中文摘要 本研究的主要目的,是以國小三年級數學領域之「整數」相關指標為例,嚐試採用以機率推理為基礎的貝氏網路作為分析工具,探討將此分析工具應用於診斷學生錯誤類型之可行性。建立一套以貝氏網路為基礎的能力指標測驗編製及動畫補救教學,提供學生在診斷測驗後,能依據學生施測後的結果,即時進行適合其程度的補救教學。 研究中首先分析能力指標。藉由專家及教師所分析的能力指標,建立有上下位關係的專家知識結構,從結構圖的節點中獨立出來變成貝氏網路的子技能。依此子技能命題,透過紙筆測驗,分析學生常見的錯誤類型。並建立貝氏網路試題結構與電腦診斷測驗題庫,接著在電腦測驗後,學生即可針對能力指標學習不足之處進行補救教學。 總而言之,本研究成果欲達到下列目標: 一、探討國小三年級數學領域「整數」相關能力指標錯誤類型的發生情形。 二、應用貝氏網路於分析國小三年級「整數」相關能力指標錯誤類型,並建置測驗題庫及貝氏網路架構圖。 三、建立一套以錯誤類型為基礎之電腦補救教學動畫。 四、驗證電腦化適性補救教學動畫是否達到效果。 關鍵字:貝氏網路、錯誤類型、補救教學、整數
Abstract The major purpose of the paper is to research the competence indicators of the “whole number” on Grade 3 and to analyze student mistaken types based on Bayesian Networks. Moreover, we want to establish the Learning Educational Program in order to offer the remedial instructions and Flash movies in accordance with the test result. First, we establish the causal relationships expert knowledge structure after analyzing the competence indicators. Then we pick up the Framing nodes from the structure as Bayesian Networks’ sub-skills, and finally design the questions based on sub-skills and analyze the mistaken types from the paper test result. According to the students’ mistaken types, the Learning Educational Program can offer the interactive remedial instructions like Flash movies we make. In a word, the study is used to achieve the targets as below. 1. Discussing the competence indicators of the “whole number” on Grade 3. 2. Appling Bayesian Networks to analyze the mistaken types of the relevant competence indicators of the “whole number” on Grade 3, and forming a quiz database as well as Bayesian Networks Framings. 3. Establishing a set of computer-aid Flash movies as remedial instructions in accordance with the student mistaken types. 4. To examine if the computer-aid Flash movies as remedial instructions are effective. Keywords: Bayesian Networks、Mistaken Types、Remedial Instructions、whole number