運用狀態轉換圖於高中數學轉移矩陣教學之研究

Abstract

高中數學「轉移矩陣」課程的教學設計多為示例教學，一般教材多將冗長的文字敘述轉化為表格呈現，表格是一個很好的文字訊息結構，然要了解訊息之間的關聯必須行列交錯瀏覽，以致於造成較重的負荷，因此學生初學之際常未能完整掌握訊息之間的關聯。狀態轉換圖則可清楚呈現訊息間的交互關係，學生比較容易從中擷取重要關聯訊息進行分析與處理，應可促進對轉移矩陣的理解。

本研究主題為轉移矩陣，採準實驗研究法，主要以課堂教學進行。實驗組為運用狀態轉換圖之數位教材，對照組為運用表格之數位教材，目的為探討學生的階段學習成就測驗與上課感受是否產生顯著差異。

研究結果顯示：

1. 對整體學生來說，實驗組之學生階段學習成就較佳，達顯著差異。 但上課感受皆無顯著差異。 2. 對高成就學生來說，實驗組之階段學習成就較佳，達顯著差異。 且實驗組有較高的「上課意願」，達顯著差異。 3. 對中成就學生來說，實驗組之階段學習成就較佳，達顯著差異。 但上課感受皆無顯著差異。 4. 對低成就學生來說，實驗組與對照組之階段學習成就無顯著差異。 但對照組有較多的「投入努力」，達顯著差異。 5. 對就讀自然組學生來說，實驗組之階段學習成就較佳，達顯著差異。 且實驗組有較高的「理解程度」，達顯著差異。 6. 對就讀社會組學生來說，實驗組與對照組之階段學習成就無顯著差異。 且上課感受皆無顯著差異。 7. 在轉移矩陣的教學上，運用狀態轉換圖之數位教材未產生專業知識反轉效應。

Worked examples, in which lengthy word descriptions are transformed into table representations are frequently used when teachers teach high school students transition matrix. Tables are a good word message structure. Nevertheless, if students want to understand the connection between words, they have to read carefully through the lines. This is a heavy load for beginners, making them fail to connect the messages. Contrarily, state transition graph clearly presents the interconnection between the messages, which enables students to grasp, to analyze and to process the information more easily and thus, assists them in learning transition matrix.

The topic of the study is transition matrix with the application of quasi-experimental design in a class teaching. Digital teaching materials of state transition graph are applied in the experimental group while digital teaching materials of tables are applied in the control group. The study aims to find whether there is any significant effect in students’ learning performances and self-perception in class.

The major results of this study can be summarized as follows: 1. The learning performances of the experimental group were superior to the control group and the effect was significant. However, in the self-perception part, there was no significant effect. 2. For high achievers, learning performances of the experimental group were superior to the control group and the effect was significant. The experimental group has higher willingness for learning, and the effect was significant. 3. For middle achievers, learning performances of the experimental group were superior to the control group and the effect was significant. However, in the self-perception part, there was no significant effect. 4. For low achievers, there was no significant effect in learning performances between the experimental group and the control group. The control group involved more efforts than the experimental group, and there was significant effect. 5. For students in science group, learning performances of the experimental group were superior to the control group , and the effect was significant. The comprehension of the experimental group was higher, and there was significant effect. 6. For students in social group, learning performances of the experimental group were superior to the control group , and the effect was significant. However, in the self-perception part, there was no significant effect. 7. No expertise reversal effect was found in teaching transition matrix with state transition graph.