I blame word
problems. They give a badly wrong impression of the relation between
mathematics and reality. “Bobby has three hundred marbles and gives 30% of them
to Jenny. He gives half as many to Jimmy as he gave to Jenny. How many does he
have left?” That looks like it’s about the real world, but it’s just an
arithmetic problem in a not very convincing disguise. The word problem has
nothing to do with marbles. It might as well just say: type “300 − (0.30
× 300) − (0.30 × 300)/2 =” into your calculator and copy down the
answer!
But real-world
questions aren’t like word problems. A real-world problem is something like “Has the recession and its aftermath
been especially bad for women in the workforce, and if so, to what extent is
this the result of Obama administration policies?” Your calculator doesn’t have
a button for this. Because in order to give a sensible answer, you need to know
more than just numbers. What shape do the job-loss curves for men and women
have in a typical recession? Was this recession notably different in that
respect? What kind of jobs are disproportionately held by women, and what
decisions has Obama made that affect that sector of the economy? It’s only
after you’ve started to formulate these questions that you take out the
calculator. But at that point the real mental work is already finished. Dividing one number by another
is mere computation; figuring out what you should divide by what is
mathematics.
