Investigation On Mathematical Representation Of High School Students

Mathematical representation is the embodiment of mathematical thinking,and an important ability to mathematical learning and mathematical problem solving,which has an important impact on students' in-depth understanding of mathematical concepts,so it has always been the focus of international mathematics education research.On the one hand,mathematical representation is often regarded as one of the core competencies of mathematics in the mathematics curriculum reforms and their curriculum standards in many countries;on the other hand,international assessment programs related to mathematical ability(such as PISA,TIMSS,etc.)also generally pay attention to mathematical representation.Although Chinese high school curriculum standards do not describe "mathematical representation" as a mathematics key competence,it has penetrated into mathematics key competencies such as mathematical abstraction,mathematical modeling,and intuitive imagination,which has become indispensable mathematics competencies for high school students in China.The purpose of this study is to measure the mathematical representation of high school students.Research questions are as follows:(1)What is the performance of mathematical representation among high school students?(2)Are there gender differences in mathematical representation among high school students?(3)What is the relationship between the mathematical representation and their academic achievement in mathematics among high school students?In this study,mathematical representation is defined as: Firstly,the learner converts the representation system in the problem situation into a more suitable representation system,then deducts it,and finally obtains and explains the result.The learner should evaluate its rationality during mathematical representation.Based on the literature review,this study constructs an evaluation framework for high school mathematical representation.The evaluation framework consists of three elements:mathematical representation system,mathematical representation process and mathematical representation level.The results are as follows:(1)The average level of high school students' mathematical representation is 1.83.Among them,students perform best in the process of mathematization,followed by deduction,followed by interpretation and evaluation.(2)There is no significant difference between boys and girls in mathematical representation ability.Boys are slightly better than girls in "mathematization ",and girls are slightly better than boys in "deduction" and "interpretation and evaluation".(3)There is no statistically significant correlation between the mathematics academic performance and mathematical representation in Class A,while there is a significant correlation between the mathematics academic performance and mathematical representation in Class B.Finally,some suggestions are put forward for mathematics education researchers and mathematics teachers.