本研究旨在探討高中學生在局部推理實驗教學活動下，其數學證明能力發展的情形。主要研究目的包括有下列兩項 (1) 設計局部推理的教學活動，並因應發展數學局部推理的教學套件(包括偵錯、排序、配對、接龍)，以及評估數學證明教學實驗活動的成效。(2) 探討高中學生在數學證明教學實驗活動中認知、情意及態度等特質。
本研究之研究方法可分為問卷調查法及準實驗研究設計。
針對本研究之目的，主要的研究結果如下：
一、本研究教學實驗活動分別在三個高二班級進行，根據前測、後測及延後測所得成績分析顯示，在實驗教學活動後發展數學局部推理能力方面：實驗組一局部推理小組合作學習與實驗組二局部推理較傳統教學對照組有較佳的表現。而在兩個月延後測發展數學證明能力方面：實驗組一局部推理小組合作學習與實驗組二局部推理活動均較傳統教學對照組為佳。
二、在不同教學法下，局部推理能力的發展與數學證明能力的發展有顯著相關。
三、在進行實驗教學後在數學論證試題記憶性與數學證明能力推論的學習遷移性方面：實驗組一局部推理小組合作學習有較佳的學習成效。
四、根據教學回饋問卷顯示在實驗教學後，實驗組一局部推理小組合作學習及實驗組二局部推理活動均較對照組無論是在證明能力自我評估方面或是對數學證明興趣方面均有提昇。
本研究除對研究結果加以分析討論外，研究者並提出在證明教學活動及未來後續研究發展上的具體建議。

The purpose of this study was to examine the mathematical global reasoning ability development of senior high school students who participated in the experimental teaching of local reasoning. There are two main goals: (1) to design teaching activities for local reasoning, develop the corresponding sets for teaching activities (including detecting, ordering, matching, solitaires) and evaluate effects of all the activities, and (2) to explore senior high school students’ cognitive characteristics and attitudes in experimental local reasoning teaching activities.
The methods for this study are questionnaire method and quasi-experimental research design.
The main findings of this study are:
1. In this experimental teaching activity, three sophomore classes were divided into three groups: the experimental group A (local reasoning interactive group cooperation), the experimental group B (local reasoning interactive teaching), and the contrastive group (traditional teaching). The pretest, posttest, and delay-posttest scores show that, compared with the contrastive group, the experimental groups have better achievements in local reasoning after the treatment. And the two-month retention scores reveal that the experimental groups also do better in developing mathematical global reasoning ability.
2. Under different teaching methods, the development of local reasoning and mathematical global reasoning ability are highly related.
3. After the experimental teaching, the experimental group A do better in terms of mathematic reason question memory and the transfer learning of mathematical reasoning ability.
4. Findings of the feedback forms show that, after the treatment, the experimental groups have significant improvements in self-evaluation of mathematical reasoning ability and the interests towards reasoning.
In addition to the analysis of and discussions on the findings, the researcher also provides suggestions for teaching reasoning and for the follow-up researches.

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