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>> There's been a lot of research done on the differences between experts and novices,
and so I'd like to point to a term that I think is really helpful in thinking about the kinds
of expertise that we want to develop in our students.
So here on this graph you'll see these two axes.
One is efficiency and one is innovation.
So you can think about having students solve different types of problems
or take on different kinds of tasks.
Sometimes you need to solve those problems or do those tasks very efficiently and accurately.
Sometimes solving the problem or tackling a challenge requires some creativity,
some innovation, maybe it's a type of challenge you haven't seen before.
And so if you look at how novices develop expertise,
sometimes we see what are called routine experts.
These are folks that can take, have standard problems
where solution techniques are fairly well known and apply them efficiently and accurately
and repeatedly and do really well for solving those types of problems.
Then we have this term from the literature called adaptive expertise.
This describes the kind of expertise that can tackle new problems,
problems that haven't quite been solved before or a little bit different than the types
of problems that have been, that the expert has seen before.
And so that's the goal, really, in developing expertise in our students.
You can kind of think of our job as instructors as helping students develop from novices
in a particular domain, helping them develop expertise over time.
It's great when we can help them develop routine expertise, and certainly I see this a lot
in the math classes I teach as students learn how to use certain formulas
and computational techniques and use them accurately and effectively.
But I'd really like them to develop adaptive expertise
so they can solve problems they haven't seen before.
Let me draw another comparison here.
So not everyone uses these terms this way, but I tend to think of the difference
between exercises in the textbook and problems.
So exercises are those math questions that come at the end of the section.
And everyone knows you're supposed to use the techniques
from that section to solve those questions.
The solution strategy is known for exercises.
The hard part is carrying out that solution strategy efficiently and accurately.
Problems, on the other hand, are a little more open ended.
You can kind of think of the problems maybe at the end of a chapter
where a student sees a problem and they know they've got maybe six
or seven different solution strategies that may be relevant, but they have to figure
out which one is most appropriate for that type of problem.
That requires a certain level of adaptation.
And so this is the kind of expertise that we like our students to develop.
If all they can do is solve exercises in our textbooks, then when they leave our course
and see problems in the real world that don't fit those textbook exercises,
they won't really they won't necessarily know how to solve those problems.
But if we can help them develop this adaptive expertise so that they are able
to solve nonstandard problems, then they'll be much more effective when they leave us.
Here's another way to think about it.
This is another term from the literature that I think is really helpful, this idea transfer.
So here I'll use a little bit of an example from my own hobbies, I would say.
So I'm an amateur photographer.
I love taking photos.
I love looking at photos.
These are all photos that I took.
And, in fact, they're all photos of photographers.
And so if you can imagine maybe me, right, I was in all four of these scenes,
and I had my camera, and I had my skills, such as they are, what I know about light
and aperture and focus and composition.
And then I've got my camera.
And as I go into these new contexts, I have to take my skills and my equipment,
and what I like to do is to try to take the best photos that I can.
I have to transfer what I know about photography from context I'm familiar with to new contexts,
new situations, new environments that I've never been in before.
And so that's the idea of transfer.
Ideally we'd like our students to be able to take what they've learned in our classes
and transfer that to other situations that they haven't seen before.
And so that requires this kind of adaptive expertise.
I'll also add that transfer is really hard.
This is not something that's very easy.
We get good at solving certain types of problems in certain contexts.
And when you change that context, it can be really hard to do this transfer.
So this is a hard teaching goal, I would say, for us to meet.
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