數學臆測可以激發學生互相學習的動力，進而展開數學論證。本研究採個案研究，旨在針對在補習班透過數學臆測教學模式的前三個階段，探討五年級學生從未知的數學問題到完成解題導向中的數學論證表現。

研究初步顯示，第一次接觸臆測教學的學生在小組論證的論據都是非證據
論述，所有論據都來自於工作彙整單的數據資料，但隨著臆測教學持續進行時，學生可以開始連結甚至於模仿他組的資料，發現另一種證據，而開始發表觀察之結果，學習用憑據說理，說服他人。全班兩組學生採同質性分組，對於中低成就的學生經過臆測教學的洗禮，第二階段到第三階段的論據內容及論證表現由平乏至充實，完成解題目標。而中高成就的學生在證據的內容有不錯的表現，有效論據品質的次數較多。不過兩組學生的反駁次數，只有中低成就的學生在組內分享時，提出反駁類型但符合有效反駁只有兩次，其餘為無效反駁，全班真正有反駁例為零，可能在於學生的論據內容多屬雷同性質，無法產生反駁。

學生在臆測教學的循環過程中，歷經一次次的自我反思及他人的檢驗，為
了要捍衛自己的想法，而引發學生的論證，論證結構的論據元素多元且完整，則論證品質就提升。要發展論證教師設定的目標、教學任務設計的內容以及教師的臆測教學經驗與專業知識，也會影響學生的論證結構而使得論證表現及品質有所影響。

Mathematical Conjecturing can motivate students to learn from each other, and then develop mathematical arguments. This study is a case study aimed at exploring the first three stages of the teaching model through mathematical conjecturing in the cram school, to explore the performance of fifth grade students from the unknown mathematical problem to the completion of the problem-solving oriented mathematical argument.

The research shows that the first time of students who have been exposed to mathematical conjecturing teaching are in non-evidence argumentation. All the arguments come from the data of the worksheet, but as the conjecturing teaching continues, students can start to connect even Imitating the data of his group and found another kind of evidence, and began to publish the observation results, learn to use evidence to reason, and persuade others. The two groups of students in the class are grouped in a homogeneous manner. For students with low and medium achievements, after the baptism of conjecturing teaching, the content and argument of the second stage to the third stage are ranging from ordinary to full understnading, and the problem is solved. The students of middle and high achievements have a good performance in the content of the evidence, and the number of valid arguments is high. However, the number of rebuttals of the two groups of students, only the students with low and medium achievements shared the type of rebuttal in the group, but only met the effective rebuttal twice, and the rest were invalid rebuttals. There are really zero rebuttal examples in the class, which may be the student’s argument. The content is mostly likely the same natures and cannot be refuted.

In the course of conjecturing teaching, students have undergone repeated self-reflections and other people's tests. In order to defend their own ideas, students' arguments are triggered. The argument elements of the argument structure are diverse and complete, and the argument quality is improved. It is necessary to develop the goals set by the teachers, the content of the teaching task design, and the teachers’ conjecturing teaching experience and professional knowledge, which will also affect the students’structure of the argument and affect the performance and quality of the argument.

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