Stuff I learned in school

More reasons for apparently useless subjects.

In the past couple of weeks three of our tutoring consultant’s students have asked, in various ways, “Why do I have to learn this, anyway?”  It must be that time of year: reviewing the mass of material they’ve learned since September, much of it now fuzzy or completely forgotten, they despair of ever hanging on to enough to pass the final exam.  And certainly, after they graduate, much of their mathematics in particular won’t be used again.  So why bother?

Well, we set out one reason in a post some time ago: it’s not the details of the mathematics so much as the mental exercise, the students using their minds to learn and solve problems.  But recently we’ve concluded that there is more, and much that is directly useful in later life.

It is true that few geometry students will be asked, as adults, to write out a two-column proof of this or that proposition about triangles.  We do hope that the idea of a rigorous proof survives.  But after a year of looking at drawings and figures, we think students develop a feel for Euclidean space.  They might not be able to articulate it, but they do understand measurements of distances and angles and relations between them.  There are few adults indeed who will never be concerned with a floor plan or the size of their yard, and architects and construction-industry people (to name two examples) will deal professionally with geometry in their work.

It’s safe to say that most students view logarithms and exponentials with distrust at first.  They don’t behave like the more familiar x-squared things.  And many of the calculations they do in class, they’ll never do again.  But compound interest is as near as anyone’s bank account, exponentials govern the spread of a disease, and half-life comes in to many things besides radioactivity.  Logarithms allow us to put the very big and the very small in the same picture, and though we may not notice it, we often think in a logarithmic way.

And calculus?  Well, scientists and engineers will certainly use that subject as an indispensible tool.  Even if they rely on computers for their actual answers, they have to know what’s going on inside.  But we contend that, even if a particular student never does another integral, understanding the relationship between rate-of-change and the function itself is a gain.  It applies to something as common as driving a car.

Another tutor pointed out that even something so esoteric as the measures of curvature of a function, things calculated at the end of high-school math, provide a way to describe and understand the trend of data.  The data may be any sort: financial, scientific, the number of fish in Chesapeake Bay or cars on the road.  In order to make sense of our data-driven world we need tools like this.

After graduation, the student may never again be called on to perform exactly the sort of problems found in the textbook.  But a more general understanding of mathematics is part of adult life.