An Action Research On Promoting Students' Conceptual Understanding Of Fraction Based On Multiple Representation Theory

Fraction are internationally recognized as the most important and complex concepts of elementary school.Multi-representation theory provides a scaffold structure for teaching.On the basis of reading literature and related theories,the author defines related concepts,summarizes the theory,and summarizes the concepts of fractional mathematics,the representation of fractional concepts,the teaching of fractional concepts,and the teaching of fractional concepts under the guidance of multiple representational theory.Diversity,advancement,flexibility are the three characteristics of fractional concept,propose the multivariate representation schema of fractional representation,and summarize the research status.This research first attempts to discuss whether multi-representation involvement in fractional concept teaching is beneficial to the understanding of concepts.Secondly,trying to discuss the implicit representations of students by observing and analyzing the usual representation forms of students,and asking the following research questions.I.What is the cognitive basis of the preconcept of fraction,halving concept and the definition of fraction for fifth grade students??.Under the guidance of multiple representation theory,how different is the understanding degree of teaching intervention on the fractional concept,measurement definition and equivalent fraction of grade five students??.From the three dimensions of the definition of fraction,the proof of equivalent fraction and the explanation of improper fraction meaning,what tendency do fifth graders have for representation choice? This research uses the action research method to pre-test the cognitive base of the fifth grade students of Xiamen Binhai Primary School on the concept of fraction preconcept.Focusing on the core concepts of fractions,choose three classes: "The Meaning of Fractions","Fraction and Division",and "Basic Character of Fraction" to carry out multi-representation teaching practice activities.Finally,the effectiveness of teaching intervention is tested by post-testing,and three conclusions are obtained:?.Cognitive basis of the concept of equipartition in the fractional preconcept: In the concept of equipartition,students can better grasp the equipartition is the premise of learning fraction,but is limited by the concept of narrow equipartition.The problem-solving situation in the definition of the number of copies is ideal,but "1" is limited to the whole and it is difficult to mathematicalize from the "number ratio" to the "number of copies ratio".?.After multi-representation intervention teaching,there are significant differences in the understanding of the concept of equipartition and the concept of measurement,but there is no difference in the equivalent fraction.It shows that teaching under the guidance of multiple representation theory can promote students' understanding of the concept of fraction.?.Regarding the choice of representational tendency,in the problem of the definition of the number of copies,students tend to discrete representation.Proof of equivalent fraction,students tend to continuously characterize.When explaining the meaning of improper fraction,the continuous representations are rich in variety and are selected by more students.