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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 one-lesson-multiple-design and to provide the whole scope and visualized analysis with GSM and MSM.

“If a person neglects education, he will miss the future”. In the 21st century, education carries more the professionalism and modernity than ever. The course of introduction to education is one of the professional basic education courses, covering a wide range, such as philosophy, psychology, sociology, and shifting territory when accompanied by new elements such as digital migration technology, ecology and cultural anthropology. For students majoring in education of regular training 4 years and those students studying education, they must have been aware of the overarching and comprehensive professional education after one semester, it is clear not simple. Simultaneously, with those responsible for teaching this course, challenges to achieve effective as anticipated clearly not small in the context of learners bring different traits include: motive for registration, belonging to different departments, as college students and graduate students, study attitude are also different [

To understand and manage the effectiveness of teaching and learning in course of introduction to education, this study has applied the mathematical tools of research and development towards transdisciplinary research on subjects for students to choose school this subject, aim to: 1) Understand the structural concept of the course focused on the topic of the course and the course, 2) Discriminate the structural conceptual attribute and the development, open this broad concepts, 3) Provide a basis for teaching standards with different textures for the same subject [

Due to the social requirements of network and postmodernism multi-awareness, effectiveness of education and educational standardization has become the key point interested in the renewal and reform of education. Applying mathematical models to combine the development of science and technology in educational research activities conducive to the development, conversion and modernization as well as receiving the evaluation and supervision from community on education. Therefore, the purpose of the study is to: 1) Recognize the right way of distinctness of the original act in the learning process, build knowledge structures according to the trend of learner as nuclear; 2) This study is scientific and so that possible replicative. The progress of research can be mathematized and visualized from examining the data and calculations, mathematical reasoning to structural analysis; 3) Propose a new model of educational research, that is the educational research project with the implementation process combining qualitative and quantitative analyses.

Based on the curriculum of domestic education research methodology, the educational academic and practical researches, educational researches are divided into qualitative and quantitative research paradigms, the former as case study, ethnographic, field study, and narrative analysis, the latter covers the design and construction survey questionnaire, data verification, statistical analysis and prediction. This is to enhance the communication of educational research, the trustworthiness of findings, as well as in response to interdisciplinary trend, the use of mathematically based system of symbolic logic are used as the characterization and analysis tools.

Based on the context of the development of education having coherence and educational research with transferability, using mathematical characterization and analysis tools, in order to: 1) Develop result analysis and interpretation of the data trend; 2) Morphological structural visualization; 3) Propose the design of new researches which have systematic, experimentation, and interpretation. Therefore, the following is introduction of mathematical tools used. This study applied Rough Set Theory of Pawlak [

The rough set theory was introduced by Pawlak in the early 1980s as a mathematical tool to deal with uncertainty. It does not need to be given quantity description or statistical probability distribution of some characteristics or attributes in advance and does not have to obey any assumptions. Rough set theory only says that the set of objects analyzed imply the knowledge and knowledge is considered a classification ability of objects [

Formally, it is an information system, and can be seen as a system:

where: i.

ii.

iii._{i}_{ }is the range of attribute r_{i}.

iv. f is a set of f_{ri}, information function.

Each attribute

According to rough set theory, for every set of attributes

The rough set approach to data analysis hinges on two basic concepts, namely the lower and the upper approximations of a set, lower approximation refers to the elements that surely belong to the set, and upper approximation refers to the elements that possibly belong to the set.

Let

the upper approximation of the set X is:

Some other concepts:

Let C and D be two indiscernibility relations in set S, C is condition attribute and D is decision attribute.

The dependence

The dependence of attribute decides significance of attribute. The significance of attribute

If

If the set of attributes is dependent, it can be interested in finding all possible minimal subsets of attributes, which lead to the same number of elementary sets as the whole set of attributes (called reducts) and in finding the set of all indispensable attributes (called core). The reduct is the essential part of an IS, which can discern all objects discernible by the original IS. The core is the common part of all reducts.

where red(IS) is the reduct of information system IS.

