全國高中教甄試題—解題之迷思與探討

National High School Teach Validation Tests-Myths and Discuss of Problem Solving

蔡韋鋒(Wei-Feng Tsai)

指導教授 ： 王牧民

中原大學/理學院/應用數學研究所/碩士(2015年)

https://doi.org/10.6840/CYCU.2015.00154

摘要

本研究旨在針對歷屆全國高中教甄試題，進行試題之分析及探討，以高中數學領域99課綱範圍為基礎加以分類，並將分析及探討的結果作為編寫高中資優數學之教材，讓教師能藉由教材使資優生能體會到數學問題的本質，並提供其多樣化的解題方法，培養學生創造思考的能力，並提升學習興趣。大綱如下：
一、因應高中教甄題目多為各國數學競賽試題，故針對高中教甄試題進行試題之分析及探討，並作為資優數學教育之教材，期望能讓學生不斷思考解題策略，並在驗證答案的過程中，培養其分析與多元思考的能力。
二、研究者就「高中課程內容，包含數列、級數、方程式、不定方程、整數論、多項式、根與係數關係、二次函數、函數圖形的對稱性、排列組合、機率與統計、三角、向量、幾何、柯西不等式、算幾不等式、極值問題、圓錐曲線、矩陣與行列式、微積分等」來做思維統整。

關鍵字

資優數學 ； 高中教甄

並列摘要

This study aims to solve the problem of national high school teach validation tests. Based on Mathematics Learning Area in Grade 10-12 Curriculum, teaching materials for these students were designed to make them understand the essence of mathematics questions. In addition, the teaching materials provided the students with various ways to solve mathematics questions, developed students' creative thinking ability, and further increased their interest in learning mathematics.
The contents in brief are as follows:
1. The problem-solving of national high school teach validation test to be the teaching materials of gifted high school mathematics allowing students to continue to think about problem-solving strategies, in answer validation process, to develop their ability to analyze graphics and diverse thinking.
2. Researchers on the " The high school curriculum, including the number of columns, series, symmetry equation, equation, integer theory, polynomials, the relationship between roots and coefficients, quadratic function, the function graph, permutations and combinations, probability and statistics, trigonometry, vectors, Cauchy inequality, few count inequality, extreme value problems, conic sections, matrices and determinants, calculus… " to do thinking integration.

並列關鍵字

gifted mathematics ； High school teach validation tests

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