學生有效的學習是教學者共同的願望。本研究擬以國小五年級數學「代數、統計與機率」的能力指標為範圍,嘗試以機率推理為基礎的貝氏網路作為分析工具,來探討應用貝氏網路診斷學生錯誤類型的可行性。並能針對學生個別的錯誤類型,進行個人化的線上補救教學,以達到「因材施教」的效果。 本研究主要有五個目的: 一、 探討國小五年級數學「代數、統計與機率」相關能力指標錯誤類型的發生情形,並建置學生在「代數、統計與機率」上的貝氏網路架構圖。 二、 根據貝氏網路,應用於診斷國小五年級學童「代數、統計與機率」相關能力的錯誤類型,並建置試題。 三、 探討不同分類決斷值對貝氏網路診斷精準度的影響。 四、 根據貝氏網路分析資料為基礎,實施個人化的線上電腦補救教學。 五、 驗證以貝氏網路為基礎之能力指標測驗編製及補救教學動畫實施,能否達到補救教學的效果。 經過研究發現,貝氏網路模式應用於診斷國小五年級數學「代數、統計與機率」錯誤類型具發生情形上,具有可行性,學生經過電腦診斷測驗,能快速找出個別的錯誤概念。 在國小五年級數學「代數、統計與機率」相關能力指標的錯誤類型發生情形上,學生的錯誤類型有明顯減少,顯示補救教學動畫實施對學生有效果。
The effective learning to students is the common wish of teachers. The main idea of the study is to research the ability of algebra, statistics and probability index on Grade 5 and demonstrate the applicable of student mistaken types on the basis of Bayesian Networks which is a probability analysis method. To reach the target, teaching students in accordance with their aptitude, by executing the individual Learning Educational Program online. Five purposes as below. 1. Studying the ability of algebra, statistics and probability index on Grade 5 and set up its’ Bayesian Networks Framing. 2. Establishing the quiz question based on the ability of algebra, statistics and probability index on Grade 5. 3. Discussing the influence of Bayesian Networks’ correctness with variety classified Decisive-Point. 4. Executing the Learning Educational Program based on the analysis data of Bayesian Networks. 5. Achieving the remedy instructions effective by executing the Learning Educational Program.