數學臆測教學下教師提問類型之個案研究

本研究欲探討在數學臆測教學課堂中，當學生分享想法，解釋想法不正確或不完善時，教師提問類型的目的，幫助學生解釋想法，完善想法。因此本研究針對教師在數學臆測教學課堂對於學生提問類型進行研究，分析教師之提問類型對於學生在解釋上的影響。本研究採取個案研究法，需要透過進入臆測較學的課堂中進行觀察，為了避免研究者主觀推論，因此透過錄影、錄音等方式進行資料的收集，以確保客觀的分析。教師提問類型的分析主要以Franke,Webb,Chan, Ing ,Freund與 Battey （2009）所提出的提問類型架構為基礎進行修改，分為五種提問類型分別為探索性提問、具體性提問、引導式提問、一般性提問以及其它提問，將這五種提問類型的目的細分為十一種進行教師提問的分析。研究初步發現，教師在數學臆測教學三階段中，需要請學生進行分類理由或猜想的分享，因此教師提問類型以引導式提問為主，透過引導式提問按部就班引導學生進行解釋上的完整以及修正，循循善誘的引導，不只讓學生學生能夠理解其猜想法，更能夠幫助其他學生了解思考的脈絡；探索性提問在三階段中最常被教師用來引出學生的初步解釋，擬定方法幫助學生進一步的修正，可能是利用其他的提問類型，抑或是其他教學策略；在數學臆測三階段中一般性提問最常被用來向學生進行理解及共識的確認，當學生皆能接受及理解時，教師才進行下一步的教學；然而在數學臆測教學三階段中，具體性提問較少被使用，由於數學臆測教學主要是讓學生透過觀察發現關係並將想法以文字描述寫下，較少使用計算類型的布題進行教學，導致具體性提問的出現次數也隨之減少。

關鍵字

數學臆測；教師提問；數學提問

並列摘要

This study is intended to explore the purpose of the type of teacher questioning in helping students explain ideas and improve their thinking in the classroom of mathematical conjecturing. When students share ideas and explain incorrect or imperfect ideas. Therefore, this study is aimed at teachers in the mathematical conjecturing teaching class to study the types of student questions, and analyze the influence of teachers' questioning types on students' interpretation. This case adopts a case study method, which needs to be observed through the classroom of entering the test. In order to avoid the subjective inference of the researcher, the data is collected through video recording and recording to ensure objective analysis. The analysis of teacher question types is mainly based on the questions type structure proposed by Franke, Webb, Chan, Ing, Freund and Battey (2009). The five questioning types are exploring questions, specific questions, and leading questions, general questions, and other questions, the purpose of these five types of questions is subdivided into eleven kinds for the analysis of teacher questions. The preliminary study found that teachers need to ask students to share the reasons for classification or conjecture in the three stages of mathematics conjecturing teaching. Therefore, the types of teachers' questions are mainly leading questions, and the students are lead to complete the explanation and correction through leading questions. Lead by enthusiasm, not only allows students to understand their conjectures, but also helps other students understand the context of thinking; Exploring questions is the most common explanation used by teachers in the three stages to lead students out. The method is to help students to further correct the problem. It may be to use other types of questions or other teaching strategies. In the three stages of mathematical conjecturing, general questions are asked. Most commonly used to confirm and understand the understanding of the students, when the students can accept and understand, the teacher will carry out the next step of teaching; however, in the three stages of mathematics conjecturing teaching, specific questions are rarely used, due to mathematical conjecturing teaching is mainly to let students discover the relationship through observation and write the idea in words, and use less computational type of questions to teach, which leads to the reduction of the number of specific questions.This study is intended to explore the purpose of the type of teacher questioning in helping students explain ideas and improve their thinking in the classroom of mathematical conjecturing. When students share ideas and explain incorrect or imperfect ideas. Therefore, this study is aimed at teachers in the mathematical conjecturing teaching class to study the types of student questions, and analyze the influence of teachers' questioning types on students' interpretation. This case adopts a case study method, which needs to be observed through the classroom of entering the test. In order to avoid the subjective inference of the researcher, the data is collected through video recording and recording to ensure objective analysis. The analysis of teacher question types is mainly based on the questions type structure proposed by Franke, Webb, Chan, Ing, Freund and Battey (2009). The five questioning types are exploring questions, specific questions, and leading questions, general questions, and other questions, the purpose of these five types of questions is subdivided into eleven kinds for the analysis of teacher questions. The preliminary study found that teachers need to ask students to share the reasons for classification or conjecture in the three stages of mathematics conjecturing teaching. Therefore, the types of teachers' questions are mainly leading questions, and the students are lead to complete the explanation and correction through leading questions. Lead by enthusiasm, not only allows students to understand their conjectures, but also helps other students understand the context of thinking; Exploring questions is the most common explanation used by teachers in the three stages to lead students out. The method is to help students to further correct the problem. It may be to use other types of questions or other teaching strategies. In the three stages of mathematical conjecturing, general questions are asked. Most commonly used to confirm and understand the understanding of the students, when the students can accept and understand, the teacher will carry out the next step of teaching; however, in the three stages of mathematics conjecturing teaching, specific questions are rarely used, due to mathematical conjecturing teaching is mainly to let students discover the relationship through observation and write the idea in words, and use less computational type of questions to teach, which leads to the reduction of the number of specific questions.