A Survey Research On The Reduction Ability Of Mathematical Gifted And Talented Students In Senior High School

Reduction is a fundamental and important mathematical thinking method.In the process of solving mathematical problems,unfamiliar problems are often reduced to familiar ones,complex problems are decomposed into simple ones,and abstract problems are transformed into concrete ones.All of these can be regarded as the embodiment and application of the reduction mathematical thinking method.In 2022,at the 63 rd International Mathematical Olympiad,China’s top group of mathematical gifted students in senior high school won gold medals with full marks for all members.A small group of mathematically gifted students with strong math learning abilities and remarkable talent have also received increasing attention.Against this backdrop,this study investigates senior high school mathematically gifted students from the perspective of their reduction ability.Specifically,this study focuses on:(1)how high school mathematically gifted students perceive the use of reduction to solve mathematical problems and whether there are gender differences in their perceptions?(2)the current status of high school mathematically gifted students’ reduction ability and whether there are gender differences in their ability.This study developed a survey questionnaire and test paper for high school mathematically gifted students based on the characteristics and connotations of the reduction mathematical thinking method,and surveyed approximately 80 mathematically gifted students from three key high schools in Shanghai.SPSS software was used to analyze the students’ perceptions of the use of reduction to solve mathematical problems in the survey questionnaire,and the students’ reduction ability levels were classified using the SOLO taxonomy in the test paper.In addition,this study interviewed two experienced mathematically gifted education workers to further explain the results of the survey questionnaire and test paper and reveal their causes.The study found that:(1)More senior high school mathematically gifted students are familiar with reduction,and male students are significantly more familiar with it than female students.Only students who are very familiar with reduction will use it more frequently in solving mathematical problems.However,students generally perform poorly in specific reduction strategies.(2)High school mathematically gifted students have a very positive belief in reduction,but their self-efficacy in using reduction to solve mathematical problems is generally low,and there are significant gender differences.(3)The reduction ability of high school mathematically gifted students is mainly at the relational structure level,and only a few students can reach the extended abstract level.The proportion of students at the multistructure level and unistructure level and prestructure level is significantly affected by different reduction strategies.Regarding gender differences,male and female students have significant differences in reduction abilities corresponding to generalization and specialization reduction strategies as well as semantic transformation reduction strategies.Based on the above research conclusions and teacher interviews,this study provides some suggestions for teaching and learning the reduction mathematical thinking method,which can be used as a reference for teachers and students.