The Influence Of Three Different Situation Creation Methods On The Level Of Mathematical Concept Understanding Of Junior High School Student

Mathematical concepts are the basic units of thinking and the foundation of all declarative knowledge.How to help students understand mathematical concepts vividly and effectively through a lesson is a topic that educators have been constantly exploring.Equations are not only an important tool to help students portray quantitative relationships and build model ideas;they are also one of the important contents in middle school mathematics.Carrying out the teaching of quadratic equation concept helps develop students’ ability of analogy and helps them construct quadratic equation models independently;at the same time,the learning of quadratic equation content also affects the understanding and mastery of subsequent quadratic function concepts.The study of the effects of three different context creation approaches on students’ level of understanding of the quadratic equation concept addresses the following questions:(1)What are the main context creation approaches used in the teaching design of the quadratic equation concept in the current domestic junior high school mathematics textbooks and instructional design literature?(2)Are there any differences in the effects of different contextualization approaches on students’ understanding of quadratic equation concepts? If so,are the differences significant?(3)Are there differences in the effects of different contexts on students’ conceptual understanding of quadratic equations at different academic levels? If there is a difference,is it significant?The study first used the literature analysis method to sort out the textbooks and teaching design research literature related to the concept of quadratic equation,and to compile the commonly used contexts for creating the concept of quadratic equation.Based on the suggestions of front-line teachers,three main contexts were identified: realistic contexts,systematic contexts,and exploratory contexts,according to which the teaching design and experiments of quadratic concepts were conducted.The concept test paper was prepared according to Professor Shi Ningzhong’s theory of quantity and quantitative relations,and the content of the post-test paper was modified several times on the basis of consultation with experts and pre-tests to determine the content of the post-test paper.After that,three parallel classes were selected to carry out the quasi-experimental study: class 1 took a realistic context,class 2 took a systematic context,and class 3 took an exploratory context.Immediately after teaching,the post-test paper was used to test students’ conceptual understanding,and SPSS23.0 was used to analyze the experimental data,combined with an interview outline for each class to assist in analyzing the experimental findings.The findings of the study were:(1)At present,there are five types of teaching contexts,namely,realistic,systematic,problematic,inquiry,and cultural contexts,and the teachers mainly used realistic,systematic,and inquiry contexts in teaching the concept of quadratic equation.For teachers in the mainland who are in the secondary school level,the concept of "quadratic equations" is taught in realistic,systematic and exploratory contexts.(2)For students in urban public junior high schools in mainland China,the use of different contexts significantly affects students’ understanding of the quadratic concept,and systematic contexts are better than realistic contexts and inquiry contexts in terms of overall teaching effectiveness and different stages of conceptual understanding.The difference effects were between the medium and large effects.(3)For students in the middle level of urban public junior high schools in mainland China,the effect of using different contexts on students’ understanding of the quadratic equation concept varies according to their academic level.The effect on the level of conceptual understanding was significantly different between the high and middle groups.(4)The effect of different contextualization methods on students’ conceptual understanding is also affected by the different contents of the teaching,so the careful selection of contextualization methods and the organization of classroom teaching need to be considered in the context of various factors.Based on the results and conclusions of the study,we propose the following teaching suggestions on the concept of quadratic equations:(1)to create a complex teaching situation with attention to students’ cognition and interest;(2)to improve the induction process and strengthen the knowledge system of equations;(3)to pay attention to students’ differences and implement tiered assessment.