GSM was also proposed by Nagai in 2005, which is based on grey system theory and like interpretive structural modeling, its purpose is to analyze structure of system because it can find out the relationship from observed value indirectly such as statistical graphical modeling [

In grey system theory, GRA is an effective mathematical tool to treat the uncertain, multiple, discrete and incomplete information. This study refers the localized grey relational grade which is proposed by Nagai [

The original vectors in GRA:

The reference vector

The formula of localized grey relational grade is:

And formula of globalized grey relational grade is:

GSM draws digraph by using three parameters: distinguish coefficient

MSM was proposed by Nagai in 2013 [

Based on the multi-matrix method of interpretative structural modeling, it is simply known as multi-matrix interpretative structural model.

The combined set of system:

The combined set

where

The structure system theory of MSM is contracted as the following:

Establish the structure system theory of MSM

where i.

ii.

iii.

Because f is a reachability function, so f satisfies the following:

1) Reflexive law:

2) Anti-symmetric law:

3) Transitive law:

In practice, the MSM cluster matrix calculates amount and scale size using structural new relation matrix as purpose based on the generating of multiple matrix relation and the creating of organization structure, the first one is derived from the relationship between the various elements of attributes, and second one, it is the cluster related structure of the purpose orientation [

The research objects are 21 third-year students of higher education and 15 syllabus researchers, the former has been the introduction to education of the first year, the latter is chapters in detail of the introduction to education of this semester, aimed to: 1) Understand two learning objects to explain the differences, 2) Form the structure of unit nuclear knowledge, 3) Make a standard reference basis for the teaching of introduction to education in future.

The research process is divided into qualitative and quantitative analysis stages (see

cept learning difficulty, on the contrary, the concept learning easier. Thirdly, after testing the reliability of data, using rough set to excavate information; the GSM constitutes isomorphism of “core”, analyzes body of knowledge and structure; MSM characterizes its structural relation. Finally, according to the proposal of structural analysis and directed hierarchy diagram, the diagram is explained.

Towards globalization, technology, and Internet of Things (IOT) era, introduction to the basic theory of education from the traditional philosophy, psychology, sociology, new cultural anthropology, ecology, science and technology and culture, etc., are only selecting the concepts on the first four fields as follows (see

It is worth mentioning: Educational political science and educational finance of sociology aim to: 1) Initiated by the post-modern pluralism, the overall educational practice strategizing becomes necessary, and thus more and more important in educational political science; 2) Facing the globalization of competing interests, profit trends, while input and output performance become the focus of education, on the other hand under the austerity policies being squeezed available funding for education, educational return on investment become truth to be faced; 3) The World is Flat [

Next, combining concepts and pedagogy to constitute the Q matrix (

Finally, combining graph theory and interpretive structural modeling (ISM) [

Subject | Concept | Meaning teaching | Discovery teaching | Eclectic teaching |
---|---|---|---|---|

Philosophy | Epistemology | 1 | 0 | 0 |

Metaphysics | 0 | 0 | 1 | |

Axiology | 0 | 1 | 0 | |

Psychology | Cognitive development | 1 | 0 | 0 |

Personality development | 1 | 0 | 0 | |

Positive psychology | 0 | 0 | 1 | |

Sociology | Structural functionalism | 1 | 0 | 0 |

System theory | 1 | 0 | 0 | |

Educational politics | 0 | 0 | 1 | |

Educational finance | 0 | 1 | 0 | |

Globalization | Regional culture | 0 | 1 | 0 |

Authenticn and criticism | 0 | 0 | 1 |

Firstly, the data of the four-year undergraduate education including 21 third-year students and 15 syllabus researchers in primary education course, all are tested for reliability, Cronbach’s alpha coefficients are shown in

Secondly, based on grey relational analysis the degree of relation between the discrete elements which is calculated by formula of Nagai [

Finally, based on “We Are Student-Centered” (WASC) [

Object\table type | S-P table | P-S table |
---|---|---|

Third year student | 0.82 | 0.86 |

Researcher | 0.82 | 0.92 |

Student\Concept | A9 | A13 | A10 | A14 | A8 | A6 | A3 | A7 | A11 | A12 | A5 | A4 | Gamma |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Max | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 7 | |

