The Researches On Understanding Level Of Group Concept From The Investigation Of Mathematics Majors

Group theory is a required course of mathematics in universities, which is of great importance in abstract algebra. Understanding and mastering the concept of group play an important role in improving the accomplishment of accepting any new mathematical concepts. The paper aims to investigate the present situation of the understanding of group concept and analyze the level of the understanding among the students who major in mathematics. Moreover, this paper puts forwards some suggestions to improve the teaching of abstract algebra on the basis of the conclusion.Based on the four dimensions (perception, representation, connection, application) and eight indexes, this paper investigates students’levels of understanding group concept in two schools. Further investigation is done to analyze whether the school, the profession and the gender differences have an effect on the level of understanding the theory.The paper comes to the conclusion that students’understanding levels of perception, representation and connection, one the whole, lie in multi-structural level, while the understanding level of application is uni-structural. By analyzing the collected quantitative data with t-test, it is not difficult to find that there is no obvious gender differences in the level of understanding the group theory for mathematics students. However, the school and the profession have an obvious difference, which is showed in the scores of testing. From the data,we can find that A school is significantly better than B school, and non-normal students do better than normal students in the test. Finally, this paper puts forward the teaching suggestion of group concept.