People often rely on external rewards to get kids to do
something—a school rewards a class if the students' score proficient on a test;
a parent rewards a child if the child gets all A’s. What's your take on this?

My take is what 50 years of behavioral science tell us.
There are certain kinds of motivators, what I call "if-then"
motivators, as in "
If you do this,
then you
get that." Those motivators, science tells us, are pretty effective for
simple, short-term, algorithmic tasks. But if-then rewards are far less
effective for more complex, creative tasks. The problem we have in schools and organizations is that we
tend to use those if-then rewards for
everything rather than for
the areas in which they work. Trouble is, in both the workforce and education,
people now rely less on these routine kinds of skills and more on work that
requires greater judgment, creativity, and discernment. In many ways, how we
motivate people hasn't caught up to the reality of our times.
Now, let's be clear. We all love rewards. If you dangle a
prize in front of people, it gets their attention, but—and here's the important
point—it gets their attention in a narrow way. That's OK for certain things—for
example, if you're stuffing envelopes or turning the same screw the same way on
an assembly line. Rewards for things like that can actually improve
performance. But if people have a completely narrow view of a task that
requires more creativity or judgment—designing a new piece of software, inventing
a product the world doesn't know it's missing, and so on—then they're not going
to do as well.
What's more, this carrot-and-stick approach confuses two
types of goals. Research by Carol Dweck and others has shown that there's a
difference between learning goals and performance goals. A learning goal is,
"I want to master algebra." A performance goal is, "I want to
get an A in algebra." The research shows that reaching performance goals
doesn't necessarily mean that you have hit a learning goal. If people are
single-mindedly focused on performance goals—and they achieve them—it doesn't
mean they've learned anything, improved their capabilities, or mastered
something complex. The kid is less likely to retain what she learned to get the
A, less likely to persist when the going gets tough, and less likely to
understand why algebra is important in the first place.
However, if a kid is single-mindedly focused on a learning
goal—mastering algebra—chances are he's going to do pretty well. In the
process, he'll probably attain that performance goal and get his A. So it's
best to simply go for the learning goal and use the grades and scores as
feedback as the student works toward mastery.