資訊科技融入國小五年級數學「數量關係」單元數位學習教材與測驗研發

A Research of Intergrating Information Technology into the Development of Elearning System and Digital Teaching Materials of「Quantitative Relationships」for the Fifth Graders

蔡幸如(TASI SHIN-RU)

指導教授 ： 施淑娟 郭伯臣

亞洲大學/資訊學院/資訊工程學系碩士在職專班/碩士(2010年)

摘要

本研究以國小五年級「數量關係」數學領域能力指標5-a-03為例，並以「數量關係」常發生的錯誤類型為診斷單位，採用以機率推論為基礎的貝氏網路作為分析工具，研發一套輔助指導教材，並結合以「知識結構」與「貝氏網路」為基礎的電腦適性診斷測驗，設計一套完整的教學、評量以及補救教學活動，將其應用於教學實驗中，以評估此模式的教學成效。
本研究的研究成果，可得到以下結論：
一、本研究研發之數位教學教材與數位補救教材包含了三本手冊：教師教學手冊、學生單元講義、學生加油手冊及兩種多媒體輔助教材：教學用PPT、補救教學用多媒體。
二、使用研究者自編數位教材進行教學後，實驗組前測分數91.95優於控制組的87.14，經檢定達顯著差異。顯示自編數位教材具有學習成效。
三、實驗組學生經由以資訊融入補救教學，前測平均分數91.95，後測平均成績為96.26，經檢定達顯著差異，顯示自編之補救教材，確時能幫助學生的學習。
四、實驗組延後測平均分數為93.52分，高於控制組延後測的83.78分，相差高達9.74分。經檢定達顯著差異，顯示研究者自編之數位教材對實驗組學生之延宕成效優於對照組之延宕成效。
五、實驗組錯誤類型平均發生率後測比前測減少9.5%；對照組錯誤類型平
均發生率後測比前測減少5.2%。實驗組平均錯誤減少的幅度比對照組
大。實驗組後測的子技能平均達成率為94.05%，控制組的後測的子技
能平均達成率為76.53%，實驗組平均達成率增加的幅度明顯比對照組
大許多。
六、電腦適性測驗能有效節省 58％以上的題目，且能達到 93％以上的預測精準度。
七、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 93.78 ％，後測達 96.61％，延後測達 95.87％。

關鍵字：數量關係、知識結構、貝氏網路、資訊融入教學、電腦適性測驗

關鍵字

數量關係 ； 知識結構 ； 貝氏網路 ； 資訊融入教學 ； 電腦適性測驗

並列摘要

Abstract
This research take fifth grade "quantitative relations" nine-year mathematics proficiency targets 5-a-03 as an example, the purposes of the research are to design supplementary teaching curricula containing activities applied to teachings, evaluations and remedial instructions, and to investigate the teaching effects after instructional experiments. In this study, the computerized adaptive diagnostic test based on the Bayesian network and knowledge structure theories is combined with the teaching design. Besides, the error patterns usually occurred in this unit is adopted as the diagnostic implement and the Bayesian Network based on probabilistic reasoning is taken as the tool for analysis.
The conclusions resulted from the study are listed bellowed:
1. In addiction to multimedia-based curriculums like PPT, the digital presentations used in the mathematical teachings and multimedia materials adopted to the remedial instructions, manuals for teachers, lecture notes and handbooks for students are also included in the digital and remedial instructions.
2. By using the digital curricula developed by the researcher for the remedial instructions, it is found that students of the experimental group obtain higher average score in the pretest than students of the control group (91.95>87.14). The remarkable difference after the examination shows that the self-designed digital curricula are effective for students’ learning.
3. By integrating information technology into remedial instructions, the average scores for students of the experimental group in the pretest is 91.95,the average scores in the post-test is 96.25.Comparing with these scores , the difference attained by the examination shows that the remedial teaching materials designed by the researcher are truly helpful for students’ learning.
4. The average grade which the experimental group students get in the postpone test is 93.52. On an average, the control group students score 83.78 points in the delayed test. The fact indicates that students of the experimental group get higher grades than students of the control group. The notable difference attained by the examination reaches as high as 9.74. It shows that the continuous effects resulted from the digital curriculum designed by the researcher on the experimental group is superior to the continual efficiency on the control group.
5. Experimental group, the average error patterns Incidence of post-test reduce than the pre-test by 9.5%; control group, the average error patterns Incidence of post-test measured less than the pre-test by 5.2%. Experimental group, the average error magnitude of less big than the control group.
Experimental group, the average post-test sub skills reached a rate counted was 94.05% in the control group's post-test sub skills reached a rate counted for the 76.53 percent average of the experimental group, the average increase reached a magnitude of rate counted obviously much larger than the control grou Great many.
6. It is estimated that over 58% of questions can be saved by using the Bayesian Network based Computerized Adaptive Test (BNAT) and the accuracy rate of predication is above 93%.
7. When the computerized adaptive diagnostic test deduced from the Bayesian network is done to the full and well adapted, the uniformity rate of the error patterns and sub-skills can reach 93.78% in the pretest, 96.61% in the post test and 95.87% in the postpone test respectively.

Keyword：quantitative relationships , knowledge structure , Bayesian networks, Integration of Information into Teaching , the computerized adaptive diagnostic test

並列關鍵字

quantitative relationships ； knowledge structure ； Bayesian networks ； Integration of Information into Teaching ； the computerized adaptive diagnostic test

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