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

The concept of function is the key content of the high school mathematics, in themeantime,it is also a difficult content.Function run through the whole high school. So tospeak,the understanding of the concept of function plays a vital role for the high schoolmathematics learning.Based on the important position of the concept of function,thisstudy is based on the learning theory of APOS,designing the evaluation standard ofunderstanding level about the function concept on the basis of APOS theory,designingthe questionnaire, understanding the actual situation about understanding of the functionconcept by the investigation,and putting forward some advices on the teaching andlearning, provides the certain basis for teachers’ teaching and students’ learning.After asurvey of No.1middle school and the second middle school of NeHe, draw thefollowing conclusions:1.The level of understanding and discipline of fresh students of high middle schoolto the concept of function(1) In the process of constructing the concept of function, most of the students havereached Action and Process, some of the students reached Object, only a few studentscan achieve schema.(2) Students’ representation on the function mostly is confined to graph of thefunction,a part of the students adopt the list method, only a few students used a morecomprehensive representation of the function.(3) Through the questionnaire answers of the last two questions can be concludedthat only a small part of students’ application of the concept of the function is better,most of the students in the application of the concept of function is still relativelylacking.(4) The results of students have not a direct impact on the understanding of theconcept and its relevance is not big.(5) A most of the students in understanding the nature of function concept is notenough.When given an image or a live situation, determine whether it is a function of,although a considerable number of students make the right judgement, but the reason given is very far-fetched.This shows that the students do not grasp the essential attributeof the function.2. Several factors affecting the level of understanding of the concept of function:key high school and ordinary high school, liberal arts and science, key classes andregular classes, genders.(1) The key high school in each phase of the comprehension of the concept offunction is better than ordinary high school.(2) In various stages of construction of function concept,science classes inunderstanding of the concept of the function is better than that liberal arts as a whole,but no significant difference in the Action.(3) The students of the major work classes is better than the regular class studentsat every stage of the concept of function construction.(4) In each stage of constructing the function concept,boys and girls’ understandingof the concept of the function is no significant difference.Finally, combining the results of the survey, this study puts forward the followingsuggestions in allusion to the current function concept teaching:(1) Pay attention to the knowledge internalization of students, grasp the essentialcharacteristics of the concept of function.(2) In the process of preparation, teachers should use appropriately APOS theory toelaborately design teaching of the concept of function.(3) Attach great importance to the formation of the concept.(4) Focus on the function of conversion between a variety of expressions.(5) Concerned about the function of the intrinsic link with other knowledge toenrich the knowledge of system function.(6) Guide and encourage students to focus on the function model of daily life, topromote the application of the concept of function, achieve the real understanding of theconcept of function.