16 - History of Statistics and Students' Difficulties in Comprehending Variance

Summary

Introduction

Although variation is central to statistics (e.g., [28, 29]), before the end of the 90's not much attention was given to it in didactical research, as Bakker [1, p. 16], Reading [33] and others have remarked. Only recently have there been some systematic studies on the development of students' conception of variation (e.g., [43, 33, 34, 3, 14, especially pp. 382–386]). However, although didactical research on variance and standard deviation (s.d.) is very limited, it still points out that students face important difficulties in understanding these concepts. Mathews, Clark and their colleagues [25, 5, 14, pp. 383, 385–386, 388] examined students in four tertiary USA institutions, shortly after they had completed their introductory statistics course with an A. The majority of the students had not understood even the basic characteristics of the s.d.: (i) one third of them considered the s.d. simply as the outcome of an algorithm to be given and performed, did not understand its meaning and were unable to calculate it if the formula was not given; (ii) some confounded the s.d. with the Z-values; (iii) others believed that the s.d. of an ordered set of numbers depends on the distance between the successive values of this set and expresses a kind of mean value of these distances. Although these students got an A, they had not even formed the simplified idea that the s.d. is a kind of an average distance from the mean.