Research On Fractional Concept Teaching Based On APOS Theory

In the study of algebraic concepts in junior high school,algebraic equations are expanded from numbers to equations,and fractions occupy an important place in algebraic equations.Fractions are the basis of fractional equations,inequalities,and inverse proportional functions,and they play an irreplaceable role in solving practical problems.However,fractions are not difficult to learn compared with integers which are also rational equations.In this thesis,we combine APOS theory with the teaching of fractional concepts to achieve the purpose of helping students learn fractional equations efficiently.The APOS theory,put out by American math instructor Dubinsky,is a constructivist learning-based approach to teaching mathematical ideas.In this theory,Dubinsky divided the learning of concepts into four processes:Action,Process,Object,and Scheme,and the name"APOS" is derived from the initials of these four words.In this thesis,we analyze the feasibility of applying APOS theory to teaching fractional concepts and conclude that it is feasible to combine the two;we summarize the principles and strategies of APOS theory to guide the teaching of fractional concepts based on the theory,and apply the above conclusions to prepare an instructional design from fractions to fractions and conduct a classroom comparison to test its teaching effects.This thesis uses literature analysis,experimental research,questionnaire survey and other research methods to draw the following conclusions:(1)APOS theory provides ideas and theoretical guidance for front-line teachers to innovate their teaching design.The four stages of APOS theory are logically connected and lead students to complete the construction of conceptual schemas step by step;(2)The APOS theory-guided fractional concept instructional design has a degree of positive effect in improving students’ performance on the fractional concept accompanying test;(3)The APOS theory-guided fractional concept instructional design has a degree of positive effect in improving students’ interest and learning mood towards fractional concept.The purpose of this thesis is to combine APOS theory with fractional concepts in order to increase students’ interest and effectiveness in learning fractional equations.This should not only provide a design direction for teaching fractional equations,but also,hopefully,a reference perspective for teaching other mathematical concepts.