以知識結構與貝氏網路為基礎之數位教材與評量研發-以六年級柱體體積單元為例

The Research and development of Digital Teaching Materials and Evaluation Based on Knowledge Structure and Bayesian Networks-taking Cylinder Volume unit of The sixth grade as an example

楊淑菁(yang shu ching)

指導教授 ： 劉湘川

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

本研究主要在建立一套以知識結構與貝氏網路為基礎之數學教材與電腦適性測驗，以提供教師進行教學及補救教學使用。Sternberg（1997）指出，學生的思考風格是可測量的。因此，本研究亦欲藉由分析不同思考風格的學生，在學習柱體體積單元之表現來探究：不同學習風格對學習效果是否造成影響，又在子技能及錯誤類型之表現會形成什麼差異。
首先以知識結構為基礎分析「柱體體積」的教材內容，編製一套電腦適性診斷測驗，以貝氏網路作為分析工具，推論出學生的錯誤類型及子技能，以做為補救教學的依據。同時研發一套以「柱體體積」為內容之教材及教學媒體，實施分組教學實驗，同時，學童必須填寫學習思考風格量表， 再根據實驗數據配合學生的作答結果做比較分析，以檢驗此套自編教材與電腦適性診斷測驗的成效並做風格類型相關的探究。
研究結果摘要如下：
一、使用以知識結構為基礎之自編教材進行實驗教學後，實驗組學生之平均分數高於控制組且達顯著差異，表示此套教材具有良好學習成效。
二、實驗組學生的前測成績為83.59分，經使用此套補救教材補救後的後測成績
為90.167分，經檢定達顯著差異。顯示此套自編補救教材在補救教學成效
上，確實能提昇學生的學習成效。
三、電腦適性診斷測驗平均能節省58.96％左右的題目，並且達到93.62%的預測
精準度。
四、貝氏網路的在適性選題與完整作答下對錯誤類型和子技能的一致性，前測的
一致性為97.96％，在後測的一致性為98.70％。
五、以風格類型與學習情況區辨：
以功能類型及複合類型來看，自編數位教材及補救教材對自主型風格的學童
較具有學習成效。
六、以各種風格類型與概念類型之分析比較：
（1）實驗組的自主型學生在概念14和概念17有較優異的學習成效。
（2）實驗組的自主型學生較不易犯錯誤類型14的錯誤。
（3）實驗組自主-巨觀型學習風格的學生在概念14的表現優於其它類型的學
童。

關鍵字

柱體體積 ； 知識結構 ； 貝氏網路 ； 電腦適性診斷測驗 ； 思考風格

並列摘要

The purpose of this research is to establish a knowledge structure and Bayesian networks based mathematical teaching materials and computerized adaptive testing. Sternberg(1997) pointed out, the thinking styles of students are measurable. Thus, this study was to examine learning difficulties and analyzed the differences among various situations in math for students with differential thinking styles.
First, we analyzed the curriculum based on the knowledge structure and edit the evaluation items according to the construction. Then, establish mathematical materials of experimental teaching. Applying the Bayesian Network to infer the mistaken type and skill as the reference of remedial instruction. In the same time, students were required to fill in thinking style scale form. After the experiment, analysis the data.
Some finding are briefly outlined as follows：
1. After taking the experimental teaching, experimental group students; average
grades were better than comparison group’s significantly. It shows this teaching material is valuable for using.
2. After experimental group students taking the remedial instruction, they have
significant progress on their average grades(post-test > pre-test, 90.16>83.59).It shows this teaching material is valuable for remedy.
3. The rate of saving items by KSAT is above 58.96％ and prediction accuracy
can reach 93.62%.
4. Analysis the regularity of error types and sub-skill under the CAT and full
response. The regularity of pre-test is 97.96％ ,and the post-test is 98.70％
5. The experimental group students with legislative styles have higher average
grades in Cylinder Volume unit than those with judicial styles and executive
styles.
6. Distinguishing the error type and sub-skill performances based on different
thinking styles
(1) Error made by the experimental group student with legislative styles was
Less than those with judicial and executive styles in error type 14.
(2) The experimental group student with legislative styles with sub-skill 14 and
17 was more significant than those with judicial and executive styles.
(3) The experimental group student with legislative-globe styles with sub-skill
14 was more significant than those with judicial and executive styles

參考文獻

林鎂惠，陳易芬（2008）。國小學童學習思考風格量表之編製。中國測驗年會 2008

曾彥鈞(2007)。以知識結構為基礎的適性診斷測驗系統及降低猜測機制之研發。

陳光勳、譚寧君(2001)。我國國小學童測量概念發展之研究（III）。國科會專題研究計畫成果報告(NSC77-0111-S153-001-A)。

陳鴻綸(2005)。國小學童在幾何問題的解題表現研究－長方體的體積和表面積為

究。國立彰化師範大學教育研究所。未出版，彰化市。