Senior Middle School Students' Understanding About The Concept Of Slope

The concept of slope, which is a preliminary one in the plane analytic geometry, has various representations, such as geometric, algebraic, trigonometric, physical, functional, even those in other subjects, and is intimately connected with many relevant knowledge. Therefore, it is necessary for the students to comprehend this concept from different viewpoints.This paper is a report of an empirical study on the senior middle school students' understanding about the concept of slope. Through a test conducted to 412 students of three grades from two senior high schools, data were collected with respect to their understanding of various representations of slope, mistakes, and grade, class and gender differences. The following conclusions are arrived at:(1) The students grasp many representations of slope, but their ability to transfer these representations is poor;(2) The students of different grades, classes and gender show a significant differences on representations and application of the slope. The individual differences are mainly reflected in applying the slope to solve mathematical problems;(3) The students grasp various representations of slope after learning it, but the levels of their understanding with respect to each representation are inconsistent and they lack the ability to connect each representation.(4) "Soundness of the error" in the concept learning always leads the students to make some unintentional mistakes.At the end of the paper, based upon the above conclusions, some teaching suggestions are put forth.