A Study On The Teaching And Learning Of Linear Function

The function is one of the basic concepts in junior middle school, and it is difficult forstudents to learn. Being the first function to learn for junior-middle-school students ineighth grade, the linear function plays a crucial role in subsequent learning of function forstudents, as well as in improving mathematical literacy. Studies have shown that the eighthgrade was a turning point in the development of the concept of function for students.Consisting of various facets, the representation of linear function includes symbol asformal concept (y＝kx＋b), function machine as colloquial concept (input-output machine).And it has geometric feature (equation), numeric feature (table) and symbolic feature(graph). The layer that students achieved from different facets of understanding linearfunction forms the cognitive structure of the student’s unique concept of linear function.Only when teachers start from students’ practical cognition, he can effectively design ofteaching. This paper tries to use the framework of David Tall in the linear function. Theauthor chooses one of students from top students, secondary students and poor studentsrespectly, adopts semi-structured interview to collect data on three cases, and establishesthe cognitive structures. Based on the students’ cognitive status, the author refers themathematics curriculum standard, compiling teaching designs about linear function.The paper is composed of six sections. The first section points out the importance oflinear function in mathematical learning and practical teaching and puts forth severalquestions. The second section introduces the studies of Tall and his PhD DeMarois, thestudies of linear function, and related studies of function by the way of literature review.The third section presents the designed format of the research, including techniques andsubjects of the research and the choice of research tool. The fourth section contains the results of the interview and related analysis, the establishment of the cognitive structures ofthese three students, and the contrast among them. according to the research, the papercompiles cases of junior-middle-school linear function teaching design in the fifth section.And the final section presents conclusions of the research and some reflections concerningthe topic.