長團隊專業對話、教師教學日誌、諍友討論等資料的蒐集與分析，進行教學反省及改進，讓研究者對於學生的學習情形及自身的教學專業有更多的了解及成長。
研究結果發現，一個設計良好的數學臆測任務，可以讓數學臆測教學的進行更加順利，因此，教師的數學專業知識及分析教材能力，對於設計數學臆測任務是有所幫助且重要的。在實施數學臆測教學方面，「造例組織觀察」階段透過臆測任務的活動設計能讓學生建立多例來組織觀察出規律；「發現關係並提出猜想」階段要鼓勵學生寫出自己的數學想法及發現，來引動學生的豐富猜想；「驗證猜想」階段讓學生經由發表及聆聽，判斷此猜想的正確性，當小組提出的猜想經過驗證，就成為全班的猜想；「猜想一般化」階段是將從有限例觀察得到的全班猜想繼續擴充到其他所有類型，但因為三年級學生的數學知識尚未完整，因此只能以「限制條件」擴充；「證明一般化」階段則是培養學生能運用已知的事實或所學的數學知識進行演繹推理來證明尚未證實的猜想，但因為三年級學生的數學知識還不夠豐富，因此可以運用說理來說服別人。最後，本研究對於有興趣進行數學臆測教學的教育者分別對數學臆測任務設計、數學臆測教學及未來研究方向提出建議。

This research describes the process of merging the designing of conjecturing task into 3rd grade math classes. During the designing mathematics conjecturing task and the teaching of mathematical conjecture teach, the problems faced with and the strategies come up by the researcher are demonstrated, in order to understand the issues of the teaching and learning process. My professional and teaching knowledge in math has been broaden by the strategies aforementioned.
The researcher takes her own classes as the research area and incorporates cross-school teacher professional growth team into mathematics conjecturing teaching during her master degree in math and science. She performed the analysis of teaching material and pretest with the given math textbooks for two chapters: Circle (the first semester) and Area (the second semester). Throughout the process, the insufficiency of the material and the confusion of the students inspired the mathematics conjecturing task. Thus, the five stages in the framework of mathematics conjecturing teaching mode (product - organization - observing example, discovering relations and proposing hypotheses, verifying the hypotheses, generalizing the hypotheses and generalizing the proofs) are included in the math teaching activities to complete the teaching goals. During the research, the researcher has gained improvements and self-reflections through the analysis of teaching material and pretest, the recordings of classes, student worksheets, conversations among the growth team, teaching journals and discussions between critical friends . As a result, the researcher is able to enhance her understaning of the profession of teaching and the learning process of students.
From the result, a well-designed conjecturing task in mathematics helps teaching progress more smoothly, so a teacher's professional knowledge and the ability to analyze the teaching material is critical as well as benefical for designing conjecturing task. From the aspect of applying conjecturing task in mathematics, the stage of " product - organization - observing example "" helps students to construct more cases to find patterns through conjecturing task. "Discovering relations and proposing hypotheses" encourages students to express their thoughts and discovery as well as stimulate their creativity. "Verifying the hypotheses" allows students to determine the correctness of the hypotheses by presenting and listening. When a hypothesis from a group is verified, it becomes the hypothesis of the entire class. "Generalizing the hypotheses" expands the observations to all types from that of limited examples. Due to the incomplete knowledge in math of the third grade students, the expansion is only through limited constraints. "Generalizing the proofs" educates students to exercise induction with known facts to prove the hypotheses. Since the math knowledge is not enough for 3rd grade students, they can convince others with reason. Lastly, this research proposes suggestions to educators who are interested in designing and teaching of mathematics conjecturing as well as research directions in the future.

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