應用貝氏網路進行國中數學二元一次聯立 方程式單元之學習診斷測驗編製及適性補 救教學設計

Application of Bayesian Network–Use Two-Variable Linear Equation Unit in Junior High School Mathematics Course to Diagnostic Test Design and Adaptive Remedial Instruction

洪敏甄(hung min jen)

指導教授 ： 劉湘川

亞洲大學/資訊學院/資訊工程學系碩士班/碩士(2007年)

摘要

本研究以國中七年級數學「二元一次聯立方程式」單元為例，以貝氏網路作為 推論工具並加入OT 演算法以決定測驗試題順序結構，發展一套適用於本單元的電 腦適性診斷測驗及電腦適性補救教學系統，探討貝氏網路應用於診斷學生錯誤類型 及子技能的效能並驗證此一系統的成效。 研究結果發現： 一、利用貝氏網路來診斷學生學習「二元一次聯立方程式」單元時的錯誤概念及應 具備的基本能力，與專家人工判定有九成以上的相符程度，顯示貝氏網路能精 準且快速地診斷學生學習時的錯誤類型及子技能。而貝氏網路選取動態分類決 斷值比固定分類決斷值能有更好的診斷辨識效果。 二、此電腦適性補救教學系統使全部受試者與高分組、中分組及低分組受試者在施 測成績上均有顯著進步，且有效降低學生的錯誤類型及增強其子技能，並發揮 適性化的功能，使測驗成績相同但錯誤類型及子技能不全然相同的受試者皆能 得到適合的補救教學，且學習成效有所提昇。 三、此電腦適性診斷測驗能節省約四成的測驗試題，而在試題作答反應、錯誤類型 及子技能診斷的預測準確率達九成以上，顯示雖然減少施測的題數，但其診斷 的結果與完整測驗所得結果仍有九成以上的相似程度，成效良好。

關鍵字

貝氏網路、電腦適性診斷測驗、電腦適性補救教學

並列摘要

The study was to develop a system based on the probability reasoning of Bayesian
Network and OT theory into Two-Variable Linear Equation Unit in seven year’s
mathematics course of junior high school to induce the error types that students made and
to validate the effect of the system.
The results were as follows.
First, Bayesian Network was employed to diagnose the error concepts and the basic
skills that students should have. The results had the ninety percent correspondence with
the expert judgment. Therefore, Bayesian Network could diagnose the error types and
sub-skills exactly and efficiently. In addition, the dynamics threshold of Bayesian
Network had better effects than the motionless threshold in diagnosis and classification.
Second, the significant differences were shown in grades among the high achievers,
middle achievers and low achievers in the computerized adaptive diagnostic testing. With
the design, the error types were decreased and the sub-skills were increased. The testees
could receive the proper adaptive remedial instruction in time and enhance their learning.
Third, the computerized adaptive diagnostic testing could save forty percent of test
items. The reaction of the test answers, the error types and sub-skills could be predicted
and the accuracy achieved ninety percent. It showed that in spite of a few test items, the
results were similar with the complete test.

並列關鍵字

Bayesian Network, Computerized Adaptive Diagnostic Testing, Computerized Adaptive Remedial Instruction

參考文獻

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