S7 | 9 | 7 | 7 | 8 | 9 | 7 | 9 | 8 | 8 | 9 | 8 | 7 | 1.00 |

S2 | 8 | 8 | 8 | 9 | 8 | 8 | 8 | 6 | 7 | 7 | 7 | 7 | 0.93 |

S4 | 9 | 9 | 6 | 5 | 8 | 9 | 5 | 7 | 5 | 6 | 7 | 4 | 0.69 |

S15 | 9 | 5 | 8 | 3 | 9 | 7 | 8 | 9 | 6 | 7 | 6 | 5 | 0.69 |

S8 | 8 | 4 | 9 | 4 | 9 | 9 | 8 | 4 | 6 | 7 | 8 | 5 | 0.66 |

S16 | 7 | 7 | 7 | 7 | 7 | 6 | 5 | 5 | 6 | 6 | 5 | 4 | 0.63 |

S18 | 7 | 3 | 6 | 5 | 9 | 7 | 8 | 8 | 8 | 5 | 6 | 4 | 0.62 |

S13 | 8 | 8 | 7 | 8 | 9 | 8 | 6 | 9 | 3 | 2 | 7 | 5 | 0.61 |

S21 | 8 | 6 | 8 | 7 | 3 | 9 | 3 | 7 | 9 | 7 | 4 | 6 | 0.58 |

S11 | 9 | 5 | 8 | 3 | 8 | 5 | 5 | 8 | 6 | 7 | 4 | 3 | 0.53 |

S10 | 9 | 6 | 7 | 5 | 8 | 5 | 5 | 9 | 3 | 2 | 6 | 5 | 0.48 |

S9 | 6 | 4 | 5 | 6 | 9 | 7 | 3 | 8 | 8 | 9 | 3 | 2 | 0.48 |

S17 | 7 | 5 | 6 | 5 | 8 | 9 | 4 | 9 | 4 | 3 | 7 | 1 | 0.45 |

S6 | 8 | 2 | 6 | 4 | 8 | 4 | 7 | 5 | 4 | 4 | 7 | 7 | 0.43 |

S5 | 8 | 4 | 9 | 4 | 7 | 3 | 7 | 6 | 2 | 3 | 9 | 3 | 0.38 |

S19 | 9 | 6 | 8 | 3 | 6 | 6 | 6 | 4 | 6 | 2 | 3 | 2 | 0.36 |

S12 | 7 | 2 | 5 | 3 | 6 | 6 | 5 | 3 | 7 | 7 | 4 | 1 | 0.30 |

S1 | 4 | 6 | 7 | 7 | 5 | 6 | 5 | 5 | 2 | 3 | 3 | 1 | 0.28 |

S3 | 6 | 6 | 7 | 7 | 3 | 4 | 2 | 3 | 6 | 4 | 2 | 2 | 0.24 |

S14 | 6 | 4 | 8 | 2 | 3 | 5 | 2 | 1 | 4 | 1 | 5 | 7 | 0.11 |

S20 | 5 | 3 | 2 | 4 | 5 | 1 | 5 | 6 | 2 | 1 | 2 | 1 | 0.00 |

Concept\Student | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 | S10 | S11 | S12 | S13 | S14 | S15 | S16 | S17 | S18 | S19 | S20 | S21 | Gamma |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Max | 7 | 9 | 7 | 9 | 9 | 8 | 9 | 9 | 9 | 9 | 9 | 7 | 9 | 8 | 9 | 7 | 9 | 9 | 9 | 6 | 9 | |

