國中基本學力測驗量尺分數的另類表示方法

An Alternative Method for Representing Scaled Scores of the Basic Competency Test for Junior High School Students

汪慧瑜(Hui-Yu Wang) ； 余民寧(Min-Ning Yu)

《測驗學刊》 53卷2期 (2006/12) Pp. 205-237

https://doi.org/10.7108/PT.200612.0205

摘要

本研究的目的在以試題反應理論為基礎，建立另一種量尺分數的計算和呈現方式，希望能夠兼顧學理的嚴謹性和使用上的方便和易懂，使基本學力測驗結果的表達方式更為合理和公平。
本研究採用BILOG-MG軟體程式的3-Parameter Logistic Model為依據，使用貝氏估計法來估算考生的能力估計值θ，再將能力估計值轉換為以平均值30，標準差為7.75的量尺化能力值。分析結果顯示，答對相同題數的考生，其量尺化能力值有差異，此差異的大小會隨著答對題數的多寡不同，而呈現不同的分佈情況。一般而言，答對相同題數的數量約在中間至偏低比例的考生，其所對應的量尺化能力值高低差距較大，而答對相同題數的數量約在兩極端的考生，其所對應的量尺化能力值高低差距較小；在不同科目中，量尺化能力值差距的最大值分別為：國文科差距10.37分、英語科差距10.72分、數學科差距11.30分、社會科差距13.00分、而自然科差距11.61分。當五個科目的量尺化能力值（或量尺分數）加總成為考生的得分時，這樣的量尺化能力值差距將更為明顯，這對考生在選擇申請入學或分發入學高中職校上，將產生相當大的影響，這亦顯示出現行量尺分數計分方式的公平性問題頗值得重視。最後，本研究根據結論提出具體建議，以供實務應用之參考。

關鍵字

基本學力測驗 ； 試題反應理論 ； 量尺分數

並列摘要

This study aimed to develop an alternative scaled score method, based on Item Response Theory, to report the results of the student basic competence tests in a more reasonable way. The scaled score method designed by the present study is characterized not only by its theoretical basis but also by the ease of use and understanding.
This study employed the BILOG-MG software system with 3-ParmeterLogistic Model and Bayesian EAP method to estimate student ability value θ s. The value θ s were in turn transformed into scaled scores with a mean of 30 and standard deviation of 7.75. Different scaled scores were found among the students who had the same number of correct items on the tests. The range of the scaled score difference was related to the number of correct items on the tests. In general, in the cases that the students' numbers of correct items were between medium and slightly below medium, the differences of the corresponding scaled scores tended to span a wider range. The scaled scores also differed in subject areas. The widest range of the difference shown within each subject area is presented respectively as follows: Chinese with 10.37 points, English with 10.72 points, math with 11.30 points, social science with 13.00 points, and science with 11.61 points. Subsequently, totaling the scaled scores of the five subjects made the differences even greater among the students who had the same number of correct items, which has a profound influence on students' chance of entering high schools. It is therefore justified that the fairness of the scaled score system currently used should be taken into serious consideration. Finally, some suggestions were proposed on the basis of the discussions provided in this study for future applications.

並列關鍵字

basic competency test ； item response theory ； scaled scores

參考文獻

人本教育札記(2001)。基本學力測驗會不會太簡單，考不出程度。人本教育札記。144

王逸慧(2001)。基本學力測驗之時師：問題與展望。教育研究資訊。9(1)，15-31。

余霖(2000)。對國民中學學生基本學力測驗之評論與期望。教師天地。109，30-32。

何文慶(2001)。從基本學力測驗談起。師友。405，34-36。

何雅娟(2000)。多元入學多元思維－談台北市高中多元入學方案。教師天地。109，33-44。