本研究的目的，在於以認知心理理論與近代測量理論之精義，發展先進的詮釋系統及分析模式，來建立學生之凸透鏡成像理解的觀察實體與理論實體間有效的邏輯關係，從而建構凸透鏡成像理解的解釋性模型。本研究的特性兼具了定性與定量的考量，並捨棄專家系統的概念分析，而從學生自我建構的心智模型作為建立潛在特質能力變項的參考架構，再以Rasch部分給分之測量模型對此能力變項作精準的度量，以作為診斷分析學生凸透鏡成像理解的詮釋基礎。

　　　　　The purpose of this research is to develop, by way of the essence of cognitive psychology and modern measurement theory, an advanced interpretative system and an analytic mode. We can thus set up logical relationship between the observable entity and the theoretical entity of students' understanding toward image of convex lens and, on the basic of this, construct an explanatory model of understanding image of convex lens. We combine qualitative and quantitative consideration, abandon the conceptual analysis of expert system, and only take students' mental model as the reference frame of constructing ability variable of latent trait. After exact calibration of this ability variable by means of Rasch's partial credit model, this reference frame can be taken as the interpretative basis to diagnose and analyze students' understanding toward image of convex lens.