What Results are We Getting from Graphic Algebra?

I feel that I should explain to you that my acquaintance with the work of the secondary schools is entirely second hand and it may be that my ideas on the subject of graphics in secondary work are colored by what I may wish were possible instead of being entirely true to the facts. In my own experience as an instructor of freshmen I have found but little evidence indicating previous instruction in graphics and frequently the subject is thrust suddenly upon a freshman by the immediate needs of his college work. In many cases it is looked upon as only another novelty introduced to make college mathematics a thing to be dreaded and avoided if possible. I assume that it is proper for an instructor in first-year college work to expect a greater or less degree of familiarity with graphics on the part of incoming students and from this standpoint consider the question as to what may be gained by the study of graphics in connection with all branches of elementary mathematics. The subject should appeal to teachers of mathematics for at least three reasons, first, it is the simplest of our many symbolisms for magnitudes and in the order of nature precedes all the others: second, it often appeals to certain pupils who would otherwise be uninterested: third it affords connecting links among all branches of mathematics.