探討三年級學生問題解決歷程與課室討論文化的關係

摘要
本研究為探討課室討論文化教學模式與三年級學生問題解決歷程的關係。研究者以實地參與教室觀察的方式，蒐集學生解題歷程相關資料，從中分析以瞭解課室討論文化教學模式下，課室社群成員的對話類型，及社會數學規範的磋商形成，對學生問題解決歷程的發展。
本研究結果分為三個面向加以描述：第一面向，探討課室社群成員的對話類型與問題解決歷程的關係，對話類型分別為：理解性對話、解釋性對話、關聯性對話、批判性對話、規範性對話。第二面向，探討社會數學規範的形成與問題解決歷程的關係，社會數學規範分別為：可接受的數學解釋、多樣性的解題策略、精簡的解題紀錄。可接受的數學解釋，包括：以說明算式填充題連結問題情境、以說明解題紀錄連結問題情境、以數學語言說明解題紀錄連結數學概念。第三面向，探討社會數學規範暨對話類型的交互作用與問題解決歷程的關係。
在本研究中，研究者發現規範性對話促使社會數學規範的形成，而豐富對話類型的對話內容，尤其是批判性對話，學生對於他人的提問，不再只是重複解題算式的數字，而是說明解題情境的建構歷程，分享解題歷程，而促進學生問題解決歷程的發展。因此，研究者認為，對話類型、社會數學規範與問題解決歷程有相互影響的關係。
本研究建議教學者注意教學語詞的使用，及適時善用學習機會點觸發關聯性對話，促進課室成員對於數學知識的連結。

關鍵字：問題解決歷程、課室討論文化、對話類型、社會數學規範。

A study of relationships between the processes of problem solving and the mathematics class discussion culture of the third- grades
Abstract
This study discusses the relationships between the processes of problem solving and the mathematics class discussion culture of the third-grades. The researcher gathered data from observing the processes of students’ problem solving in class under the “cultural conceptual competent learning of teaching model（CCCLT）”. The researcher analyzed how the types of the students’ discussion and the development of sociomathematical norms to affect the processes of problem solving.
The results of this research revealed as the follows three apart. First, exploring the relationships between the types of the students’ discussion and the processes of the students’ problem solving. There are five types of the students’ discussion: reasoning discussion; explaining discussion; relational discussion; critical discussion; normal discussion. Secondly, exploring the relationships between the development of sociomathematical norms and the processes of the students’ problem solving. There are three kinds of sociomathematical norms: acceptable mathematical explanations; multiple solving strategies; sophistical solving records. Acceptable mathematical explanations include: using fill-in the blank problem connected with problem situations, explaining solving records connected with problem situations, using mathematical language to explain solving records connected with problem situations. Thirdly, exploring the relationships between the sociomathematical norms interweaving with the types of the students’ discussion and the processes of the students’ problem solving.
In this study, the researcher found that the normal discussions prompted the students to form sociomathematical norms, the rich discussion content in the type of the students’ discussion can accelerate the development of students’ problem solving. For example, as the students discussed others’ proving questions in the type of critical discussion, they can explain others’ solving problem situation and share theirs solving processes rather than just repeat the numbers in the solving records. Therefore, we supposed that there are corrections between the types of the students’ discussion, sociomathematical norms and the processes of solving problem.
This study suggested that teachers should take care of using teaching language, and they appropriately adopted learning opportunities to stimulate the students to form the relational discussion and encourage students to connect their mathematical knowledge.

Keyword: the processes of the problem solving, the culture of the class discussion, the types of the students’ discussion, sociomathematical norms.

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