Factors Affecting Combinatorial Reasoning In High School Students

Permutation and combination, which are based on the two fundamental principles of counting, are two important methods of counting. As the way of thinking involved in permutation and combination is distinctive, the instruction of this topic can enhance students' capabilities of logic thinking, mathematical modeling and reading and establishing proper conceptions of mathematics. Moreover, permutation and combination are the basis of probability. Therefore, they play an important role in senior middle school mathematics. However, it is difficult for the students to grasp and for the teacher to teach permutation and combination, and middle school students often make mistakes in combinatorial reasoning, which has also been revealed by several researches finished by foreign scholars. How to effectively improve on teaching of this topic is an important task facing the mathematics teachers in senior middle schools.The two fundamental steps of doing this are identifying the variables contributing to the difficulty in learning permutation and combination and understanding the nature of mistakes made by students when solving combinatorial problems. This thesis is a report of an empiric research on factors affecting combinatorial reasoning of senior middle school students and various errors made by them, purporting to offer empirical evidences for improving on the instruction of permutation and combination.A test, which includes 13 problems on permutation and combination each of which belongs to a certain combinatorial model and involves a certain combinatorial operation, were given to 867 senior middle school students, of whom 507 have learned permutation and combination and 360 have not in February, 2006. It is revealed that instruction and combinatorial operations significantly affect...