應用虛擬題庫理論-電腦化方塊計數測驗之實作

Designing a Computer Cube Enumeration Test System based on Virtual Item Bank Theory

廖文偉(Wen-Wei Liao)

指導教授 ： 何榮桂

國立臺灣師範大學/教育學院/資訊教育學系/博士(2013年)

摘要

立方體(方塊)為體積的基本單位，因此常用來介紹體積概念。在測驗方面，方塊計數測驗，也常被用來測量或促進立體幾何物件的心像與操弄能力。方塊計數測驗通常隱密且不公開，一般人對其的瞭解也侷限於坊間書局所出版的練習題本。不公開之主要原因在於維持測驗的安全。本研究結合古典測驗理論(CTT)、電腦化測驗(CBT)、自動化試題產生理論(AIG)、虛擬題庫理論(VIB)及方塊計數測驗等相關理論，建立方塊計數測驗之虛擬題庫及方塊計數學習系統。方塊計數之虛擬題庫並無實際題目存在，取而代之的是物件及題目產生之方法。而在測驗當中，測驗受試者之題目，將由物件配合測驗理論直接產生，故題庫不會有試題曝光率之問題。本研究之受試者為國小六年級學生共267名學生，本研究最後發現：

1. 題目可翻轉會導致試題難度降低，但可翻轉試題有助於空間能力之教學。
2. 方塊完整度及方塊隱藏個數皆影響試題難度。
3. 測驗的結果顯示男女學童在前青春期的空間視覺能力上並無顯著差異。
4. 電腦化虛擬題庫方塊計數測驗亦可測量受試者之空間視覺能力。
5. 應用方塊計數學習平台進行學習也有助於提升受試者空間能力。

關鍵字

AIG ； CBT ； CTT ； VIB ； 空間能力 ； 方塊計數

並列摘要

Cube is the basic unit of volume and hence it is often used to introduce its concepts. For tests, cube enumeration is always used to measure or promote mental images and manipulation ability of 3-D geometric objects. Cube enumeration tests usually are not open for the public whose understanding is only limited to exercise books found at general bookstores. The main reason for this limitation is to maintain the test security. This study combined Classical Test Theory (CTT), Computer Based Test (CBT), Automatic Item Generation (AIG), Virtual Item Bank Theory (VIB) and theories related to cube enumeration to construct a VIB-based cube enumeration test and a learning system. The item bank of the VIB-based cube enumeration test was a virtual one. The VIB contained only basic element – cube. With these cubes, items would be directly generated and therefore there wouldn’t be item exposure problem for the item bank. 267 sixth graders of New Taipei City elementary school participated in this experiment. Their mid-term math grades were used as the external criterion in the test.
This study found out that:
1. Both the number of invisible cubes and the integrity of cubes were positively correlated to item difficulty.
2. In addition to the number of invisible cubes and the integrity of cubes, whether test items could be rotated also influenced item difficulty.
3. Based on the results of both tests, there is no significant difference in spatial visualization ability between male and female preadolescence students.
4. The scores of the computerized cube enumeration test also indicated that this system could measure their spatial visualization ability.
5. Applying the cube enumeration learning system did improve users' spatial ability.

並列關鍵字

Spatial Ability ； Cube enumeration

參考文獻

Ackerman, T. A. (1989). Unidimensional IRT calibration of compensatory and noncompensatory multidimensional items. Applied Psychological Measurement, 13(2), 101–125.

Baker, F. B. (1992). Item response theory: Parameter estimation techniques. New York: Marcel Dekker.

Battista, M. T. (1999). Fifth graders’ enumeration of cubes in 3D arrays: Conceptual progress in an inquiry-based classroom. Journal for Research in Mathematics Education, 30, 417-448.

Battista, M. T., & Clements, D. H. (1996). Student's Understanding of Three-Dimensional Rectangular Arrays of Cubes. Journal for Research in Mathematics Education, 27(3), 258-292.

Ben-Haim, D., Lappan, G., & Houang, R. T. (1985). Visualizing rectangular solids made of small cubes: Analyzing and effecting student's performance. Educational Studies in Mathematics, 16(4), 389-409.