Introduction to education is one of the basic courses in teacher education professional education, it covers a wide range of subjects. Thus, in order to practice the management teaching goals, the interdisciplinary developed mathematical tools are applied for the study. The participants of this study are students in course of introduction to education, and the research instruments applied are rough set, grey structural modeling (GSM), and matrix based-structural modeling (MSM). The purposes of this paper are: 1) To logically analyze educational datasets to practice the scientific traits in education; 2) To benefit from directed hierarchical analysis to identify and propose action planning; 3) To construct core-oriented educational structure as the criterion-reference for onelesson-multiple-design and to provide the whole scope and visualized analysis with GSM and MSM.

This paper presents an educational praxis of classroom assessment in curriculum and learning outcomes of “Introduction to Education”, and constructs assessment tool and analyzes them based on the mathematical modeling, the former with Q Matrix and ISM (Interpretive Structural Modeling), the latter mainly with Nagai’s GSP (Grey S-P) Chart, RaschGSP Curve, GSM (Grey Structural Modeling) and MSM (Matrix Based Structure Modeling). It aims: (1) To use and implement numerical value as the code for processing data, (2) To analyze and diagnose based on raw numerical values, (3) To illustrate and explain in visual diagraph analysis. Moreover, it is worth mentioning that applying mathematical logic in educational research, and such tools are not in favor of the quantitative approach, rather claimed unique feature of math logic, in benefit to: (1) Interface qualitative contextual analysis and quantitative numerical characters as the whole, (2) Convert teaching-learning praxis into binary numerical data, (3) Address alternative interdisciplinary educational research.

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Professionalism has been estimated as the most important fundamental impetus in progress. Teacher profession as the most important within-school factor has been emerged to explain effective teaching and learning by research. In viewing of teacher in-service training, professional development and innovation is thus highlighted as key prerequisite for high quality teaching. Factor analysis of teacher professional development and evaluation based on math methods was primarily to identify factorial sequences of activity involving two teamwork in the classroom. The purpose of this study is to perform to: 1) Couple quantitative and qualitative accesses to display teaching research, 2) Deliver the differences of pedagogical reasoning between graduate students and undergraduate students, 3) Analyze and visualize the educational practices based on math methods, the former is to embody educational performance in academic features, the latter is to communicate concretely and contextually. Research techniques herewith are Nagai's proposals of Rasch model GSP curve (RaschGSP curve), Grey structural modeling (GSM) and Matrix-based structure modeling (MSM) have been applied to illustrate structural analysis.

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