A Investigation Of Understanding The Concept Of Function Of The Students In Grade One In Senior High School

One of the major tasks of the current education is to implement comprehensive learning, but the process of mathematics comprehension is not accomplished at one stroke. This thesis, based on the APOS theory, with the function concept taught in senior one as the starting point, designs different testing items for senior one students from two different types of classes around the four stages of action, process, object and scheme to examine their comprehension of the function concept. The main research questions of the thesis are listed as follows:(1) What’s the comprehension state of students from class A and class B after their learn the function concept? How do the students from two classes perform in the four stages of the APOS theory? Around which stage are the comprehension barriers mainly centered? (2) Students from average and German classes inevitably differ in their math learning, but are there differences in their understanding of the function concept during each stage? At which stages are the differences most significant?According to the analysis of the survey results, the following two conclusions are drawn:(1) In general, most senior one students reach the stage of action and process in their comprehension of the function concept. More than half of the students arrive at the stage of object, and only a small number of students reach the stage of scheme. Students’comprehension barriers of the function concept are mainly centered in the stage of object and scheme in the APOS theory.(2) From the perspective of class differences, there’s no significant difference between class A students and class B students in their function concept learning in the stage of action and scheme. In the stage of process and object, there appear significant differences. Students from German class perform better than the ones from average class, which indicates different teaching modes have impact on the stages of process and object, while the stage of scheme requires continuous cycles to be reached.Finally, according to the research conclusions, considering the classroom teaching practice of different classes several teaching suggestions are put forward to promote students’ comprehension of the function concept.