| Being able to analyse problems with a mathematical perspective and apply mathematical methods to solve practical problems in social life are essential skills for modern society.Mathematical model thinking,as an important mathematical idea,was first introduced in the Mathematics Curriculum Standards for Compulsory Education(2011 Edition)and is one of the ten core concepts.In the newly revised Mathematics Curriculum Standards for Compulsory Education(2022 Edition),model thinking is refined into model awareness at the primary level and model concepts at the junior secondary level,which shows the importance of model thinking in the teaching of mathematics.At the junior school level,quadratic equation and quadratic functions contain a wealth of mathematical ideas and methods,among which modeling ideas are particularly important.Modeling ideas help students to establish connections between mathematical knowledge and real life,cultivate their innovative spirit and practical skills,and have become an indispensable part of mathematics teaching and learning at the junior secondary level.In Lhasa,however,the classroom teaching of modeling ideas into quadratic equations and quadratic functions in Lhasa is not satisfactory due to the complex structure of teachers,the low promotion of modern educational technology application,and the weak foundation of students.Therefore,this study firstly adopts the literature analysis method to understand the development of modeling ideas at home and abroad,and analyses the current situation of research on the integration of modeling ideas into junior high school mathematics teaching.After combing through the relevant literature,the concepts of model thinking and mathematical modelling were defined.A questionnaire was designed and distributed to students to explore their learning of quadratic equations and quadratic functions as well as their understanding of modelling ideas,divided into four dimensions based on the general curriculum objectives of the "three skills".The questions are divided into four topics based on the Mathematics Curriculum Standards for Compulsory Education(2022 Edition),examining students’ basic computational skills in quadratic equations,practical problem solving skills in quadratic equations,mastery of the graphs and properties of quadratic functions,and practical problem solving skills in quadratic functions.The teacher’s interview outline was designed.The teacher interviews were designed to cover three main areas: understanding of modeling concepts,teaching of quadratic equations and quadratic functions,and opinions and suggestions on the integration of modeling concepts into teaching.The following conclusions were drawn:(1)On the whole,Year 9 students seem to have a certain awareness of mathematical modeling ideas and mathematical modelling,and have a strong willingness to understand and apply them to mathematics learning;(2)Gender has a greater impact on students’ learning of quadratic equations and quadratic functions and their cognitive ability of modeling ideas,with boys performing slightly better than girls on the whole;(3)Only half of the students have a good understanding of quadratic equations and quadratic,only half of the students were at a high level in mastering the basic knowledge of quadratic equations and quadratic functions and applying their knowledge to the actual question answering,the students as a whole were not firmly grounded in both foundations,the integration of model ideas into their learning was not good and their basic modelling skills were not sufficient;(4)Most teachers felt unfamiliar with the idea of models and did not pay enough attention to it.Again,the results of student questionnaires,student test questions,and teacher interview outlines were summarized,and teaching examples of Modeling Ideas: Quadratic Equations and Quadratic Functions were designed based on constructivist learning theory,metacognitive theory,and Polya’s theory of problem solving strategies,implement and listen to the suggestions of frontline teachers for reflection and conclusion.Finally,combining the findings of the survey and analysis with the feedback from the teaching examples,four suggestions for integrating modeling ideas in junior high school mathematics teaching are proposed:(1)Improving students’ reading comprehension;(2)Strengthening mathematical thinking methods and building a knowledge system;(3)Linking with real life and organising mathematical modelling;(4)Deeply appreciating the requirements of curriculum standards and deeply exploring the content of modeling ideas in teaching materials,which provide reference for teaching practitioners. |
PDF Full Text Request