Fuzzy models in learning and teaching Mathematics

Abstract

This thesis entitled Fuzzy models in learning and teaching mathematics newlineconsists of six chapters. Chapter 1 is introductory in nature which unfolds the newlinecentral theoretical background of the thesis. This chapter summarizes an newlinehistorical review of fuzzy model and other contents covering the thesis. Chapter newline2 introduces the model for teaching mathematics. In this chapter, the teachers newlinecharacteristics under assessment are represented as fuzzy subsets of a set of newlinelinguistic labels characterizing their performance and the possibilities of all newlineteacher profiles are calculated. Chapter 3 discusses the fuzzy triangular and newlinetrapezoidal model for analyzing teachers group performance and also compared newlineviii newlinewith traditional methods. Chapter 4 deals with a mathematical fuzzy model to newlineanalyze the students mathematical learning skill. Further this chapter enlightens newlinethe degree of satisfaction for various subjects matter in mathematics. Chapter 5 newlinepresents a model to analyze the student s mathematical skill using fuzzy newlineinference system (FIS). This chapter explains the comparison of two different newlinemembership functions and getting more or less similar and also explains a fuzzy newlineexpert system and logic reasoning for evaluation of Mathematics students newlineMathematical skill based on fuzzy logic techniques with MATLAB. The newlinemodeling and simulation was worked in MATLAB-SIMULINK. The results of newlinesimulation proved the validity of proposed technique.Chapter 6 deals with to newlinemeasure the students expectations and teachers beliefs on learning newlinemathematics using fuzzy conjoint model. In this model, the scores of students newlineexpectations and teachers beliefs were changed into degree of similarity and newlinelevel of agreement for attributes. These similarity measures are used for newlinemeasuring teachers beliefs and students expectations on learning mathematics.