Mathematical Preliminaries

Abstract

One of the fundamental problems in today’s mathematics education is the lack of proper teaching on how to draw a simple graph of scores on, for example, a mathematics test ($X_{1}$) and an English test ($X_{2}$). It is reasonable to assume that $X_{1}$ and $X_{2}$ are generally correlated (i.e., those who score high on the mathematics test tend to score high on the English test). Yet, irrespective of the correlation between the two tests, the teachers typically instruct their students to plot the mathematics scores on the horizontal axis and the English scores on the vertical axis. Notice that we use these orthogonal axes for two tests, irrespective of their correlation. Do you see any inconsistency in this combination of orthogonal axes and correlated test scores? This is the problem we are discussing now.