High School Students' Understanding About Number Sequences

The number sequence, a carrier of many mathematical ideas, is one of the most important topics in senior high school mathematics. Because of its ample practical background and wide application in problem solving, it has been one of the key topics in the yearly college entrance examination.How well do the high school students understand about the concept and representation of a number sequence and the existence and certainty of the formula for its general term? These are problems facing senior high school mathematics teachers.This paper is a report of a study on high and normal school students' understanding about number sequences with questionnaire survey and interviews. Two tests on number sequences were conducted with 229 students from two senior high schools and one normal school. Based upon the analysis of the statistical data and the results of interviews, the following conclusions are arrived at:(1) It is easier for the students to accept the normal representation of a number sequence; high school students do better than preservice teachers in understanding the definition of a number sequence, the relationship of a number sequence and a set, tabular and mapping representation of a number sequence; generally speaking, the subjects show no gender difference in understanding the concept of a number sequence.(2) Most of subjects accept the existence of the formula for the general term of a number sequence, but have difficulty in understanding the general terms of those finite number sequences other than the arithmetic and geometric ones and the infinite sequences with only the first few terms given. Generally speaking, senior high school students do better than preservice teachers in understanding formulas for general terms of number sequences, but neither of them shows gender difference.(3) Generally speaking, subjects show poor understanding about the idea of wholly eliminating terms incorporated in the derivation of the sum of a geometric sequence. Senior high school students show higher problem solving ability than preservice teachers, neither showing gender difference.(4) Most of subjects have poor consciousness of applying the properties of functions to solve problems of monotonous sequences. Generally speaking, senior high school students do better than preservice teachers in understanding and applying the fundamental definitions, but the latter show wider and more flexible thinking. Neither of these two types of subjects shows gender difference in applying geometric properties of functions to solve relevant problems.