國小整數加減乘除法和分數加減法的物件化動態運算呈現研究
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2007
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Abstract
本研究結合 World Wide Web Consortium (以下簡稱 W3C )標準組織制定的MathML (Mathematical Markup Language，數學標記語言)和 SVG (Scalable Vector Graphics，可縮放向量圖形)推薦標準，發展國小數學整數加減乘除運算和分數加減運算，物件化動態運算呈現輔助學習工具，針對國小一至二年級的二位數整數加、減、乘、除運算和三至四年級的同分母分數加、減運算，提供SVG物件化動態運算，藉由解題運算過程的物件化動態呈現，輔助學習低成就兒童學習解題運算概念以及熟練解題運算程序。另外，若學童在練習解題運算時，可以藉由本工具的物件化動態運算過程展示，觀察解題步驟與結果，協助學童精熟整數加減乘除運算和分數加減運算的能力，亦可做為教師進行補救教學的教學輔助工具。
研究方法採用 W3C 標準組織制定的 MathML （Mathematical Markup Language，數學標記語言）推薦標準，發展在網頁上呈現數學符號及運算式，以改善使用 HTML 標籤或點陣圖形模式呈現的缺點。並且採用 W3C 標準組織制定的 SVG （Scalable Vector Graphics，可縮放向量圖形）推薦標準，發展數學運算式運算過程的物件化動態呈現，以改善使用 JPG、 GIF、 PNG 等點陣圖格式檔案及使用 Flash 動畫格式檔案呈現數學運算式運算過程的缺點。另外，採用 AJAX （Asynchronous JavaScript and XML，非同步 JavaScript 及 XML），以非同步資料更新方式，在使用者電腦的瀏覽器背景環境，進行圖形資料下載以及與伺服器端進行資料庫查詢等工作，有效減少前端使用者等待網頁畫面資料更新的時間。
研究結果歸納如下：
1.使用 SVG 物件呈現數學算式的運算過程，將整數加、減、乘、除運算和分數加、減運算的解題過程，轉換為 SVG 文件，可以和其他符合 XML 規範的學習平台整合應用與資料交換。
2.本研究發展的物件化動態運算呈現學習工具，可做為國小學童整數加、減、乘、除法運算和分數加、減法運算的補救教學輔助工具，透過動態展示運算過程等設計程序，可以讓學童反覆觀察和操作解題的步驟與結果，協助學童精熟整數加減乘除運算和分數加減運算的能力。
E-learning is a kind of study way that can not be limited by time and space. In accord with modern plural society's different study demand and way, E-learning can really implement lifelong education. So, how to use information science and technology to set up an environment of e-learning is the important research topic in recent years. The purpose of this research is to implement a web-based tool with SVG. The tool is used not only in integer arithmetic operation of addition, subtraction, multiplication and division but also in fraction arithmetic operation of addition and subtraction. It provides a dynamic presentation of mathematical integer arithmeticoperation and fraction arithmetic operation for the k1-k4 students. While students have troubles in integer arithmetic operation or fraction arithmetic operation, the tool assists them with a dynamic presentation and practices by themselves. It also assists the low achievement students to study the concept of arithmetic operation and obtains the skill of operational process.
E-learning is a kind of study way that can not be limited by time and space. In accord with modern plural society's different study demand and way, E-learning can really implement lifelong education. So, how to use information science and technology to set up an environment of e-learning is the important research topic in recent years. The purpose of this research is to implement a web-based tool with SVG. The tool is used not only in integer arithmetic operation of addition, subtraction, multiplication and division but also in fraction arithmetic operation of addition and subtraction. It provides a dynamic presentation of mathematical integer arithmeticoperation and fraction arithmetic operation for the k1-k4 students. While students have troubles in integer arithmetic operation or fraction arithmetic operation, the tool assists them with a dynamic presentation and practices by themselves. It also assists the low achievement students to study the concept of arithmetic operation and obtains the skill of operational process.
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數位學習, 可縮放向量圖形, 數學標記語言, E-learning, SVG, MathML