關於高中學生數學建模指導之研究

Abstract

數學建模是國內數學教育改革中一個新興的議題，尤其是新修訂的高中數學課程綱要（草案）中，即明確指出要發展學生數學建模的基本能力。

本論文首先針對數學建模作理論上的介紹（第一章），探討學習數學建模的意義，以及數學建模在國內外的發展狀況。數學建模之受到重視，實肇因於透過數學解決現實生活中的問題，許多人文社會及自然科學的學術研究都需要數學的參與。在高中的數學基礎教育階段，指導學生進行簡易的數學建模，培養數學建模的思維亦有其意義（第二 章）。從近幾年的大學入學考試試題中，可以發現數學建模概念題是相當受重視的，這些題目可以成為我們指導學生進行數學建模的題材(第三章)。

許多數學軟體可以協助我們解決數學建模中不可避免要處理的各種數據資料，其中亦有免費的自由軟體如Scilab 及Maxima。本論文將對它們的功能做簡單的介紹，並實際運用於數學建模的過程中（第四章）。結合前述理論上的探討，我們將針對研究過程中所探討的數學建模相關課題作細部介紹(第五章)。

Mathematical modeling is a current issue in mathematics education in Taiwan or even worldwide; in particular, the ability of handling mathematical modeling is among the core abilities claimed in the Mathematics Curriculum (draft 2006) for the senior high school students in Taiwan.

Mathematical modeling will be first recalled from the theoretical view point in Chapter 1,including its significance, the status in developing mathematical modeling in Taiwan and other countries. It must be emphasized that the problems in real life have continuously been solved by mathematical ideas and methods as well in the framework of mathematical modeling, and mathematics has always played a vital role in academic researches such as humanities and social sciences, natural sciences. The significances of instructing students with the abilities in thinking and handling mathematical modeling will be surveyed in Chapter 2. The concept of mathematical modeling has also been one of the focuses in the college entrance examination recently, some of these problems are collected in Chapter 3 followed by some detailed analysis from the view points of mathematical modeling.

Many mathematical softwares, including freewares such as Scilab and Maxima, are now available for treating complicated and huge mount numerical data involved in mathematical modeling. Their functions used in the processes of mathematical modeling will be provided in Chapter 4. Some problems with real immediate applications involved in this research are provided in the final Chapter 5 together with detailed analysis.