Investigation Of Mathematical Thinking Obstacles In Senior Students

The basic consensus of mathematics education circles is to "cultivate students' initiative spirit, overcome various obstacles of mathematics education, and pay attention to the spread of mathematical thought and method"(ICME-9). The process of mathematics thinking always contains the concept, principle, problem solving and so on. However the obstacle of thinking is the main obstacle of mathematics learning in students. Due to the difficulty and particularity on the research of thinking obstacles, the current research of mathematical thinking is still not deep and systematic. Senior high school is the key period of the development of students' independent personality, it has special significance to the development of students' individual and society that eliminate mathematical thinking obstacles in senior students.In this paper based on the cognitive theory of learning,constructivism learning theory, Sternberg's theory of triple intelligence, using literature research, questionnaire survey and other research methods. On the basis of the analysis of mathematical thinking characteristics, quality, structure, defined the concept of mathematical thinking obstacles, namely mathematical thinking obstacles is that the students which do not have scientific and complete mathematical thinking structure face mathematical problems, then can't correct analysis to solve mathematical problems and exhibit poor mathematical thinking quality. Therefore, the generation of mathematical thinking obstacles can be divided into internal and external factors. Internal factor mainly refer to the obstacles in the operation, material and monitoring systems of mathematical thinking. External factors mainly refer to caused by poor mathematics emotion of mathematical thinking obstacles in senior students. And the mathematical thinking obstacles into six types(mathematical thinking ability obstacle, mathematical thinking language obstacle, mathematical thinking concept obstacle, mathematical thinking knowledge obstacle, mathematical thinking meta-cognition obstacle and mathematical thinking emotional obstacle).And then combined with the advice of first mathematics teachers to the questionnaire, to a high school 303 students(103 fresh of senior high school, 98 senior two students and 102 senior three students) as the sample in Nanchang City. The present situation of mathematics thinking obstacles of senior high school students were investigated by questionnaire. The degree of mathematical thinking obstacles of senior high school students was analyzed and the differences all grade in six types of mathematical thinking obstacles were compared through the study of survey data. By comparing the number of poor students and the number of good students in mathematics with emotional differences to explore the relationship between mathematical emotions and mathematics performance.The results of this study are:(i)The high school students have a certain degree of obstacles in the six types of obstacles, among them, the degree of mathematical thinking concept obstacle and mathematical thinking meta-cognition obstacle is the most serious;(ii)Senior three students in six types of obstacles on degree is lower than senior two students. Senior two students in five types of obstacles except mathematical thinking concept obstacle is lower than freshman of senior high school students. In general, the degree of mathematical thinking obstacles in senior students all grade decreased in turn.(iii)Among the senior high school students, there are significant differences in mathematical thinking knowledge obstacle and mathematical thinking meta-cognition obstacle. In the mathematical thinking ability obstacle and mathematical thinking concept obstacle, the difference is not significant; In mathematical thinking language obstacle, the difference is not significant between freshman of senior high school and senior two students, but senior two students and senior three students have significantly different.(iv)Mathematics learning motivation and self-confidence have a significant effect in math scores, anxiety has little effect in math scores, math scores in turn affect learning experience in senior students. In a word mathematics emotion has a great influence on mathematics achievement.Based on the research results, this paper analysis the cause of mathematical thinking obstacles status in senior students. there are three main points:(i)high school students lack of the consciousness of mathematics application;(ii)differences of mathematics knowledge and skills;(iii) differences of learning motivation.At the end of this paper, according to the results of the study proposed relevant solutions: pay more attention to the knowledge of the network teaching, deepen the student's knowledge structure, overcome the students' mathematical thinking knowledge obstacle; show the thinking process, improve thinking ability, overcome the students' mathematical thinking ability obstacle; understand mathematical language, improve the ability of communication, overcome the students' mathematical thinking language obstacle; understanding of the history of mathematics, feeling the beauty of mathematics, overcome the students' mathematical thinking concept obstacle; Clarify the purpose of solving the problem, Rethinking the process of solving the problem, overcome the students' mathematical thinking meta-cognition obstacle; enhance mathematics emotion, stimulate internal motivation, overcome the students' mathematical thinking emotional obstacle.Integrated the above research, we can draw the following conclusions as follows:(I)The degree of mathematical thinking concept obstacle and mathematical thinking meta-cognition obstacle in senior students is the most serious. The results shows the lack of mathematics application awareness in senior students, the neglect of the value of mathematics and the lack of mathematical literacy;(II)with mathematics basic knowledge and skills continue to improve in senior school, mathematical thinking obstacles continue to change, the degree of mathematical thinking obstacles in a certain type will be weakened;(III)Mathematics emotion has a great influence on mathematics achievement. The results shows that learning motivation, learning beliefs and learning attitude have a great influence on the development of mathematical thinking;(IV)Teachers in teaching should pay attention to the teaching of network knowledge and mathematical language, attention to show the process of mathematical thinking, cultivating students mathematical problem solving in metacognitive ability and the correct conception of mathematics, enhance students' mathematics emotion and stimulate the internal motivation of learning, guide students to overcome all kinds of mathematics thinking obstacles, expand mathematics thinking space and enhance the ability of mathematics thinking.