國中三角五心教材之研究

本研究旨在國中資優數學教育裡三角五心教材之研究與編撰。目標為增進國中學生利用圖形加強邏輯思考的判斷與想法。研究主要以蒐集、整理、分類、解析相關試題，藉由教材讓學生對數學問題有更深層的思維，了解到其本質上之多樣性，活化並刺激學生的學習。本研究經文獻探討語試題分析得到以下結論：一、國中資優數學教育之三角形五心問題的教材，能使學生從不同層面分析解題，進而培養國中學生多角化思考的能力。二、研究者所提出的解題手法整理如下： (1)多方思考並嘗試根據題意作圖 (2)輔以先前所學之概念,試做輔助線，協助解題 (3)利用定理與性質輔佐驗證解題思維之正確性

關鍵字

資優數學；三角形五心

並列摘要

This research is aimed to discuss questions and principles of gifted mathematics in some courses of Triangular Five Center Questions in junior high school in order to improve junior high school students' judgement and realization of logical thinking. In this research, related questions are collected, organized, classified and analyzed. And through these materials, students an contemplate more deeply what is behind the questions and learn a variety of methods of solving questions. Thus, students' learning can be activated and stimulated. After demonstrated literature review and item analysis, the researcher has come to the following conclusions: A. Materials of Triangular Five Center Questions in gifted mathematics in junior high school can lead students to acquire different strategies and techniques to solve mathematical questions. Meanwhile, students' diversified thoughts are developed. B. Strategies and techniques that the researcher proposed are showed below: 1. Think in various ways and try to make graphs according to the questions' statement. 2. Apply techniques and strategies taught before and make auxiliary lines to help solving problems. 3. Use theorems and properties to assist verify the correctness of the problem-solving thinking.