A Teaching Experiment Research Of The Problem Of Quadrilateral Existence In The Context Of Quadratic Function

According to Mathematics Curriculum Standards for Compulsory Education(2011 Edition),mathematics is a science that studies quantitative relations and spatial forms.“The mathematics curriculum includes not only the results of mathematics,but also the formation process of the results and the mathematical ideas and methods contained therein.” The problem of quadrilateral existence in the context of quadratic function is a comprehensive problem of function and geometry,which mainly involves two important knowledge points of junior high school,that is,mathematical numbers and algebra,and graphics and geometry.Over the years,many provinces and cities has often used quadratic functions and geometric synthesis as the grand finale in the senior high school entrance examination,and the last question often examines the existence of quadrilaterals.Quadrilateral existential problem in the context of quadratic function is a difficult point in junior high school teaching,but also a carrier for cultivating students' comprehensive ability to solve problems.Students have made many mistakes in solving such problems,so it is of great practical significance to conduct experiment research on the existence of quadrilaterals in the context of quadratic functions,find out students' learning difficulties,figure out corresponding teaching strategies,and provide some help for teachers' teaching and students' learning.In this study,research methods as testing,teaching experiment and interviewing method were applied to conduct experiment research on 45 subjects recruited in the third grade of the school where the author teaches.There are two experiments in this research: teaching experiments of the parallelogram existential problem and the rhombus existential problem in the context of quadratic function.Each experiment tests the subjects to understand the learning barriers of students to solve such problems,on the basis of which effective teaching strategies are explored,targeted teaching designs are made.After that,the teaching experiments are conducted on subjects and they are tested again immediately after each class.10 of the subjects are interviewed to explore the effects of teaching experiments and those of students' learning.Based on this,the study attempts to answer three research questions:(1)What are the obstacles students have in solving the quadrilateral existential problem in the context of quadratic function?(2)What are the teaching strategies for the quadrilateral existence problem in the context of quadratic function?(3)What is the teaching experiment effect of quadrilateral existence problem in the context of quadratic function?Judging from the experimental results,both experiments have extremely significant effects.In this process,the obstacles students have can be classified into the following 6 categories: knowledge barriers,skills barriers,logic barriers,reading disabilities,expression disorders and computational disabilities.In view of these obstacles,4 teaching suggestions are proposed:(1)Pay attention to the review of the pre-knowledge;(2)Pay attention to the representation of geometric features in the coordinate system;(3)Focus on the infiltration of mathematical thoughts;(4)Pay attention to the normative use of mathematical expressions.Through this experimental study,the effective teaching strategies can be further promoted to other similar classroom teaching,so as to find better teaching methods that can help students,improve teaching effects and students' learning effects,and provide some reference for other teachers and students.