國中資優數學中因式分解解題思路的探討

本研究是為了解決國中數學資優生的特殊學習需求，在普通班級中常被忽視的問題。故以國中數學領域課綱範圍為基礎，探討國中資優數學中關於因式分解的重要觀念及題型。故以國中因式分解課程為研究基礎，包含提出公因式，乘法公式，十字交乘法，代換法，一元二次方程式的判別與應用，教師能藉由教材，讓資優生能體會到數學問題的本質，並提供給學生多樣化的解題方法，培養學生獨立研究思考的習慣，提升學習興趣。大綱如下：一、國中資優數學中因式分解解題思路的教材，能提供學生不同的解題策略且在驗證答案的過程中，培養學生多元思考的精神。敏銳的觀察力與足夠的數學技巧能幫助學生做豐富及多元的推測有足夠的知識連結即能推敲出解題關鍵及技巧，並以此完成因式分解。二、研究者就常見的因式分解之題目分類並做分析。

關鍵字

因式分解；資優數學

並列摘要

This study aims to solve the problem of the mathematically gifted junior high school students’ special learning needs, which is usually neglected in regular classes. Based on Mathematics Learning Area in Grade 1-9 Curriculum,It investigate the important concepts and questions about Factorization based on the analysis of teaching curriculum in junior high school, especially for mathematically-gifted students. The analysis includes teaching materials on the common factors, multiplication formula, cross method, packet disassembly,and discrimination and application of quadratic equations, teaching materials on the Factorization 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, cultivated their habit of independent thinking, and further increased their interest in learning mathematics. The contents in brief are as follows: 1. The teaching materials in the present study provided students with different strategies and techniques to solve mathematics questions. Furthermore, in the process of answer validation, students’ diversified thoughts were built. Good observation and enough mathematical knowledge can help students extensive speculated con jectures, with adequate knowledge links that can associate with solving keys and skills, and help students solve problems. 2.Researcher analyze the common formulas of factoring prombles.