本研究目的為探討在數學臆測教學下引出學生論證元素的教師提問。本研究採個案研究法，研究對象為1位進行多年臆測教學的教師與25位歷經一年臆測教學的四年級學生。本研究資料蒐集的方式是教學觀察影帶及學生的猜想單。資料分析的焦點是教師提問與學生論證，先對師生對話進行編碼，再畫出提問圖，編碼的過程會利用影片與錄音進行來回比對以求信度。
研究結果顯示在數學臆測教學的階段中有以下發現：
（一） 在效化階段中，每個討論主題都能引出資料、證據、支持和修飾，而且經過一連串討論後再回到討論主題能幫助學生思考，還有當猜想寫法不同時修改成相同寫法能幫助學生理解。
（二） 在一般化階段中，因為經過效化階段充分的討論，能使學生容易達成共識，而且教師利用建構結果的提問更容易引出學生的論證。
（三） 在證實階段中，連續的教師提問更能引出學生的論證，而且在討論證實的順序時教師和學生都不會以資料說明想法，在討論證實的策略時教師利用描述做法來徵求學生的策略且用演示做法來說明該策略，在討論證實的做法時教師會使用確認、推測和理由引出資料、證據和支持來說明該做法。
研究結果顯示在數學臆測教學的論證元素中有以下發現：
（一） 大部分的資料能使用單一提問引出，其中確認是最容易引出資料的教師提問，當學生越回答不出來時可以引出資料來說明。
（二） 主張能被所有的教師提問引出，但在討論證實的順序時不容易引出主張，而在合併想法時可以使用以前的結論、術語與建構結果來引出主張。
（三） 證據能被所有的教師提問引出，在效化階段時用單一提問就能引出證據，而當證據不明顯時需要問尋求想法來引出證據，當教師用追問的方式提問更容易引出證據。
（四） 反駁容易被確認、推測和建構結果引出，而且反駁後會伴隨著證據與修飾。
（五） 支持容易被教師提問引出尤其是確認和理由，在討論證實的做法時可以用尋求真實答案、尋求想法與尋求說明引出支持。
（六） 修飾容易被確認、術語與描述做法引出，在證實階段時可以利用推測或建構結果來引出修飾。
（七） 反反駁必然在反駁剛出現就被引出，教師可以用推測來促使反反駁被引出。

The purpose of this study was to explore how teacher’s question to elicit students’ argumentation in mathematically conjecturing teaching. A case study method was adpted. The subject of the research was an experienced teacher who has been teaching conjecturing teaching for 5 years amd 25 fourth-grade students with one year engaging in conjecturing. The main data collection of this study was observation teaching tapes and students’ conjecture. The focus of data analysis was teacher’s questioning and students’ argumentation, and then decodeing, and then drawing the questioning diagrams. When I code, I used to compare the video and the recoding for reliability.
The research result shows the following finding in mathematically conjecturing teaching:
(1) At the stage of validation, every topic can elicit Data, Warrant, Backing and Qualifier; after a series of discussions, going back to discuss the original conjecture can help students understand; when conjecture different ways of writing, you can change the same way of writing to help other students understand.
(2) At the stage of generalization, student easily reach consensus, because they have fully discussed; and teacher ask Constuct Reasult easily elicit student’s argumentation.
(3) At the stage of justification, teacher’s continuous questioning is more able to elicit students’ argumentation; when they discuss to arrange the order of justification, teacher and students are not use Data to elaborate the idea; when they discuss the strategy of justification, teacher use Describe a Method to ask students’ strategy, and use Demonstrate a Method to elaborate the strategy; when they discuss the method of justification, teacher use Identification, Conjecture and Justification elicit Data, Warrant and Backing to elaborate the method.
The research result shows the following finding in the argumentaion of mathematically conjecturing teaching:
(1) If you want to elicit Data, you just need use one questioning; Identification is the easiest questioning to elicit Data; when students haven’t response, teacher can try to elicit Data to elaborate the idea.
(2) If you want to elicit Claim, you can use all teacher’s questioning; when you discuss the order of jusificaion, it’s not easily to elicit Claim; when you combine the conjecture, you can use Previous Result, Term and Construct Result to elicit Claim.
(3) If you want to elicit Warrant, you can use all teacher’s questioning; you can use one questioning to elicit Warrant in the stage of validation; when Warrant is not trivial, you can use Requesting an Idea to elicit Warrant; when teacher continue to ask, it’s easily to elicit Warrant.
(4) If you want to elicit Rebuttal, you can use Identificaion, Conjecture and Construct Result; Rebuttal will be accompanied by Warrant and Qualifier.
(5) If you want to elicit Backing, you can use Identification and Justification; when you discuss the method of justification, you can use Requesting a Factual Answer, Requesting an Idea and Requestin a Elaboration.
(6) If you want to elicit Qualifier, you can use Identification, Term and Describe a method; you can use Conjecture and Construct Result to elicite Qualifier in the stage of justification.
(7) If you want to elicit Anti-rebuttal, you can use Conjecture; Anti-rebuttal must apper after Reburral and be elicited.

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