A Study On The Current State Of Sixth Form Students’ Intuitive Skills In Geometry

Geometric intuition is one of the core concepts explicitly stated in the Compulsory Mathematics Curriculum Standards(2022 Edition)(hereafter referred to as "the Curriculum Standards(2022 Edition)"),and is an important skill that students need to develop in the learning process.Geometric intuition is embedded in all areas of mathematics learning,with a high proportion of the content in the area of ’Number and Algebra’ in primary mathematics.It is an important expression of students’ understanding and application of mathematical knowledge.This study is based on the content of the Mathematics and Algebra domain.It aims to investigate and study Year 6 students’ geometric intuitive skills,analyse the problems that exist in Year 6students’ geometric intuitive skills,analyse the factors that affect students’ geometric intuitive skills,and make recommendations for their development.Based on theories related to geometric intuition and a detailed analysis of the Curriculum(2022 edition)and mathematics textbooks,this study classifies students’ geometric intuition in the area of "Number and Algebra" into three main dimensions: describing problems using graphs,analysing problems using graphs,and describing and analysing problems using graphs.This was used as the framework for the development of a test of geometric intuition.In this study,132 Year 6 students from Primary School A in Jinan,Shandong Province,were assessed through a test survey method and some students and teachers were interviewed.The analysis of the students’ test results and interviews led to the following conclusions: in the area of "Number and Algebra",the overall ability of Grade 6 students in geometric intuition was average;the students’ ability in "describing problems using graphs" and "analysing problems using graphs" was average."There is a positive correlation between the three dimensions of geometric intuition and the gender differences in the geometric intuition of Year 6 students are not significant.Problems with students’ geometric intuition include a lack of flexibility and completeness in transforming mathematical language,difficulties in describing arithmetic using graphs,a low awareness of using graphs to test results,and a weak ability to synthesise and analyse problems using graphs.Factors affecting students’ ability to use geometric intuition include students’ own learning levels and characteristics,teachers’ understanding of geometric intuition and their ability to develop it,and the development of homework content and assessment systems.Based on the above findings,the following suggestions were made to improve students’ geometric intuition: strengthen the teaching of reading and drawing strategies to improve students’ ability to convert mathematical language;focus on exploring reasoning with shapes to improve students’ intuitive representation of arithmetic;infiltrate the idea of combining numbers and shapes to cultivate students’ habit of testing with graphs;strengthen thinking training to improve students’ ability to analyse graphs;and strengthen the practice of homework after class to cultivate students’ habit of applying geometric The students will also be able to practice after class to develop the habit of intuitive application.