Investigation And Research On The Status Of Function Concept Learning Of Grade Nine Students Based On APOS Theory

As the core content of mathematical learning,the concept of function is self-evident in its importance in mathematics.In our country,the students begin to contact the function in the junior middle school.A cvcnd the students in grade nine have already studied the function preliminarily and have a rough understanding of the function.But they were still not ideal in actual learning process.Education comes from learning.Only by understanding the students' understanding of the concept of function can the function class be carried out reasonably.Therefore,based on the APOS theory,the author investigated the status of functional concept learning of nine grade students.APOS theory initially studied the process of students' learning of mathematical concepts.The theory set the process of acquiring students' conceptual knowledge into four stages: actions,processes,objects and schemas.At the same time,the concept teaching process can also be designed on the basis of APOS theory.This provides a theoretical basis for the study of students' cognitive level of conceptual learning.Through literature research,questionnaire survey and classroom observation,the author chooses two different levels of urban middle school students in grade nine.The author first designed a test paper based on APOS theory to carry out a questionnaire survey for grade nine students.Having had a Quantitative analysis of the results of student function concept learning,combined the function of classroom observation and from teaching and learning the two aspects used APOS theory to structural analyze,it was founded there four conclusions: 1)most grade nine students could meet the function learning requirements of the action and the processes levels,but they understood the concept of function unilaterally.2)there were internal differences among the students of grade nine in the processes level,the objects level and the schemas level,and the students' learning level in different schools was different.3)the performance of the nine grade students in the schemas level was not ideal as a whole,and a few students couldreach the schemas level.4)there were differences between boys and girls in function learning.In the action level,girls performed better than boys,but in the later schemas level of study,boys were better than girls.Through classroom observation and analysis,it was found that four reasons for these problems were: 1)under the environment of exam oriented education,teachers neglected the nature of function in the later stage of function teaching.2)the students in grade nine were still in the early stages of dialectical logic thinking,and the transformation from "static" mathematics to "dynamic" mathematics still took a period of time.3)there was a phenomenon that the teaching class emphasized the conclusion and reduced process.4)the students' cognitive level of mathematical concepts was different.In view of conclusions and the reasons,the author got the teaching enlightenment: 1)take the concept of understanding as the core throughout the function class.2)properly combine of different forms of function for teaching.3)attach importance to the connection of other knowledge.4)the concept of function can be taught at a level based on APOS theory.Finally,based on the results and inspiration,the author made three instructional designs on the related content of the function under the guidance of the APOS theory.