A9 | 4 | 8 | 6 | 9 | 8 | 8 | 9 | 8 | 6 | 9 | 9 | 7 | 8 | 6 | 9 | 7 | 7 | 7 | 9 | 5 | 8 | 1.00 |

A13 | 6 | 8 | 6 | 9 | 4 | 2 | 7 | 4 | 4 | 6 | 5 | 2 | 8 | 4 | 5 | 7 | 5 | 3 | 6 | 3 | 6 | 0.92 |

A10 | 7 | 8 | 7 | 6 | 9 | 6 | 7 | 9 | 5 | 7 | 8 | 5 | 7 | 8 | 8 | 7 | 6 | 6 | 8 | 2 | 8 | 0.91 |

A14 | 7 | 9 | 7 | 5 | 4 | 4 | 8 | 4 | 6 | 5 | 3 | 3 | 8 | 2 | 3 | 7 | 5 | 5 | 3 | 4 | 7 | 0.79 |

A8 | 5 | 8 | 3 | 8 | 7 | 8 | 9 | 9 | 9 | 8 | 8 | 6 | 9 | 3 | 9 | 7 | 8 | 9 | 6 | 5 | 3 | 0.71 |

A6 | 6 | 8 | 4 | 9 | 3 | 4 | 7 | 9 | 7 | 5 | 5 | 6 | 8 | 5 | 7 | 6 | 9 | 7 | 6 | 1 | 9 | 0.50 |

A3 | 5 | 8 | 2 | 5 | 7 | 7 | 9 | 8 | 3 | 5 | 5 | 5 | 6 | 2 | 8 | 5 | 4 | 8 | 6 | 5 | 3 | 0.49 |

A7 | 5 | 6 | 3 | 7 | 6 | 5 | 8 | 4 | 8 | 9 | 8 | 3 | 9 | 1 | 9 | 5 | 9 | 8 | 4 | 6 | 7 | 0.45 |

A11 | 2 | 7 | 6 | 5 | 2 | 4 | 8 | 6 | 8 | 3 | 6 | 7 | 3 | 4 | 6 | 6 | 4 | 8 | 6 | 2 | 9 | 0.43 |

A12 | 3 | 7 | 4 | 6 | 3 | 4 | 9 | 7 | 9 | 2 | 7 | 7 | 2 | 1 | 7 | 6 | 3 | 5 | 2 | 1 | 7 | 0.41 |

A5 | 3 | 7 | 2 | 7 | 9 | 7 | 8 | 8 | 3 | 6 | 4 | 4 | 7 | 5 | 6 | 5 | 7 | 6 | 3 | 2 | 4 | 0.27 |

A4 | 1 | 7 | 2 | 4 | 3 | 7 | 7 | 5 | 2 | 5 | 3 | 1 | 5 | 7 | 5 | 4 | 1 | 4 | 2 | 1 | 6 | 0.00 |

Student\Concept | A3 | A4 | A5 | A13 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A14 | Gamma |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Max | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 6 | 9 | 7 | |

S1 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 8 | 9 | 6 | 6 | 7 | 1.00 |

