數位線性規劃教材設計與教學實驗

研究者準備設計動態幾何環境來幫助學生學習線性規劃的原理，經過分析各版本有關於線性規劃的教材，再透過 Dubinsky 的 APOS 認知理論提出起源分解（genetic decomposition）的概念，假設出學生學習線性規劃的軌道，藉此探討學生學習線性規劃的認知結構，說明一個特定的數學概念要如何學習以及應該如何教，才能對學生的學習有所助益，而起源分解並不是唯一的，甚至在同一個主題下也有可能會發生不同的起源分解，探討學生對一數學概念之起源分解的認知特性，有助於瞭解學生概念建構歷程，因而提供研究者動態幾何教材設計的參考，接著再探討學生透過動態幾何教學後，其不同環境下學習者的學習表現。本研究採用量化分析和質性分析，透過動態幾何環境來輔助學生學習，分為實驗組與對照組，探討不同學習方式的同學，在線性規劃的原理上其學習表現的差異，得到 p=0.001 有顯著差異，再經過半結構式的訪談，探討兩個組別高中低在學習過程中是怎麼學、怎麼想，並重新建構起源分解結構圖，從個案學習過程與跨個案分析去探討學習困難的地方以及動態幾何有甚麼幫助。

關鍵字

二元一次不等式；線性規劃； APOS理論；心智結構

並列摘要

Researchers are prepared to design dynamic geometric environments to help students learn the principles of linear programming, after analysis of the domestic version of the textbook on the linear programming and then through Dubinsky's APOS cognitive theory put forward the concept of decomposition (genetic decomposition). Suppose that students learn the proper track of linear programming, so as to explore the cognitive structure of students learning linear rogramming, It is helpful to explain how a particular mathematical concept is to learn and how to teach it, and the genetic decomposition is not unique, and even under the same subject, The cognitive characteristics of the genetic decomposition of the mathematical concept can help to understand the course of student concept construction, thus provide the reference of the researcher's dynamic geometric teaching design, and then discuss the learners' learning performance in different environments after dynamic geometry teaching. This study uses quantitative analysis and qualitative analysis，assist students in learning through dynamic geometry，divided into experimental group and control group，students who study different ways of learning have different learning performance in the principle of linear programming，there was a significant difference for p = 0.001，and after a semi-structured interview, we discuss how the two groups learned in the learning process and how they think. And reconstruct the original decomposition structure map, from the case study process and cross-case analysis to explore where learning difficulties and dynamic geometry help.