理性的判斷與感性的度量-從模糊統計的角度來探討試題難度

Abstract

在試題難易度分析上，傳統方式常以答對率或得分率的高低來認定試題的難易度。然而，要能得到這些難度值須蒐集實徵數據，在高風險考試中，題目無法預試，只能在闈場內靠著專家學者的專業知識來判斷試題難度。然而，常常專家的判斷和應試者在答題時的感受差異很大。本研究提出一種新的方法，來估算試題難度。過去研究指出，影響數學科試題難易度的主要因素有三方面：評量的數學內容、解題時的思考策略及解題所需的步驟數。本研究則針對這三個主要因素進行分析統計，以模糊統計的角度，提出非固定權重因子之二維模糊數的難度指數。此外，本研究亦針對不同族群進行難度認知差異的分析與檢定。

Traditionally, the percentage correct is considered as an index of item difficulty. However, for the high stake assessment, this is very difficult to collect the pre-test data for estimating the item difficulty. Previous study shows that three factors can affect the item difficulty in mathematics - test content, problem solving strategy, and the required steps to solve the problems. This research analyzed the item difficulty from the perspective of fuzzy statistics. A two-dimension fuzzy number will be presented with non-fixed weighted factors. By applying the absolute distance concept of fuzzy number, the fuzzy item difficulty is calculated. In addition, the item difficulty indices from different groups will be compared with nonparametric significance test.