- So this is Sal Khan, founder of the Khan Academy.
And this is a very exciting Skype call that we're on.
I'm with Ben Hedrick,
who's the lead for AP Calculus.
What do you at the College Board?
- Really, anything with AP Calculus and AP Statistics
is something that I have a little bit of control over.
So for example, for AP Calculus,
anything with the curriculum, anything with the assessment
is something that I work with.
- And I'm sure that you're as excited
as I am and, you know,
several hundred thousands of students are around the country
for the AP exams that are coming up
in roughly a little less than a week.
And I thought a fun place to start would be
when you guys write the test,
what are you trying to assess?
What's the spirit of the questions?
Both on the multiple choice and the free response section.
- So what we're looking for from students
is evidence of good, conceptual understanding in calculus.
Now, we have some things that are gonna test procedures,
but really, we want students to understand what's going on
with the calculus rather than just calculating things
or putting numbers on paper.
A lot of thinking questions, a lot of insight
to make sure that whatever good calculus those students
have learned in their courses,
we're assessing it on the AP exam.
- And I've done a bunch of example problems for the AP exam,
and yeah, my sense of it is
you sometimes will do some of the minutiae work
or you'll give the formula,
and you're really trying to understand
whether students understand the essence
of what an integral is,
or the essence of derivative as a rate of change,
or the slope of a tangent line.
So, if you were preparing for this exam,
if you were the students,
what you suggest to them?
You know, obviously we have a little less than a week
for this current test,
so what advice would you have for those students?
And then just generally, as students go through the year,
how should they think about it?
- Yeah, the advice I would give
is dependent on how much time the students have
to prepare, so the advice that I give
at the beginning of the year is different from the advice
that I give now, several days before the exam.
Getting ready for it, first, relax.
You know, this is a calculus exam.
We're not gonna be throwing anything at you from left field.
It's calculus.
You need to know limits.
You need to know derivatives.
You need to know integrals.
In terms of preparation, make sure you're taking the time
to review the basics.
Every question that they see
is gonna hit one of those big topics,
so make sure you know your derivative rules,
make sure you know your integral rules.
Take a look at the old exams
and see how we're asking questions.
And you'll at the patterns and see that we're always asking
about understanding what a derivative means,
understanding integration or the idea of accumulation.
There are no secrets on the exams,
so really stick with what we've done.
Make sure that you're thinking of ways
to apply to your good knowledge,
and just review your basics.
- And my experience with the exam is there's a lot of,
as you just said, really the mainstream, meaty topics.
You know, chain rule, fundamental theorem,
or theorems of calculus, things like that.
What's your sense of the more,
what I would concern maybe a little bit more, the minutiae,
some of the more special case derivatives,
or special case integrals, you know, arc tangent and,
how much does that play into the exam?
- You know, I think, Sal, you've actually answered
your own question in asking that,
is it is the minutiae.
So really, at this point in time, if you're getting ready
for the exam, spending time on minutiae
is not where you're gonna be best served with your time.
You should be hitting the major things,
and you said it right at the beginning, chain rule.
I mean, any kind of question we do with derivatives,
you know, if you're doing maxes or mins,
if you're doing tangent lines,
if you're doing a related rates problem,
they're all derivatives, derivatives, derivatives.
And if you're having trouble with chain rule,
it doesn't matter how much minutiae you spend time with,
the chain rule's gonna come up.
So I would say don't sweat the minutiae.
There might be something on the exam
that you haven't reviewed as much as you want to,
but it's gonna be one single, solitary question.
Basic derivatives are going to form, well,
the basis for all those problems.
So that's where your time is best spent.
- Yeah, I definitely get that sense.
Especially, you know, how do you interpret the first,
second, you know, derivatives, concavity.
Things like that, those seem to show up a lot.
But once again, that's a conceptual idea of derivatives.
And on the integration side,
I've been doing a bunch of the free response.
It just seems like, I mean, you know,
what happens if you swap the bounds of integration,
or if you add integrals.
So a lot of the properties and the conceptual understanding
of what an integral is,
but not necessarily the fancy tricks.
At least at this point, if you're studying.
- Absolutely, there's nothing that we go after
the fancy tricks.
We're not trying to ask trick questions
or play any gotcha moments on it.
It's really assessment of calculus.
And for the students who have been going through
these great courses all year,
this is a wonderful opportunity to show us
everything that you know
and get a really great score on the exam.
- And what about calculator?
I mean, I was doing some of the free response.
