A brilliant formulation from David Pierce: The real world
consists of what *matters*. It is interesting that the verb
“matter” occurs naturally here, since it is derived from the
noun that is used for what the “real world”—the physical
world—is supposedly made of. But if we ask, “What’s the matter
with Fatma?” we may be asking about a physical ailment, or we
may be asking about an *idea* that is causing Fatma to behave
strangely. Ideas matter. The whole point of education is to make
things real for students, things that were not real for them
before. [Things like fractions, for example.] I recall an
example in a letter in the Notices of the AMS, some time in the
1990s. Calculus students worried that on Problem X, their answer
was 0.5, but the book’s answer was 1/2. “But they are the same
thing!” says the teacher. The students then use a calculator to
divide 1 by 2, getting the answer 0.5. “Oh” they say. Fractions
are not real for those students.