S2 | 9 | 9 | 9 | 6 | 9 | 7 | 6 | 4 | 3 | 6 | 9 | 6 | 0.58 |

S3 | 9 | 9 | 9 | 7 | 9 | 3 | 7 | 5 | 6 | 4 | 7 | 4 | 0.58 |

S4 | 8 | 9 | 7 | 9 | 9 | 9 | 6 | 4 | 5 | 6 | 3 | 4 | 0.53 |

S5 | 9 | 9 | 9 | 9 | 8 | 4 | 5 | 6 | 7 | 3 | 8 | 1 | 0.52 |

S6 | 8 | 8 | 8 | 9 | 5 | 6 | 7 | 9 | 6 | 4 | 4 | 1 | 0.51 |

S7 | 9 | 9 | 9 | 6 | 6 | 8 | 9 | 3 | 5 | 4 | 6 | 2 | 0.50 |

S8 | 9 | 9 | 7 | 7 | 7 | 7 | 7 | 4 | 4 | 2 | 4 | 2 | 0.41 |

S9 | 8 | 8 | 8 | 4 | 7 | 7 | 4 | 6 | 5 | 5 | 3 | 3 | 0.40 |

S10 | 9 | 9 | 9 | 5 | 8 | 3 | 1 | 5 | 6 | 4 | 4 | 2 | 0.25 |

S11 | 7 | 2 | 7 | 8 | 5 | 7 | 6 | 4 | 3 | 2 | 7 | 1 | 0.23 |

S12 | 8 | 6 | 6 | 6 | 6 | 4 | 6 | 4 | 1 | 2 | 4 | 2 | 0.18 |

S13 | 3 | 3 | 4 | 3 | 8 | 3 | 4 | 7 | 6 | 3 | 6 | 4 | 0.16 |

S14 | 9 | 7 | 5 | 4 | 7 | 2 | 1 | 4 | 5 | 3 | 3 | 1 | 0.05 |

S15 | 6 | 3 | 6 | 6 | 7 | 4 | 7 | 1 | 1 | 6 | 2 | 1 | 0.00 |

Concept\Student | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 | S10 | S11 | S12 | S13 | S14 | S15 | Gamma |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Max | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 8 | 9 | 8 | 8 | 8 | 9 | 7 | |

A3 | 9 | 9 | 9 | 8 | 9 | 8 | 9 | 9 | 8 | 9 | 7 | 8 | 3 | 9 | 6 | 1.00 |

A5 | 9 | 9 | 9 | 7 | 9 | 8 | 9 | 7 | 8 | 9 | 7 | 6 | 4 | 5 | 6 | 0.92 |

A6 | 9 | 9 | 9 | 9 | 8 | 5 | 6 | 7 | 7 | 8 | 5 | 6 | 8 | 7 | 7 | 0.91 |

A4 | 9 | 9 | 9 | 9 | 9 | 8 | 9 | 9 | 8 | 9 | 2 | 6 | 3 | 7 | 3 | 0.79 |

A13 | 9 | 6 | 7 | 9 | 9 | 9 | 6 | 7 | 4 | 5 | 8 | 6 | 3 | 4 | 6 | 0.71 |

A8 | 9 | 6 | 7 | 6 | 5 | 7 | 9 | 7 | 4 | 1 | 6 | 6 | 4 | 1 | 7 | 0.50 |

A7 | 9 | 7 | 3 | 9 | 4 | 6 | 8 | 7 | 7 | 3 | 7 | 4 | 3 | 2 | 4 | 0.49 |

A12 | 6 | 9 | 7 | 3 | 8 | 4 | 6 | 4 | 3 | 4 | 7 | 4 | 6 | 3 | 2 | 0.45 |

A9 | 8 | 4 | 5 | 4 | 6 | 9 | 3 | 4 | 6 | 5 | 4 | 4 | 7 | 4 | 1 | 0.43 |

A10 | 9 | 3 | 6 | 5 | 7 | 6 | 5 | 4 | 5 | 6 | 3 | 1 | 6 | 5 | 1 | 0.41 |

A11 | 6 | 6 | 4 | 6 | 3 | 4 | 4 | 2 | 5 | 4 | 2 | 2 | 3 | 3 | 6 | 0.27 |

A14 | 7 | 6 | 4 | 4 | 1 | 1 | 2 | 2 | 3 | 2 | 1 | 2 | 4 | 1 | 1 | 0.00 |

standardization of education is urgently needed. Applying models of educational engineering constructed with mathematical logic in education are adequately proposed approaches.

This paper has used ROSE2 software of Laboratory of Intelligent Decision Support Systems of the Poznan University of Technology on the URL http://www-idss.cs.put.poznan.pl (2014) [

Activities in the classroom, one can see the instructor transmitting knowledge, shows the world we are living is featured in the characterization of the design, on the other hand it shows how the learners think and learn knowledge, judge and understand knowledge in thinking norms, to master the essence of things and phenomena of the world.

It is noteworthy that, the key concepts and knowledge matter to the content, characterization of the content is denoted by the world, the first thing, to acknowledge curriculum, the code is fundamental; the second thing, to identify systematic structure of knowledge manipulating the process of teaching, during shuttling back and forth such as specific vocabulary, interactivity, awareness, misunderstanding or understanding, wrong solution etc., judgment criterion manifests the truth of existence object, reality and adaptability. Based on the complexity and variability of understanding in learning, grasp and diagnostic of learning results are becoming increasingly important.

