A Classroom Ethnography Study Of Understanding Linear Function For Students With Learning Difficulties

Mathematics education circles at home and abroad generally believe that the ultimate purpose of mathematics learning is to understand mathematics,and promoting students' mathematical understanding is the only way to reform teaching practice.Therefore,many scholars hold this purpose and try to explore how to promote students' mathematical understanding from pedagogy,psychology or brain science.Junior high school students spend most of their time studying in the classroom.The source of their knowledge is the interaction between teachers and students in the classroom.So how to improve students' mathematical understanding by improving the classroom is particularly important.Dulangkou Middle School in Liaocheng City,Shandong Province is a well-known model junior high school in China.This learning model gives full play to students' subjective initiative and promotes their understanding of knowledge.Although students with learning difficulties have always been concerned by all walks of life,in practical teaching,they have become neglected vulnerable groups because of various subjective and objective factors.This study takes three students in the eighth grade as a research object and uses the research methods of classroom ethnography to find out what they encountered in the classroom when they learned about function concepts,images,and practical problems through classroom observationsand interviews.The problems mainly include that they can only speak a single message of the concept,they are not clear about the relationship between the proportional function and the linear function,they cannot distinguish between the linear function and the binary linear equation,they do not use the method of drawing points to draw a function image,and it is difficult for them to convert between images.The nature of a linear function can not be seen through the images,and the problems arise when solving two types of practical problems: distance and time,and choice of solutions.After analyzing this study,it is found that the reasons for the above the problems of the three students are the inaccurate thinking,lack of profoundness,weak foundation,weak combination of numbers and figures,weak working memory capacity,and epiphany process.A student lacks the ability to retrieve the function knowledge once,and his or her symbol awareness is weak.Based on the analysis of the above problems and their reasons,this study gives teachers the following suggestions in teaching: teachers should pay attention to the basic knowledge of students with learning difficulties,should focus on cultivating the thinking of mathematics students with difficulties,should strive to improve the symbol awareness of students with learning difficulties,and should give more praise to students with learning difficulties in order to help teachers improve the teaching effect of Linear function.