Papers by Keyword: Concept Structure

Abstract: Building relationship between conceptual knowledge and the procedures of mathematics contributes to long-term memory of procedures and to their effective use. So we know that symbols could enhance concept and procedures apply concepts to solve problem efficiently. 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.

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.

Abstract: The purpose of this study is to integrate a knowledge management which provides graphic representation on concept structures based on clustering technique. The polytomous student problem chart (S-P chart) is adopted to classify students into proper learning styles according to response pattern with caution index and score. Furthermore, weighted polytomous ordering theory (OT) is used to construct graphic concept structure of each learning style. The integration of polytomous S-P chart and weighted polytomous OT could help knowledge management for students. In the study, the empirical data is the assessment of linear algebra from university students. The results show that each learning style has its own features of cognitive characteristics. In short, the integrated methodology can improve knowledge management for students more feasible. Finally, some recommendations and suggestions for future studies are discussed.

Abstract: Euclidean distance function based fuzzy clustering algorithms can only be used to detect spherical structural clusters. The purpose of this study is improved Fuzzy C-Means algorithm based on Mahalanobis distance to identify concept structure for Linear Algebra. In addition, Concept structure analysis (CSA) could provide individualized knowledge structure. CSA algorithm is the major methodology and it is based on fuzzy logic model of perception (FLMP) and interpretive structural modeling (ISM). CSA could display individualized knowledge structure and clearly represent hierarchies and linkage among concepts for each examinee. Each cluster of data can easily describe features of knowledge structures. The results show that there are five clusters and each cluster has its own cognitive characteristics. In this study, the author provide the empirical data for concepts of linear algebra from university students. To sum up, the methodology can improve knowledge management in classroom more feasible. Finally, the result shows that Algorithm based on Mahalanobis distance has better performance than Fuzzy C-Means algorithm.