從TIMSS 2007臺灣八年級學生數學科作答反應檢視古典測驗理論和試題反應理論特性和測驗分析結果

Inspecting the Characteristics of the Classical Test Theory and Item Response Theory by Using Test Analysis Results and the Responses of Taiwanese Eighth-Grade Students in the TIMSS 2007 Database

本研究之主要目的在於透過TIMSS 2007臺灣八年級學生數學科的作答反應瞭解古典測驗理論和試題反應理論的特性，並且綜合兩種測驗理論取向檢視TIMSS 2007之數學科試題，希望透過試題分析結果提供試題編制和教育相關領域教學啟發之參考。資料庫人數共287人，以題本組合一為研究工具，利用軟體R 2.13.1、Excel 2003、SPSS 12.0、ConQuest 2.0等，執行各項數值運算和圖表繪製。結果發現，兩種測驗理論均顯示測驗試題呈現難度偏易情形、兩題誘答選項呈現中間組作答比率高於低分組的情形，試題特徵曲線顯示有四題多重計分題呈現階難度失序情形。整體試題品質相當良好，少數題目呈現無法區辨中間能力者樣貌，且試題對於學生較為容易。在理論特性方面，古典測驗理論可以從信度、構念效度、試題參數、項目分析和測驗參與者總分，對應試題反應理論的測驗訊息量、構念效度和模式適合度、試題參數、試題和類別特徵曲線和測驗參與者能力等概念，試題反應理論的優勢展現在測驗訊息量、潛在特質假設、參數不變性和試題等化上。在提供試題編制和教育相關領域啟發方面，研究者對兩題試題提出調整方式建議，並認為在某特定試題上，讓學生感到作答困難的原因，或許可以和數感教育有所連結。

The purpose of this study was to investigate the characteristics of classical test theory (CTT) and item response theory (IRT) by using the responses given by eighth-grade Taiwanese students in the TIMSS 2007 database to conduct test and item analysis from 2 distinct test perspectives, to provide benefit for test design and education settings. A total of 287 students were included in the research, and Booklet 1 was selected as the research tool. Software such as R 2.13.1, Excel 2003, SPSS 12.0, and ConQuest 2.0 were used during data analysis and curve drawing. The results showed that the test difficulty ranged from medium to easy, and the 2 distractors embedded respectively in the 2 items showed that the proportion of average students was more than that of below-average students, according to the aforementioned theories. Moreover, item characteristic curves of 4 multiple-choice items were not ordered. In general, the test quality was high, despite slight flaws meaning that some items could not differentiate average students. However, items were easy for students. The reliability, construct validity, item parameters, category analysis, and overall scores of the test takers in CTT corresponded to concepts of test information function, construct validity, and model fit assessing, item parameters, item and category characteristic curves, abilities of participants in the IRT. The relative strengths of the IRT lie in test information function, latent trait assumption, and parameter invariance and test equating. Regarding the test design and educational implications, we suggest modifying presentations of 2 distractors and making connection to number sense education owing to a specific difficult item.