發展十一年級學生臆測及辯證能力－－以二進位數字樣式探究活動為例

Developing Eleventh Graders' Conjecturing and Justifying Power on Generalization of Binary Number Patterns

本研究針對五位十一年級學生參與為期四週的課外數學探究活動進行觀察，藉以了解學生如何在解決數字樣式問題的過程中發展臆測及辯證能力。研究架構以社會學習面向為基礎，主要考量學生的臆測及辯證能力發展於同儕間之互動、對話與論證等學習行為。另本研究以個案研究為主進行資料蒐集及分析，從而瞭解學生數學臆測及辯證學習行為發展過程。研究結果顯示，學生在臆測情境氛圍中能夠有機會揭露並發展內在的數學能力，此外，學生在數學臆測的過程中不僅能彈性運用特殊化及一般化策略，更能提出令人驚豔的說明為其數學想法進行辯證。根據研究發現「關係式理解」對於學生臆測及辯證能力之發展至為關鍵。

This study is due to investigate five eleventh graders of how they developing conjecturing and justifying power in the context of binary number pattern-finding problems. The framework of the research is situated in the social perspective which considers that the development of students' conjecturing and justifying power should be much relied on interactions, dialogues and argumentations within peers. Qualitative case study design and analysis strategy is adopted in the study for constructing a holistic viewpoint of students' mathematical conjecturing and justifying behavior. Research results show that students' inherent capabilities could be revealed when they are engaged in an atmosphere of conjecturing. Besides, students could not only apply specializing and generalizing strategies flexibly but also propose impressive justifications to make others convinced during the process of conjecturing. All of the findings seem to imply that relational understanding is crucial for students to develop their conjecturing and justifying power.