- [Instructor] The terms mastery learning
are used a lot these days but I wanna do a video
on 'em because they can mean different things
to different people and I wanna just talk about
what it means at least in a Khan Academy context.
So to give us some perspective, let's actually just start
with traditional learning and think about where it works
and maybe where it doesn't work
and then we could think about why mastery learning
might address some of those issues.
So let's say we are in a middle school math class
and right now, the classroom is focused on negative numbers.
We're gonna work on that for a couple of weeks.
So this is negative numbers right over here
and after a couple of weeks of lecture and homework,
we give a task and lets say a certain student
that we're following gets an 80% on that test.
So he or she knows a lot of the material
but doesn't know some of the material here
maybe doesn't know some of the material here
maybe doesn't know some of the material over here.
So these are gaps.
These are gaps in their understanding.
So these, we label these correctly, these are gaps.
And even though we've taken the trouble
of giving an assessment, a quiz a test,
and we identified these gaps,
the whole class including that student
will then move on to the next concept.
So let's say the next concept that we now work on
maybe we do it for a few more weeks
according to the lesson plan, is now basic exponents.
So this is basic exponents
and the same thing happens.
We have some lecture and homework for a few weeks
and then at the end of that we have a test
and let's say on the that test,
the student gets a 70%.
So he or she knows a good bit of the material
but there's still some pretty significant gaps.
Let me color in these gaps.
So the white is what they were actually
able to perform on these tests
and even these tests are imperfect,
they're just sampling the students' knowledge
and so what happen to be on the test
they still didn't know some of the material.
Some of it might've been careless mistakes
but some of it might've been pretty important.
For example, this gap right over here
might be what happens if I raise something to the zero power
or maybe it's building on top of a gap with negative numbers
maybe this gap was happening,
not just 'cause basic exponents are difficult
but because there's a gap in negative numbers
so the student doesn't know what does it mean
if I take a negative number to a positive exponent.
So maybe that's a gap there.
But even though we've taken the trouble
of identifying those gaps, the class will then move on
to the next concept.
The amount of time is what's fixed
and what's variable is how well
the students understand it, A, B, C, D, or F.
And then the next concept, let's say
we'll do this in another color,
so the next concept here, we are building on top of
everything that we've learned so far,
let's say it is negative exponents.
So I think you can see where this is going.
This is trouble now for the student.
There's lecture and homework, the student is trying
the best they can but things are just not really gelling.
And so all of a sudden, when you take the quiz,
the student just hits a wall after two or three weeks
and let's say they get a 30%
and so they're only able to get 30%
of the material right that happened to be on the test,
the rest they got wrong.
Now, in a traditional system, we say
"alright, the student just failed this exam quite badly.
"Maybe the student needs to work harder.
"Maybe they need to be put into a different track.
"Maybe the subject is just too difficult for this student."
but when you look at what's going on,
it's pretty clear that it had nothing to do
with the ability level of the student
and it didn't have anything to do with the difficulty
necessarily of the subject matter
but it's more that they just kept accumulating
these gaps all along the way
so at some point, those gaps become so debilitating
that the student hits a wall
and starts failing the class
and if they're not able to remediate these gaps go back,
well they're never going to really be able
to understand negative exponents
and then they're never going to be able to understand
logarithms properly and more advanced algebra
and so on and so forth and we've all seen this
either for ourselves or some of our friends
and family members.
They hit walls.
And the argument that we believe at Khan Academy
it is not because they're not bright,
it's not because the subject matter is difficult,
it's because we're forcing them through at a fixed pace.
And to realize how absurd this is on some level,
imagine if we did other things in our life that way,
say home building.
So you tell the contractor we have two weeks
to build this foundation, do what you can.
And so they build a foundation
but then two weeks later, the inspector comes
and says "Okay, the concrete's still wet right over here.
"This part isn't quite up to code.
"I will give this an 80%"
and you say, "Great, that's a C.
"Let's build the first floor."
and so again, you try to build the first floor,
maybe it rains, some of the supplies don't show up,
and so the inspector comes after a couple of weeks
and says, "Alright, I'll give that 70%"
and you say "Great, that's a D
"Now let's build the second floor"
so on and so forth then all of a sudden
while you're building that second floor,
the whole structure comes collapsing down.
And if our reaction to that is the reaction
we typically have in education,
we say "Oh, we needed more inspection"
or "we needed better contractors"
but the problem was the process.
We are artificially constraining
how long you have to do something
which pretty much ensures a variable outcome.
You take the trouble of identifying those gaps
but then you build right on top of it.
So this is traditional learning
and one could argue that if you're just pushing people
ahead at some pace like this,
gaps will accumulate for everyone
and they will all hit a wall at some point
and we've all felt that.
And so mastery learning says, "Look, instead of making
"everyone go at the same pace, let us personalize."
and personalization in this context means
let people go at their own pace.
So traditional learning, it's fixed pace
and variable understanding,
while mastery learning has personalization.
So it's more of a variable pace,
and then we assume students get
to a high level of proficiency or mastery.
So high expectations
around proficiency or mastery
and those words can mean different things
in different context, proficiency or mastery.
So in a mastery learning system, you first would
maybe the student would be ready for the negative numbers
and maybe after a few weeks,
they take some type of assessment,
to get much as much practice and feedback as possible
and they perform similarly to that first example,
the student in the first example,
maybe they get that 80% there.
In a mastery learning system,
we wouldn't just tell that student,
"Alright, let's move on to basic exponents"
what we would do is, hey, why don't you keep working
on the negative numbers here
and so that you can address those gaps.
And so it takes the student maybe a little bit more time
but eventually, they're able to fill in those gaps.
There might be still a few small gaps
but the whole point is that they can always go back
and revisit and ensure that they fill in those gaps
so that they don't become debilitating.
Ideally, they'll fill in all the gaps.
And now, they're ready for basic exponents
and I'd argue that now that you're tackling basic exponents,
one, the student actually might be able to even learn it
faster 'cause they're gonna get less confused
by the negative exponents but if they still end up
having a gap when they take some type of an assessment
or while they're doing practice,
they have as much time as they need
to go back and fill in those gaps
and so the whole principle here is
in mastery learning, the student is building
a really, really solid foundation
so that they never hit that wall
when they get to negative exponents.
They understand their negative numbers well,
they understand their exponents well
and so then they can just keep on going
and going and going and at Khan Academy
we believe that if you learn this way,
yes, certain subjects might take you
a little bit longer, but then if you invest there,
the future subjects will take less time
and you will understand more and overall
and we've seen efficacy studies to this effect,
you'll actually learn better, faster
and you won't eventually hit some type of a barrier
like the first student did with negative exponents.