An Empirical Study On The Teaching Of Absolute Value Inequality In High School Mathematics

Inequalities are one of the foundational subjects in high school mathematics curricula,the inequality is the part of the algebra.The absolute value inequality is a kind of mathematical model for our students to solve practical problems.Approaching absolute value inequalities often occurs in the National Matriculation Math paper.The high school algebra researches are mainly directed at the solution of absolute value inequalities.Instead,many papers are mainly focused on the proof methods of inequalities,Cauchy inequality and sequencing inequality,which are closely related to college mathematics curricula.Teachers and students didn't pay enough attention to the study of absolute value inequalities,thus students repeatedly making mistakes in approaching absolute value inequalities.This paper examined high school students' methods of approaching absolute value inequalities,their common mistakes,and the possible sources of these mistakes and misconceptions.Using questionnaires,we looked into some high school students who have studied inequalities.9 typical questions to approach absolute value inequalities are used to find out students' common errors and the reason why they made mistakes.Students were interviewed in order to find their ways of thinking and the sources of their misconceptions.Based on the study,teachers can understand students' thought processes and use these to find a way of solving these problems.At the end of this article,two teaching designs of absolute value inequalities are put forward.Firstly,based on the research,students' methods of approaching absolute value inequalities include: direct solving method,using the number line,using the function image,partitioning the solution,using the rules,and squaring both sides.Secondly,the common mistakes of students of solving absolute value inequalities are misconceptions of absolute value symbols,misunderstandings of logical connectives,misconceptions of the relation between equations and inequalities etc.Finally,the teaching suggestions presented in this paper include: we should improve teaching methods,decrease the use of abstract concepts,pay attention to mathematical thinking and methods,and strengthen the cultivation of mathematical thinking ability.Based on the analysis of the teaching suggestions,the teaching design of absolute value triangle inequality and the solutions of absolute value inequalities are designed.