Shortcuts Are Really Math Intuition
So we’ve told you all about shortcuts, but now we’re going
to give you some advice that might seem strange: you shouldn’t go
into every question searching for a shortcut. If you have to search
and search for a shortcut, it might end up taking longer than the
normal route. Instead of instructing you always to seek out math
shortcuts, then, we just want to advise you not to get so focused
and frantic about getting a question right that you miss the possibility
that a shortcut exists. If you go into each question knowing there
might be a shortcut and keep your mind open as you think about the
question, you will find the shortcuts you need.
To some extent, you can teach yourself to recognize when
a question might contain a shortcut through practice. For example,
from the problem above, you know that there will probably be a shortcut
for all the questions that give you the dimensions of two shapes
and ask you to compare them: you can just draw a diagram. A frantic
test taker would see the information given and then rush to the
simplest route and work out the equations. But if you are a little
calmer, you can see that drawing a diagram is the best idea.
Finally, the fact that we advocate using shortcuts doesn’t
mean you shouldn’t focus on learning how to work out a problem.
In fact, we can guarantee that you’re not going to find a shortcut
for a problem unless you know how to work it out
the long way. After all, a shortcut is just using your knowledge
to see a faster way to answer the question. To put it another way,
while we’ve been using the term “math shortcut,” we could just as
easily have used the term “math intuition.” If you don’t have that
knowledge base from which to work, you’re not going to have anything
on which to base your intuition. In contrast, you might be able
to figure out an answer by trial and error even if you don’t see
exactly how to solve the problem.