建構數學學科概念效應關係圖之方法

Abstract

測驗理論是一種解釋測驗資料間實證關係的系統化理論學說。當代測驗理論主要是以試題反應理論(IRT：Item Response Theory)為架構，考慮試題參數及受試者的反應等特性(包括難度、鑑別度、學生能力等)，因此在估計受試者個人能力時，能夠提供一個較精確的估計值。 以資料探勘的技術來架構概念效應關係圖(CERM：Concept Effect Relation Map)，若透過不成熟的資料前處裡將導致：(1)概念模糊化結果的單調性，(2)所探勘的關聯規則無法反映實際的概念效應關係及(3)產生循環迴圈的關聯規則。本文應用IRT來處裡學生概念學習的反應結果。因此，學生概念學習的反應結果加上了試題難度、鑑別度的考量下，我們提出一個基於IRT資料前處裡的概念效應關係圖架構系統(IRT-Based Data Preprocessing Concept Effect Relation Map Construction System)。 基於IRT資料前處裡的概念效應關係圖架構系統包含資料前處裡與資料探勘兩個模組。資料前處裡模組內含四個程序：試題分析、產生學習反應指標、概念分解/整合及概念學習反應指標整合結果的糢糊化；資料探勘模組內含關聯規則探勘與概念效應關係圖架構兩個程序。 我們所提出的方法透過實驗的結果證明，概念效應關係圖的效應關係可以被改進且可以減少循環迴圈關聯規則的產生。

Test theory is an explanation of empirical relationships among examination data. The modern test theory is based on the Item Response Theory (IRT), which considers the parameters of test item and the response of test-receiver (including difficulty, discrimination, ability and so on),and the estimation of its test-receiver’s ability becomes more precise. Concept Effect Relation Map (CERM) constructed by data mining with naïve data preprocessing causes: (1) monotonous concept fuzzification result, (2) the association rules may not reflect the real concept relation and (3) the circulating association rules exit. In this thesis, we apply the IRT as the assessment of students’ concept learning response. With the consideration of the difficulty and the discrimination of test item, we propose an IRT-Based Data Preprocessing Concept Effect Relation Map Construction System. IRT-Based Data Preprocessing Concept Effect Relation Map Construction System includes two modules: the Data Preprocessing Module and the Data Mining Module. The former has four procedures: Test Item Analysis, Learning Response Index (LRI) Generator, Concept Decomposition/Aggregation and Fuzzy ACLR Generator, and the latter has two procedures: Association rule mining and concept map constructor. The experiment results of the proposed Approach show that the CERM construction can be improved and the number of circulated association rules generated can be reduced.