線性規劃動態電腦輔助教材設計及其補救教學個案研究

A Case Study on Designing Dynamic Computerized Learning Materials for Remedial Instructions of Linear Programming

本研究應用電子試算表及電子幾何板設計線性規劃單元之動態電腦輔助教材。教材設計著重於能透由行動學習數學，加強表徵間意義的連結，以建立學習者穩固的數學概念。研究中選取一位學生進行補救教學。教學前學生存有錯誤概念，例如學生不了解為什麼目標函數的極值會在解集合區域的頂點產生；教學後，學生建立了正確的數學概念，能解出應用問題，並且了解所應用的原理。延後測的結果與後測一樣好，顯示教學具有良好的保留效果。教學後，學生可以寫出代表代數符號的文字情境，由此顯示個案學生對於代數符號的理解及表徵間的轉換能力有明顯的進步。

This study uses the Microsoft Excel and Geometer's SketchPad to design dynamic digital materials for learning the linear programming. The design focuses on learning by acting on objects and strengthens the connection between different representations to establish solid mathematical concepts. We choose a student for the remedial program. Before the remedial program, the subject has several misconceptions such as does not understand why the extreme value of linear goal would occur on the boundary points. After the remedial program, the subject establishes correct mathematical concepts and is able to solve the word problem successfully. The result of delayed-test is as good as the post-test, which means the conservation effect of the remedial program is substantively good. After the remedial program, the subject can translate algebraic symbols into real-life situations. This shows the subject has made significant progress on understanding of algebraic symbol and has the ability of translating into multiple representations.