摘 要 本研究旨在編製一套數位數學教材及電腦適性測驗運用於教學實驗研究。首先以國小五年級數學「體積與容積」為範圍,結合九年一貫能力指標「5-n-18」、「5-n-19」和「5-a-05」,經過教授指導及同儕討論分析出子技能與錯誤類型,並建立知識結構及貝式網路,進而設計出一套電腦適性測驗及數位數學教材。接著以數位數學教材進行教學,並用電腦適性測驗作為診斷工具,來檢測教學成效及測驗成效。 研究結果如下: 一、在經過單元教學後,實驗組前測的平均分數為81.851分,控制組平均則為77.409分,經檢定達顯著差異,因此可以判斷自編數位教材具有學習成效。 二、而在補救教學之後,實驗組後測平均分數為87.424分,控制組平均則為81.763分,且達顯著差異,證明實驗組的補救教學效果優於控制組。 三、在單元教學結束後一個月進行延後測,實驗組延後測平均分數為80.669分,控制組平均為75.331分,經過檢定後亦達顯著差異,因此在延宕成效的表現上,也是實驗組較為優異。 四、電腦適性測驗能有效節省64%的題目,並能達到92%的預測精準度。 五、以貝氏網路推論電腦適性測驗,在適性和完整作答情況下,對錯誤類型與子技能的一致性,前測達90.47%、後測達94.27%,延後測達95.36%。 關鍵詞:體積與容積、電腦化適性測驗、知識結構、貝氏網路、補救教學。
Abstract This research is for making a digital mathematic teaching material and computerized adaptive test. First, take the fifth grade math as the example, basing on benchmarks 「5-n-18」、「5-n-19」and 「5-a-05」 of Grade 1-9 Curriculum then we can find out the skills and error patterns after the discussion with the adviser and classmates. Second, we also can create knowledge structure and Bayesian networks. Third, after doing this, we design a computerized adaptive test and digital mathematic teaching material.。Finally, we can teach by using this teaching material and use computerized adaptive test as a diagnoses tool to examine teaching and test result. The results are as the followings: 1. After teaching one unit,,the first average score of Experimental Group is 81.851, and the average score of Baseline Group is77.409. After the examination, we can see the difference, so it obviously works. 2. After remedial instruction, the second average score of Experimental Group is 87.424, and the average score of Baseline Group is 81.763. It is obviously different and we can prove that the remedial instruction of Experimental Group is better then that of Baseline Group. 3. After performing the delayed posttest when finishing the unit teaching, the delayed posttest average score of Experimental Group is 80.669. We can see the delayed effect of Experimental Group is much better. 4. Computerized Adaptive Test can not only save 64% questions,but also can get 92% examination accuracy. 5. In the situation of appropriately and completely answering the questions, we can infer the consistency of wrong types and sub-skill of Computerized Adaptive Test based on Bayesian networks. The first test is 90.47%, the second test is 94.27% and the delayed posttest is 95.36%. Keywords:Volume and Capacity、Computerized Adaptive Test、Knowledge Structure、Bayesian networks、Remedial Instruction