Page 185 - A Mind For Numbers: How to Excel at Math and Science

Transfer is the ability to take what you learn in one context and apply it to
something else. For example, you may learn one foreign language and then find
that you can pick up a second foreign language more easily than the first. That’s
because when you learned the first foreign language, you also acquired general
language-learning skills, and potentially similar new words and grammatical
structures, that transferred to your learning the second foreign language. 13
Learning math by applying it only to problems within a specific discipline,

such as accounting, engineering, or economics, can be a little like deciding that
you are not really going to learn a foreign language after all—you’re just going
to stick to one language and just learn a few extra English vocabulary words.
Many mathematicians feel that learning math through entirely discipline-specific
approaches makes it more difficult for you to use mathematics in a flexible and
creative way.

Mathematicians feel that if you learn math the way they teach it, which
centers on the abstract, chunked essence without a specific application in mind,
you’ve captured skills that are easy for you to transfer to a variety of
applications. In other words, you’ll have acquired the equivalent of general
language-learning skills. You may be a physics student, for example, but you
could use your knowledge of abstract math to quickly grasp how some of that
math could apply to very different biological, financial, or even psychological

processes.
This is part of why mathematicians like to teach math in an abstract way,
without necessarily zooming in on applications. They want you to see the
essence of the ideas, which they feel makes it easier to transfer the ideas to a
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variety of topics. It’s as if they don’t want you to learn how to say a specific
Albanian or Lithuanian or Icelandic phrase meaning I run but rather to
understand the more general idea that there is a category of words called verbs,
which you conjugate.
The challenge is that it’s often easier to pick up on a mathematical idea if it
is applied directly to a concrete problem—even though that can make it more
difficult to transfer the mathematical idea to new areas later. Unsurprisingly,
there ends up being a constant tussle between concrete and abstract approaches

to learning mathematics. Mathematicians try to hold the high ground by stepping
back to make sure that abstract approaches are central to the learning process. In
contrast, engineering, business, and many other professions all naturally
gravitate toward math that focuses on their specific areas to help build student
engagement and avoid the complaint of “When am I ever going to use this?”