Research On The Teaching Design Of "Circle Circumfere Nce" In Primary School Mathematics Based On Van Hiel E’s Theory

Circle is the last flat figure taught in the field of "graphics and geometry" in elementary school mathematics.Learning circle not only allows students to experience mathematical ideas such as "turning curves into straight lines","limits",and "equal product changes",but also develops students’ spatial concepts,enhances their problem-solving and abstract generalization abilities,and thus cultivates students’ core mathematical literacy.However,the reality is that students can easily confuse the concepts of perimeter and area.According to a survey,teachers often focus on memorizing formulas and practicing calculations when teaching this part of the content.Teachers neglect students’ geometric thinking level and also underestimate the process of students’ personal exploration of knowledge generation.As a theoretical framework for teaching geometric concepts,Fanhill’s theory not only assesses students’ geometric thinking level,but also serves as a basis for instructional design.This theory emphasizes the important role of teaching in the transition of students’ thinking level.Therefore,the design of primary school mathematics teaching based on the Van Hill theory is an important teaching carrier for implementing core mathematical literacy and improving students’ geometric thinking level.By using research methods such as measurement,interview,observation,and data analysis,and taking the lesson "Circumference of Circle" in the second volume of the fifth grade mathematics textbook of Jiangsu Education Press as an example,Class A,Grade 5 of X Primary School in Yangzhou,was selected as the research object to analyze the learning needs,learners,and teaching content before the teaching design.According to the requirements of Fan Hill’s theory,the teaching objectives,teaching content,teaching process,and teaching evaluation were designed.Finally,the implementation and effectiveness analysis of this teaching design were carried out.The results showed that the classroom teaching of "circumference of a circle" in elementary school mathematics based on Fanhill’s theory can deepen students’ understanding of the concept of circumference and improve their problem-solving ability;Enhance students’ hands-on operation ability and strengthen their awareness of group cooperation;Experience the connection between graphics and life,and accumulate learning experience in understanding graphics.However,there are also the following shortcomings:inadequate consideration of classroom generation and insufficient preparation of pre class learning materials;The activity requirements and group division of labor are not clear,and the types of exercises are not rich;The students’ level of geometric thinking has been elevated,and the form of the summary process is inappropriate.In order to make up for the shortcomings and improve teaching,the following optimization strategies have been proposed:providing sufficient experimental materials to comprehensively characterize geometric shapes;Clarify the sequence of practical activities to enhance students’ operational experience;Pay attention to students’ true thinking level and achieve precise teaching;Pay attention to the transformation of text,symbols,and graphic language.