國中資優數學之二次方程式的探討

本研究旨在探討國中資優數學中關於二次方程式的重要觀念及題型。故以國中方程式課程為研究基礎，包含二次方程式的探討與其應用，並從補充教材及資優相關考題進行分析，並編寫國中資優數學關於二次方程式的教材，希望藉以提升國中數學資優生的數學學習能力。讓學生除了能利用舊經驗解題，也能建構新觀念，使數學資優生能針對題目作有系統的分析，建構有效的解題策略並有能力呈現邏輯清晰的解題歷程。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另一層的思維，了解到其本質上具多樣性，活化並刺激學生的學習。本研究經由文獻探討與試題分析後獲得以下結論： (一)在方程式的解題中，對於題意的了解為解題之第一要務。要能將文字敘述轉換成數學文字符號的過程中，閱讀能力也就非常重要。 (二) 足夠的數學知識能幫助學生做正確的推測，有了足夠的知識連結即能聯想到解題關鍵，並能以此二次方程式來解決數學問題。 (三) 清晰明確的計算過程有助於學生正確的求出答案。

關鍵字

數學資優生；二次方程式

並列摘要

This study aims to investigate the important concepts and questions of quadratic equations based on the analysis of teaching curriculum in Grade7-9, especially for mathematically- gifted students. The analysis includes discussion and application of quadratic equations. supplementary teaching materials, and tests specifically designed for gifted students. In addition to analysis, compiling teaching materials are used to enhance the ability of mathematically gifted students in mathematics earning. The results of this study could facilitate students to make use of experiences to solve problems and to construct new ideas make mathematically gifted students analyze systematically for the statement of questions, construct effective problem-solving strategies, and complete the logical clarity of problem- solving process.In this research, related questions are collected, organized, classified, and analyzed. And through these materials, students can contemplate more deeply what is under the surface questions and learn various forms of quadratic equations . Thus, students’ learning can be activated and stimulated. It should be concluded from literature reviews and the analysis of tests, as following 1. Understanding the statements is the first priority of solving problems. For being able to convert statements into mathematical symbols, reading skills are very important. 2. Getting enough mathematical knowledge can help students to make the correct conjecture, with adequate knowledge links that can associate with solving keys,and help students to solve mathematical problems by quadratic equations. 3. Clearly calculating process can help students to find out the answers correctly.