A Survey Of Junior High School Students’ Understanding Of Quadratic Functions

Mathematical comprehension is the foundation and core of mathematical learning.There are differences in the understanding of the same knowledge among different students,and the learning evaluation method based on the test scores cannot comprehensively reflect the students’ differences in the degree of knowledge understanding and methods.SOLO classification theory has the advantage of combining quantitative and qualitative,which can more comprehensively reflect students’ understanding of what they have learned.As an important part of junior high school mathematics knowledge system,quadratic function is one of the more difficult contents to understand in junior high school mathematics.Accurately grasping students’ understanding of quadratic function with the help of SOLO classification theory will help teachers to carry out more targeted teaching.Students have difficulties in solving problems related to quadratic functions,and through interviews with students,it is found that the reasons for students’ difficulties are not only not understanding the content of the knowledge,but also not understanding the meaning of the questions to a greater extent.The key to understanding the meaning of the question is to read and analyze the title,and the impact of mathematical reading on mathematical comprehension can be seen.Therefore,the main questions addressed in this study are:(1)What is the level of understanding of the knowledge of quadratic functions among junior high school students? What are the factors that cause differences in students’ comprehension levels;(2)Are there differences in math problem-solving reading among students with different comprehension levels?(3)According to the obstacles and causes of students’ understanding of quadratic function knowledge,teaching strategies to improve students’ understanding of quadratic functions are proposed.In order to solve the research problem,the research process of this research is divided into three stages: the first stage,based on the SOLO classification systems,compiles the evaluation framework of the quadratic function comprehension level;the second stage,the self-compiled "Quadratic Function Comprehension Level Test Paper" is used to survey all the students in the ninth grade of the school.On the one hand,the data of the test paper are analyzed,on the other hand,some students are selected for interviews,and the students learn the level of understanding,influencing factors and reading behavior differences in the dimensions of the quadratic function(concept representation,image nature,quadratic function model and knowledge structure)after learning the quadratic function;in the third stage,according to the survey results,effective teaching strategies are proposed in a targeted manner.The survey results show that:(1)the students have the highest level of comprehension in the dimension of quadratic function image properties,and the understanding level of the other three dimensions is generally not high,and most of them are at level two;(2)in the dimension of concept representation,students have the highest understanding level.Most of the cognition of the concept of quadratic function exists in the form of written symbolic representation,and the representation form is relatively simple.Most of the students can write y=ax2+bx+c when representing quadratic functions in symbolic language,but the proportion of students who can notice the constraints such as the coefficient of quadratic term in the concept is not 0 is relatively low.(3)In the dimension of image properties,students have a good grasp of using formulas to find vertex coordinates and symmetry axes,but are not proficient in image translation and the transformation relationship between images and properties;(4)Students are familiar with quadratic function models The practical application of it is more difficult than the mathematical application,and it is difficult to establish an accurate and complete quadratic function knowledge structure.The factors that affect students’ understanding of quadratic functions are:(1)the excellent degree of individual CPFS structure;(2)mathematical reading ability;(3)the degree of grasp of mathematical thinking methods.The differences in problem solving reading of junior high school students with different levels of understanding are mainly reflected in:(1)students with high comprehension levels are accustomed to marking when reading;(2)students with high comprehension levels are good at combing text relationships through intermediaries;(3)students with high comprehension levels are accustomed to analyzing problems with the help of graphics;(4)students with high comprehension levels tend to express problems in their own language.The teaching strategies to promote the understanding of quadratic functions mainly include teaching the concept of quadratic functions:(1)reading textbooks and paying attention to the standardization of concept expression;(2)multiple representations to enhance the firm grasp of concepts;(3)comparative analysis to promote the clarity of conceptual understanding.In terms of improving the ability to review questions:(1)communicate and display,enhance the self-confidence of reading questions;(2)do a good job of labeling to ensure the integrity of problem information;(3)improve the methodological nature of the examination process with the help of outlines;improve the CPFS structure and promote the comprehension of mathematical thinking methods:(1)draw concept maps to improve the internal relevance of knowledge;(2)expose thinking and improve the thinking of mathematical learning.