A Study Of Teaching Fraction Concepts Based On Multiple Representations

A sound grasp of fraction concepts is an important cornerstone for understanding the arithmetic of fractions and solving problems,but the abstract nature and complexity of the concepts themselves can make them difficult for students to understand.A review of the literature on multiple representations shows that a single representation in teaching mathematical concepts does not fully reflect the essence of the concept,and can compound students’ difficulties in understanding it.In order to promote a more comprehensive and intuitive understanding of concepts,multiple representations can be used.Therefore,in this study,an attempt is made to integrate theories related to multiple representations with the teaching of fraction concepts,and to further explore the teaching of fraction concepts based on multiple representations.The research methods of literature research and questionnaire survey are used to gain an in-depth understanding of the current situation of primary school teachers’ use of multiple representations in teaching fraction concepts.The study will also examine the existing problems and explore the teaching models of multiple representations of fractions.A lesson on "The Meaning of Fractions" was selected as an example,and a specific teaching design and implementation was carried out to understand the effectiveness of the actual teaching.The research questions are as follows.1.How well primary school teachers are using multiple representations in teaching fraction concepts?2.What should teaching fraction concepts based on multiple representations look like?3.How effective is the implementation of teaching fraction concepts based on multiple representations?Three main conclusions emerged from the theoretical and practical research: Firstly,teachers’ perception of multiple representation theory is one-sided;the application of multiple representation is poor;there is a lack of awareness of the need to diversify problem solving through external resources.Secondly,the overall analysis yielded five main types of representations of the concept of fractions: pictorial,symbolic,linguistic,contextual and operational.The teaching process of fraction concepts based on multiple representations includes: creating a life situation to introduce a new lesson;organizing multiple representations to construct concepts at different levels;practicing multiple representations to consolidate and apply concepts;integrating multiple representations to generalize and deepen concepts.Four strategies for teaching multiple representations are proposed: optimizing the organization of multiple representation information,focusing on the order of presentation of multiple representations,promoting the transformation between multiple representations,and strengthening the integration of links between multiple representations.By comparing traditional teaching,it is found that there are certain differences in the selection of sources of multiple representations,the presentation of types of representations and the transformation and integration of representations.Thirdly,the implementation of multiple representations-based teaching of fraction concepts has been found to be effective in enhancing students’ interest in learning,regulating cognitive load and promoting conceptual understanding.