利用知識地圖診斷數學問題之研究

An Approach to Diagnose Mathematical Problems with Knowledge Map

林伯成(Po-Cheng Lin)

指導教授 ： 賀嘉生

中原大學/工學院/資訊工程研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200378

摘要

測驗及評估是學習過程的重要步驟，它可顯示學生的學習成效以及學生學習的障礙。一般的測驗及評估活動是由學生考試得到的分數來決定學生的學習成效，老師無法針對學生所得到的成績給予不同的建議。因此本論文提出一個學習診斷的方法，來評估學生的學習成效。
知識空間理論（knowledge space theory）即是用來做為評估學生學習成效的一種方法。它必須先在測驗之前分析解題的所有操作，再針對各個操作的難易及學習上的先後次序建立前提關係（prerequisite relations），並對各個操作設計其相關的題目。知識狀態(knowledge state)是由操作(operators)形成的集合，它用來表示各個答題的可能情形，其形成是由前提關係來決定的。知識空間理論便是利用由知識狀態所組成的知識空間(knowledge space)，配合上學生答題的情形來對學生做學習上的測驗及評估。
在本論文中，是利用數學題目在知識地圖（Knowledge Map）的數學操作分佈(operator distribution)，可以較容易地分析題目的操作，在本論文將對各個題目的操作分佈做分析及討論，並且利用各個題目的操作分佈做為建立前提關係的依據，最後再以知識空間理論進行學習診斷。
本論文實作了一個學習診斷系統。老師可以輸入題目至系統的題庫中，系統會根據老師輸入的題目及其操作分佈來建立各題間的前提關係。建立完成後，當學生進行測驗時，會經由題庫選取題目，依據學生的回答來診斷個別學生的學習成果，讓學生瞭解自己的學習成果並給與學生學習上的建議。

關鍵字

操作分佈 ； 知識狀態 ； 知識空間理論 ； 知識空間 ； 知識地圖 ； 前提關係

並列摘要

Test and assessment, which show the learning efficiency and learning disability, are important steps of learning. The testing scores determine the learning efficiency of students in a traditional test; however, teachers can not give any suggestion to students. In this paper, a learning diagnosis method is proposed to evaluate the learning efficiency of students.
Knowledge space theory is an approach to assess the learning efficiency of students. In this theory, all operators in problems must be analyzed before testing, and the prerequisite relations are built according to the complexity of operators. The knowledge states, which are the sets of operators, represent the states of the testing results. The knowledge states are formed with the prerequisite relations. In knowledge space theory, test and assessment are created using knowledge states and the testing results to diagnose the learning efficiency of students.
In this paper, the proposed method, which uses mathematical operator distributions of mathematical problems on knowledge map, is able to analyze the operators of problems easily. Here, there are some analyses and discussions for operator distribution of problems. According to the operator distributions of the problems, the prerequisite relations can be found. Finally, the knowledge space theory is used to diagnose the knowledge state of students.
A learning diagnosis system is implemented to prove the above idea. In the experiment system, the prerequisite relations will be established from problems after teachers input problems to item blank. Then, the system will select the problems to quiz students and diagnose their learning efficiency of students at the same time. After the test, a diagnostic report will be generated to give some suggestions for subsequent learning.

並列關鍵字

operator distribution ； knowledge space theory ； knowledge state ； prerequisite relation ； knowledge space ； knowledge map

參考文獻

[MSS99] McClure, John R., Brian Sonak. Hoi K. Suen (1999), “Concept map assessment of classroom learning : reliability, validity, and logistical practicality complex concepts,” Journal of Educational Computing Research, Vol.4(4), 1988

[NM91] Novak, J. D., and D. Musonda. “A tweleve-year longitudinal study of science concept learning,” American Educational Research Journal, Vol. 28, pp.117-153, 1991.

[Nok79] Novak, J. D., “Applying learning psychology and philosophy of science to biology teaching,” The American Biology Teacher, Vol. 43, pp.12-20, 1979.

[RSLR01] Ruiz-Primo, Maria Araceli, Susan E. Schultz, Min Li, Richardj, “Shavelson. Comparison of the Reliability and Validity of Scores from Two concept-Mapping Techniques,” Journal of Research In Science Teaching, Vol. 38, No.2, pp.260-278, 2001.

[SMZT01] Schau, Candace, Nancy Mattern , Michael Zeilik , Kathlee. W. Teague, Select-And-Fill-In Concept Map Scores As a Measure Of Students' Connected Understanding Of Science, 2001.