國小三年級課室以數學臆測活動引發學生論證初探

The Exploration of Conjecturing Provoking Argumentation of Mathematics in a Third Grade Classroom

10.6173/CJSE.2015.2301.04

林碧珍(Pi-Jen Lin)

小學三年級 ； 數學課堂論證結構 ； 數學論證 ； 數學臆測 ； Third Grade ； Structure of Argumentation in Classroom ； Argumentation ； Conjecture

科學教育學刊

23卷1期（2015 / 03 / 01）

83 - 110

繁體中文

本研究旨在探討數學臆測活動融入三年級課堂學生所展現的數學論證歷程。本研究的數學臆測是數學課堂中，先由學生造例以建立資料；然後觀察以尋求規律性，並提出猜想；再共同檢驗猜想的正確性，及驗證猜想的一般化之歷程。數學論證是在進行臆測教學活動脈絡下產生的，故它是數學臆測的一部分；它是從建立資料及證據作為形成論述或檢驗論述的依據，以支持結論的過程。本研究採用質性研究法，觀察一位個案教師將臆測融入三年級的數學課堂教學。蒐集資料包括錄影及錄音逐字稿、學生解題紀錄、觀察記錄、任務設計簡案、教師的數學日誌。學生的論證分析以Toulmin（1958）的論證模式為基礎，並修正Reid與Knipping（2010）的論證結構圖而畫出論證結構圖。研究發現：數學臆測活動可以引發三年級學生的數學論證。對數學知識不夠豐富的三年級學生，大都是以例子作為推論依據，以捍衛自己提出的猜想，學生所展現的論證層次是落在Balacheff（1988）的原始試驗層次。臆測活動不僅可以培養學生的論證能力並意義化數學性質，並在論證過程中釐清了學生的迷思概念、修正學生不精確的數學語言。學生的論證結構圖可以顯現出教師在學生論證過程中介入的時機及次數，也可以顯示學生從提出猜想通往結論所發生的反駁、推論依據的論證歷程。

The purpose of the study was to explore how third-graders engaged in mathematical argumentation where conjecturing was integrated into mathematics instruction in a classroom. Conjecturing involving in the study is defined as a reciprocal process while facing an uncertain mathematical task in classroom, students via individual or small group construct data, observe and look for the pattern of the discrete cases, propose a plausible conjecture in accordance with given conditions, test, justify and verify the conjectures proposed. Argumentation defined in the study is the product of the conjecturing, so that it becomes the part of the conjecturing. Argumentation is a process from data to conclusion by using warrants or backings as arguments. The study adopted a qualitative research method to observe a third-grader teacher who was participating in the ＂Designing Conjecturing Tasks for Enhancing Teachers Professional Development＂ project that is designed to support in-service teachers in designing conjecturing tasks and integrate conjecturing into classrooms. The data collected for the study included videotapes and audio-tapes transcription verbatim, students' work scanned, researcher's note, and teacher's brief lesson plan. The analysis of argumentation was based on Toulmin's model (1958) and modified from Reid & Knipping (2010) argumentation structures. The results indicated that conjecturing was able to initiate students' argumentation. Third-graders mostly utilized empirical examples as warrants for supporting their conjectures. The quality of argumentation for the task used in the study was staying in Balacheff's (1988) level of naive empiricism. Conjecturing was not only to promote students' argumentation but also conceptualize the meaning of mathematical concepts or mathematics relationships, clarify students' misconception, and modify students' unprecise mathematical language. The structure of argumentation revealed the timing and frequencies of teacher's innervations. The argumentation structure displayed the frequencies of warrants and where the warrants occurred after students gave a conjecture approaching to conclusion.

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