The Study On Cognitive Understanding Of High School Students With Inequalities

In real life,there are two basic quantitative relations: equal relation and unequal relation,among which unequal relation is characterized by inequalities.For the past few years,the College Entrance Examination also increases the requirements of the inequality gradually these years.National and international teachers and students both have problems in the understanding of inequality.However,inequality isn't taught as the core education in mathematics learning.Most of the time teachers only teach students the process to solve inequalities.In order to determine the cognitive understanding level and characteristics of senior high school students and provide the suggestions for the education and teaching based on the situation and the level of students' understanding,this paper draws on Pirie & Kieren's understanding model to propose the concept of the understanding model of high school students firstly.Next the paper selects both vertical and horizontal angles to analyze and determine the inequality of cognitive comprehension of the high school students compulsory part,and then it analyzes and summarizes the characteristics and process of student conceptual understanding through testing and interviews.Finally,we can obtain the following conclusions:1.The cognitive understanding of high school students' inequality is low-level.Nearly half of the students acquire the knowledge in the preliminary characterization stage.2.In the four inequality courses content of compulsory,the inequality nature has the lowest level of cognitive understanding.Simple linear programming has a relatively good level of cognitive comprehension.Even so,the level of application ability and problem-solving capability are relatively low.3.The cognitive characteristics of most students: can not fully understand what they have learned,most students only remember the problem-solving steps to solve problems.4.The process of student concept understanding with inequalities is a holistic,dynamic,horizontal,nonlinear process of development.This paper puts forward suggestions from the teaching materials,teachers and evaluation methods based on the conclusion of this study and the present teaching situation and for reference of teachers and scholars.