運用GSP Chart、Rasch Model GSP曲線與GSM分析與表徵數學測驗－－以國小六年級數學科評量為例

Based GSP Chart, Rasch Model GSP Curve and GSM to analyze Math Test - An example on 6th graders' math subject test

成就測驗，有謂能力測驗，評量結果成為關注的焦點，其中，以數學科測驗為最。測驗分析，一則凸顯教與學效益，二則診斷與改善學習困境，三則規劃與施行第二階段教育工程細部工作（Piecemeal Educational Engineering）。運用教育工學科技分析測驗結果的目的：（1）測驗分析數理結構化與表徵視覺化；（2）認知診斷體現科學性與系統性；（3）落實行動研究。研究工具以灰色系統理論為基礎，計有Rasch Model GSP Curve與GSM，前者表徵受試者能力高低與試題品質，後者依據圖學論圖示其階層結構。

The evaluation results of achievement tests, which also called competence tests are highly discussed especially in mathematical related subjects. There are three main purposes of these tests: (1) Evaluating the outcomes of both teaching and learning, (2) Diagnosing and improving learning obstacles for conducting the second-stage piecemeal educational engineering, (3) Planning future learning and teaching. This paper applies Techniques of Educational Engineering (TEE) to analyze the results of achievement tests. The main purposes of this paper are to support teaching and learning with a scientific approach, to identify diagnosis scientifically and systematically, and to realize the activity reach. The grey system theory is used as the analysis tool in this paper, including Rasch Model GSP Curve and GSM. The former is used to characterize the qualities of the examination questions and the tested results, and the latter is used to demonstrate the layer structure of the qualities of the examination questions and the tested results by graphic theory.