The Influence Of Problem Representation On Function Problem Solution Of Senior One Students

After several teaching activities and practices, the author found the function problem was a big difficulty for students to learn mathematics all the time. To solve a basic function problem, there were four steps to follow, respectively, understanding the problem, selecting the operator, applying the operator, and evaluating the result. From the cognitive perspective, these steps could be called problem representation, pattern recognition, knowledge transfer, and thought monitor, in which the first one was the primary and the most crucial step. In this thesis, the author tried to study the following questions:(1) What’s the relationship between the problem representation and the solution to function problem?(2) How does the problem representation affect the solution to function problem?(3) How to develop students’ ability of problem representation in the teaching process?This thesis first defined the problem representation and the function problem, and divided the problem representation into three types, namely text representation, symbolic representation, and graphical representation based on the classification of CurriculumStandards issued by the NCTM in the United States and combinedwith the characteristics of the basic problem function.The coreparts of this thesis were as follows. First of all, the author employedthe investigation method to analyze the correlation between theproblem representation and the solution to function. Then, throughthe oral reports, the author analyzed students’ thoughts of problemsolving and explored the influence of problem representation on thesolution to function. Oral report is a kind of research method toreveal the individual internal cognitive process. In this thesis, theoral report is used to demonstrate the students’ thinking process sothat the author could analyze the process and find the problemsexisted in the problem representation in the process of problemsolving. On the basis of investigation and study, the author drew thefollowing conclusions:(1) Students’ ability of problem representation directly affectedsolutions to the basic function problem.(2) Students’ had some problems in the problem representation:(a) they can not understand the key words or symbols in the topiccorrectly;(b) they can not transfer the original questionrepresentation into the equivalent information;(c) the knowledgenetwork is incomplete in students’ minds.(3) The author put forward the corresponding teachingsuggestions to problems of the problem representation:(a) to trainstudent’s habit of external representation;(b) to cultivate student’stransformation ability;(c) to improve the student’s CPFS structuresystem.