A Case Study Of The Comprehension Ratio And Proportion Of Sixth Grade Students

In the process of mathematics learning,ratio and ratio are undoubtedly difficult.The ratio is different from the addition,subtraction,multiplication and division that have been learned,and the signs are also different.Some students have the basic nature of "remembering memorization" by comparison and can solve conventional problems,but they have no way to deal with new problem scenarios.Students can use it flexibly only if they really understand ratios and proportions.The sixth grade is the student's formal contact ratio and proportion.This stage is an important stage to cultivate the student's proportional reasoning ability.Therefore,it is important to understand the process of students' understanding of ratios and ratios.Although there are differences in the understanding process of each student,the author has discovered through the case study that the students have regularity in the understanding process of ratio and proportion.Teachers master the law of understanding ratio and proportion of sixth grade students in teaching.They can also intervene scientifically in the face of difficulties encountered by different students,effectively helping students find and fill gaps.This study focuses on the understanding process of the comparison and proportion of the three students,and analyzes the dynamic changes among them.In order to help teachers understand the dynamic changes of students' comprehension ratio and ratio,and help students understand and master the ratio and ratio.First of all,by summarizing the existing research,the author found that the research methods of ratio and ratio are more questionnaires.The questionnaire survey can provide a macro view of students' current understanding of ratios and ratios.But there is less research on the students' understanding process.On this basis,the author chooses the method of case study to specifically study the students' understanding process.Secondly,the author conducted a case study on three classmates in the sixth grade of a middle school in Pudong New District,Shanghai.In order to understand the types of difficulties encountered by students in the learning ratio and ratio,the author pre-tested 30 students and asked 30 students to take interviews after taking test papers.Learn the types of difficulties encountered by students at different levels in understanding ratios and proportions through answering questions and interviews.During the interview,the author tried different ways to explain the difficult problems and observed changes in students' understanding.The author summarizes the way of scientific intervention in the course of explanation.Thirdly,the author selected three students,whose math scores were excellent,upper-middle,and middle-level.The author understands the characteristics of case objects through multiple channels such as classroom observation and teacher evaluation.Through semi-structured interviews,understand the dynamic understanding process of the three students in solving two different situations.Finally,based on the interview dialogue and the author's observation records during the interview,and based on the Pirie-Kieren dynamic model theory,the interview data is analyzed.It was found that students face different ratios and proportions in different situations,and the dynamic understanding process is different.The process of mathematics understanding formed by students is different because of the different mathematics scores,adaptability,and the original knowledge of ratio and ratio.Make recommendations for teachers and students based on the research conclusions.I hope it can help the majority of teachers and students understand the ratio and proportion,and carry out teaching more efficiently.