Generally speaking, systematic structure of knowledge transferred in the classroom, one side based on proposition employed with expertise, the other side on academic profession, are implemented with teaching experience and interaction between teachers and students, the transformed principles as following: 1) Between concepts, there are implied relationships, difficulties, the difference in size and logic, 2) The attributes of concept for this hierarchy chain structure from concrete to abstract, from low level rise to high level, and 3) Mindset, cognitive understanding, cognitive learning process and only after understanding the concept below, to learn the advanced concepts and complex difficulties.

Based on the results outputted from ROSE2 software, the third year students and the syllabus researchers, who answered the work sheet, both of them have a simple core (

Concept\Subject | Researcher | Student |
---|---|---|

Epistemology | 8 | 3 |

Axiology | 6 | 3 |

Cognitive development | 6 | 7 |

Metaphysics | 6 | 2 |

Authentic and criticism | 6 | 4 |

Positive psychology | 6 | 9 |

Personality development | 4 | 8 |

Educational finance | 4 | 9 |

Structural functionalism | 4 | 6 |

System theory | 1 | 5 |

Educational politics | 2 | 8 |

Regional culture | 2 | 6 |

It is worth mentioning that, the difference between simplified form and complicated (full) form of GSM diagram are: 1)

Firstly,

Secondly, in

Based on the sorting of number value of grey relational analysis, S9 with its Gamma = 0.48 in the center (see

For the third-year students:

For the syllabus researchers (master degree program):

Synthesis of descriptions above (Figures 5-8), obtained: 1) Educational students and researchers have cognitive gap between them; 2) The special cases in simplified and full forms are possible unified; 3) The vertical direction in full and simplified forms can master the focal points of overall structure, or represent the starting point of learning advance, or making as second teaching, remedial teaching basis, or even on the table in mind the issue of distribution at below or above key points.

Combining Nagai’s matrix based structure modeling and graph theory, in order to construct the structural analysis of integrity and visualization (see

Finally, the point concepts of convergence and differentiation are: 1) The place where the conversion and transformation of knowledge hierarchy structure exist, 2) Teaching and learning are possible difficulties, 3) Making every effort for the same class with heterogeneous structure.

“For great education plan, teacher must be centered”. Introduction to education is not only one of the educational compulsory subjects, but also is a subject of structural and scientific cognitive education. With the broad scope and the main academic knowledge system of higher education, teaching and learning quality have become

the focus, so it takes the learning outcomes of the third year undergraduate educational students and master degree program researchers in primary education course to analyze for understanding. Aggregated by the concepts, the questionnaire respondents have been processed by Nagai’s grey relational analysis program, ROSE 2 software, and technique as indicated in Tables 3-6 and Figures 2-9.

Based on the systematic instructional design principles, the starting behavior of learners are based on the same class with heterogeneous structure teaching on classroom, effective control, diagnose this starting behavior is imperative. The conclusion from Figures 5-8: 1) The thinking pattern is the inductive and deductive cycles, 2)

The detail concepts converge in inductive point, from a point it can be deduced for expanding differentiation, and spiraling to construct knowledge system; 3) The focal point of directed hierarchical structure can be considered the diagnosis, grouping, evaluation, and making every effort of second education.

Finally, since the 1970s, academic education and professional development have become the norm, enhancing the educational research methodology and research method has become necessary. The combination mathematical tools with professional consensus on education in research are that the data collection and calculation, interpretation of knowledge structure and logical implication, along with systemization and digitalizing to achieve the purpose of prediction and control. Now, the use of mathematical tools to construct the context of situation of confidence interval; using Rough set to reveal the concepts in core, using LGRA to select adjacent learners and construct GSM, MSM combining with graph theory to characterize and visualize the multiple sets structure, it can be seen the following benefits: 1) Scientifically and diagnostically demo learning results between the two groups, 2) Divergence and gap emerges in structural analysis, 3) Structural analysis displays in quantization and visualization.

Hui-ChungHo,Woody Jann-DerFann,Hsiu-JyeChiang,Phung-TuyenNguyen,Duc-HieuPham,Phuoc-HaiNguyen,MasatakeNagai, (2016) Application of Rough Set, GSM and MSM to Analyze Learning Outcome—An Example of Introduction to Education. Journal of Intelligent Learning Systems and Applications,08,23-38. doi: 10.4236/jilsa.2016.81003