That first part of the free response,
knowing your calculator well helps.
- Oh, absolutely.
The calculator's a tool,
and like any tool, you want to make sure
that you're applying it appropriately and strategically,
which sometimes means using your calculator,
and using it well and correctly,
but other times not using your calculator.
I mean, even on the free response section
where the calculator is being used,
we expect students to show their work.
If you're taking an integral,
we wanna see that you've actually taken that integral.
Now, the calculator will do the work of it,
but we wanna see the notation that says
this is the integral you calculated,
and this is the answer you obtained.
And then do whatever you will with that answer
as required by the question,
but good communication through writing,
even on the calculator section, is necessary.
- And for students taking the BC exam,
above and beyond the core differentiation,
integration, you know, a lot of what you learn
about parametric equations is actually just an extension
of what you learn in differentiation, integration.
But probably some of the convergence tests
are something to become pretty familiar with.
- That would be correct, yes.
- And in terms of grading of the exam,
you know, some people,
to get a five or a high,
my understanding is you don't need to answer
absolutely every question perfectly.
- Well, like any test, if you want to do well,
you don't have to have perfection on it,
and this is a test where students are coming in
and it's a three hour timed test,
well, a little over three hour timed test,
and you know, you can do a lot of really good work
and earn a five pretty easily.
So I wouldn't tell anyone to go in there worrying
about trying to figure out what magical numbers they need
to get in order to get a perfect score on the test
or to get a five on the test
or whatever it is that they're going for.
Just go in like you would on any test,
do your best on every question,
get every point that you can,
and hopefully it'll work out fine for you.
- What advice would you have for students,
especially on the free response
where there's multiple sections,
and if, you know, on part A they say,
what, that, that's,
I don't get what that, what,
you know, should they skip to the next free,
what should they do?
- I actually have very common advice on that one
and that's to make sure that students are trying
every part of a free response question.
One of the misconceptions students have
is exactly what you said.
If you hit part A and you're freaking out a little bit
because you don't know what part A is about,
that's okay, move on to part B.
There are some questions where the answer for part b
depends on part A, but for the majority of the questions,
they're separate pieces.
So part A, part B, part C,
if there's a part D,
they might all be asking very different things.
And if you have trouble even with part C,
that doesn't mean the question
gets progressively more difficult.
Give part D a try.
And a lot of the things that we do give points for
are good, solid calculus work.
So if you can set up a problem,
maybe you don't have time to finish it,
maybe you make some mistakes along the way,
the answer point is only one little point
out of the nine.
There are other points for the setup
and the conceptual understanding of the problem,
and a lot of students have good conceptual understanding
that they could set up,
pick up a point here, pick up a point there,
but they panic a little bit,
and they move on to another question
and never come back.
And that's okay if you want to move on to another question,
but absolutely I would say,
if you're having trouble with part A,
that's all right, take a look at part B.
- And one thing that I've observed is
a lot of these questions, at first when you look at 'em,
like oh wow, this looks like some really,
you know, super deep thing,
but it really is some core basic calculus ideas,
and that if you're on the right track,
it's actually quite simple.
Would you say it's fair if a student finds himself
doing a very hairy calculation
that they might question whether they need to?
- I would go beyond might.
They should question what they're doing.
If you've done something where you feel like
you need to prove a new calculus theorem
in order to answer it,
something has gone terribly, terribly wrong.
And also, if you feel like you need
to bring in some sort of mathematics
you've never seen before in calculus,
as much as I hate to say it, you know, this is calculus.
It's limits, it's derivatives, it's integrals.
Even though there's a lot of wealth in that one,
if you're doing something beyond that,
probably something has gone wrong.
- Yeah, yeah.
Well, thanks.
I think, you know,
thousands of AP students are gonna really appreciate that.
Any other parting words for the coming test?
- You know, it's the same thing
that I used to tell my students
when I was teaching AP Calculus,
this is just another test,
and the beauty of AP is the teachers have been
prepping their students since the beginning of the year.
It's one of the few tests
where everyone knows what's coming,
so when you sit down and you've got free response questions,
you've got multiple choice questions,
you know, there really shouldn't be any surprises.
This is the stuff they've seen all year.
They know what to do.
Take a moment, take a breath,
take a look at the problem,
get all the points that you can.
Show us that good calculus.
- Awesome, and I'll throw in a plug.
We have tons of resources for the students as well,
and we're gonna have our office hours on Monday.
So, super exciting.
Thanks a bunch, Ben.
- No, thanks for having me.