A Study On The First Grader's In A Secondary Normal School Cognitive Barriers Of Solving Function Application Problems

The concept of the function is a key point in middle school mathematics and runs through the entire mathematical study. Thus the research of the function must be strengthened. The function application is not only important for the function itself but also difficult for teaching. What's more, the thorough understanding of the function is the key to function application problems because by solving function application problems, students can undergo the process—"the real mathematical problem-mathematical model establishment—mathematical problems solution—the answer to the mathematical problem", which deepens the students' understanding of the function and helps them to obtain systematic knowledge of the function.This thesis is mainly focused on the following questions. Firstly, based the survey on the learning situation, such as interests, attitudes, confidence of the first grade students in a Secondary Normal School, who are the counterparts of Senior One, the thesis paves the way for the further study. Secondly, the thesis discusses the difficulty in solving several types of function application problems including linear function, quadratic function, segmented function, integral function. Finally, the corresponding suggestions for teaching are concluded.This research conducts an intensive investigation and analysis in the forms of questionnaires, tests, and interviews, etc. The results of the research are as follows:First, learning hindrances in linear function application problems are having trouble in reading comprehension, processing, supposing the variable, and the understanding of the glossaries of mathematic concepts, in which errors in the aspect of processing are quite prominent.Second, the obstacles in quadratic function application problems are mainly due to decoding and processing. The students are confused by the quantitative relationship, making mistakes in establishing mathematical models, and are unable to discuss the ultimate value with the aid of function image monotonicity.Third, the difficulties in the segmented function application problems are mainly reading comprehension and processing. Some students can not write the form of segmented function due to the difficulties in the understanding of constant functions and the meaning of the questions.Fourth, the learning hindrances in integral function application problems are having trouble in decoding and processing. Students are poor in flexible application and problem solving.At the end of the paper, some teaching suggestions and further researches are proposed for better teaching.