三～八年級資料與可能性能力測驗的發展及信效度分析

The Development and Evaluation of Data and Chance Ability Test for Third to Eighth Grade Students

在國中小學生資料的處理、詮釋與事件可能發生的推測與判斷能力的養成，是培養學生統計素養的先備知識。本研究旨在編擬一套跨年段具信效度，適合評量學生資料與可能性能力與其複本常模測驗的工具。參考PISA、TIMSS、TASA與本國統計與機率數學課程內容，建立資料與可能性測驗架構，經命題與嚴謹的修審試題過程，取得良好之專家效度。再經前預試、預試，及正式施測，共計6,065名學生受測。主要結果如下：首先，Rasch模式適配度分析結果顯示絕大部分試題的適配度良好。其次，三年段各三個複本在三個數學主題內容、三個認知層次、試題難度分布，以及測驗訊息量大致相當。本研究以同時估計法進行垂直等化，並分別將各年段組受試者設為參照組來校準試題難度，雖然施測題目不同，但所得到的能力估計值是可以相互比較的。三至八年級的常模是以正式施測2,607名學生來建立，可提供不同年段及不同版本的數學資料與可能性能力成長變化情形。

To cultivate the ability of data analysis, interpretation, and the prediction and judgment of event probably occurring is the prior knowledge of statistical literacy in elementary and junior high school. The purpose of this research was to compile a set of credible and valid tools and their parallel norm tests suitable for evaluating students' data and chance ability. Refer to PISA, TIMSS, TASA and the content of national statistics and probability mathematics courses to establish a data and chance test framework. The test demonstrated favorable construct validity after designed items and rigorous revision process. Small-scale trial, pilot-test, and final test were conducted, in which about 6,065 students participated. The major findings could be summarized as follows. First, most of our test items demonstrated good model fit. Second, the three parallel forms of each level among the three kinds of mathematic topics content and three kinds of cognitive level, distribution of difficulty, and item information showed approximately equivalent proportion. Third, the study used concurrent estimation to achieve vertical scaling and rescaled the performance of each level group with one other level group as reference alternately. As such, it is possible to compare the estimates of their abilities with vertical scaling. The norm of 3rd through 8th grades had been established by 2,607 students in the final test. This study provided the growth of students' data and chance ability in different levels and parallel forms.