Papers by Author: Yuan Horng Lin

Abstract: The purpose of this study is to compare the reliability of Likert scale between crisp and fuzzy data. The survey data is simulated based on two kinds of questionnaire data. They are questionnaire of crisp data and fuzzy data respectively. According to the viewpoints of fuzzy logic, human thinking is multi-value and fuzzy data will be more appropriate for survey. Therefore, it is proposed that the reliability from fuzzy data will be higher. Results of the simulation show that reliability of fuzzy data performs better than crisp data. Based on the findings of this study, some suggestions and recommendations are discussed for future research.

Abstract: The purpose of this study is to investigate the performance of mathematics reading based on fuzzy clustering. Mathematics reading proficiency is an importance issue which is related to the reading comprehension, mathematics achievement and mathematics literacy. Theoretical foundation of mathematics reading consists of three components, which are general reading comprehension, prior knowledge of mathematics and specific skills of mathematics. The subject is sixth graders. The researchers develop internet system of mathematics assessment and adopt fuzzy clustering to appropriately classify students. Results show that three clusters are the best and there exist characteristics and differences among clusters. Based on the findings, some recommendations and suggestions for future research are provided.

Abstract: The purpose of this study is to provide a new Kappa coefficient based on fuzzy scoring. This new Kappa is called fuzzy Kappa. Fuzzy theory has been widely used in quantitative research and many researches indicate its positive utility. Moreover, viewpoints of measurement according to fuzzy theory conform to the thinking of human thoughts. Therefore, it is feasible to measure the scoring of decision-making or judgment. In addition, Kappa coefficient is one kind of rater reliability and it is to measure the consistency on judgment among raters. Traditional Kappa coefficient is based on the crisp measurement and it violates the psychological nature of human decision-making. Therefore, in this study, fuzzy Kappa, which is based on the fuzzy measurement, is provided. Besides, data simulation is designed to compare of these two Kappa coefficients. The results show that fuzzy Kappa performs better than traditional Kappa. Based on the findings of this study, some suggestions and recommendations are discussed for future research.

Abstract: Knowledge Management of Mathematics Concepts was essential in educational environment. The purpose of this study is to provide an integrated method of fuzzy theory basis for individualized concept structure analysis. This method integrates Fuzzy Logic Model of Perception (FLMP) and Interpretive Structural Modeling (ISM). The combined algorithm could analyze individualized concepts structure based on the comparisons with concept structure of expert. Fuzzy clustering algorithms are based on Euclidean distance function, which can only be used to detect spherical structural clusters. A Fuzzy C-Means algorithm based on Mahalanobis distance (FCM-M) was proposed to improve those limitations of GG and GK algorithms, but it is not stable enough when some of its covariance matrices are not equal. A new improved Fuzzy C-Means algorithm based on a Normalized Mahalanobis distance (FCM-NM) is proposed. Use the best performance of clustering Algorithm FCM-NM in data analysis and interpretation. Each cluster of data can easily describe features of knowledge structures. Manage the knowledge structures of Mathematics Concepts to construct the model of features in the pattern recognition completely. This procedure will also useful for cognition diagnosis. To sum up, this integrated algorithm could improve the assessment methodology of cognition diagnosis and manage the knowledge structures of Mathematics Concepts easily.

Abstract: The purpose of this study is to use ordering theory (OT) to determine existing hierarchies among items with specifically learning style. Furthermore, an empirical data of capacity concepts testing for algebra learning was analyzed based on the integrated method student-problem chart (S-P Chart) is adopted to classify all students into proper learning styles. Cooperating S-P chart and OT are as an integrated method of cognition diagnosis. The empirical data is algebra concepts test of university students. The results showed that cognition diagnosis would be feasible for remedial teaching and design of teaching materials. Finally, some suggestions and recommendations for future research and educational research are provided.

Abstract: The purpose of this study is to integrate two methodological approaches to explore concept structures. One approach is student-problem chart (S-P chart) and ordering theory (OT) and the other is fuzzy clustering and item relational structure (IRS). S-P chart is adopted to classify all students into proper learning styles. OT is to determine hierarchies of concept structures. Fuzzy clustering is soft computation to cluster features of students and combine IRS so as to determine the precondition and ordering relationship among items. The empirical data is statistics concepts test of university students. The results show that integration of these two approaches is feasible for cognition diagnosis and would be helpful for remedial instruction. Finally, some suggestions and recommendations for future research and educational research are provided.

Abstract: The purpose of this study was to apply the fuzzy structural modeling (FSM) in analyzing the concept structures of algebra for 4-graders. The authors utilized the response data of 4-graders in 2007 from Taiwan Assessment of Student Achievement. After the calibrating of equating, the distributing of the abilities of task-takers was clustered into 4 groups with the method of fuzzy clustering analysis. The authors chose the vector center for sample from each group, drew the individual concept structure graphs, and analyzed the hierarchical structures of Algebra concepts. Under the frame of IRT, the study showed the structural characteristics of Algebra concepts from Taiwan pupils. Moreover, the FSM graphs of the task-takers in each group had been analyzed and compared their differences.

Abstract: The purpose of this study was to cooperate student-problem chart (S-P Chart) and ordering theory (OT) as an integrated method of cognition diagnosis. S-P chart was used to classify students into proper learning styles, In order to use OT to determine existing hierarchies among items with specifically learning style. Furthermore, an empirical data of capacity concepts testing for fundamental mathematics learning was analyzed based on the integrated method. The results showed that cognition diagnosis would be feasible for remedial teaching and design of teaching materials.

Abstract: The purpose of this study is to integrate pathfinder and item response theory so as to manage concept structures. Concept structure is one important issue of knowledge management as to human knowledge storage. Pathfinder and item response theory are based on graph theory and psychometrics respectively and this integrated method should be feasible to represent concept structures. Besides, fuzzy clustering technique is adopted to provide features of concept structures based on homogeneity of sample. In this study, the empirical data is the assessment of linear algebra for university students. The important concepts of linear algebra consist of subspace, spanning, linear independent, R² and R³ and many literatures indicate concept structures of linear algebra will influence advanced mathematics. However, little is known about the concept structure and cognition diagnosis on linear algebra. In this study, it shows that lack of concrete examples in general dimensional space will prevent the development of the general theory. There are some limitations for students to use some materials to clarify complicated mathematic concepts perfectly. Most students could not be able to use the geometric insight and apply the Pythagorean of R² or R³. It shows that methodology of the pathfinder and item response theory will reveal important information of concept structures for students. In addition, fuzzy clustering could distinguish characteristics of concept structures on linear algebra. Finally, some limitations and suggestions as to this study are discussed.

Abstract: The purpose of this study is to develop a methodology as to the knowledge management of concept structure for learners. Fuzzy clustering is adopted to implement classification so that learners of the same cluster have homogeneity and display common features of cognition diagnosis. In addition, fuzzy clustering is based on information of concept scoring and caution index from polytomous student-problem chart. In the study, the empirical data is the assessment of statistics concepts from university students. The results show that there are four clusters and each cluster has its own cognitive characteristics. To sum up, the methodology can improve knowledge management in classroom more feasible. Finally, some recommendations and suggestions for future investigations are also discussed.