Activating Prior Knowledge

[ Music ]>>Now we talked about prior knowledge that
students have that is actually inaccurate, but students have a lot of prior
knowledge that is actually accurate. So let’s think about how we can use
that knowledge as the foundation, as the building blocks for further learning. So it might not be ready as is. We might need to be adopted and [inaudible]. So for instance, in a mathematics class,
statistics students might be familiar with some concept but not recognize
them immediately because the notation that they’ve seen in different classes
where they first learned them is different. So that’s an easy case of
just making sure everybody’s on the same page in terms of the language. Or sometimes students might have a little
bit of prior knowledge, but it’s not enough for the whole problem, but it
can certainly by capitalized. So for instance, when I start talking about
hypothesis testing, I know that, hopefully, I can rely on knowledge that students have
about measures of [inaudible] and measures of variability, that they have a sense
of means and standard deviations. And they could use that knowledge maybe to start
thinking about differences in distributions, differences between two groups and
how big those differences are relative to the variability of the distribution. They might not be able to arrive to the whole
concept of hypothesis testing on their own, but that’s a knowledge that exists there
that can be certainly incorporated. Unfortunately, there’s a step
that needs to happen first, and we’ll see that with this example. This is actually one of the most
complicated experiments in psychology. So each card has two sides with
letters and numbers on both sides, and we only get to see one side, but we
know that if we see a vowel– I’m sorry. We know that if we see a letter on
one side that there should be a number on the other side, and vice versa. And there is a rule in this situation. The rule is that if a card
has a vowel on one side, it should have an even number on the other side. Now, we’re concerned that some cards might be
breaking this rule, and so we want to check. We want to turn them over to see
if they’re following the rule. We also want to be efficient, and we don’t
want to turn over cards that we don’t need to. So the question is, what is the minimum
number of cards that we must turn over to verify whether the
rule is being followed or not? And so there’s four options there. A. A and 6. A and 7. A, 6, M, and 7. So take a second to think about this. So the answer is A and 7. A is a problem, because if it has an even
number on the other side, it’s in violation. Seven is in violation if it
has a vowel on the other side. Now, some people get confused and
think that 6 might be problem, but if 6 has a vowel on the
other side, it’s fine. And if 6 has a consonant on the other side,
there’s no rule about consonants, so 6 is fine. For the same reason, that
there’s no rule about consonants, M is also fine, and we don’t need to check that. This is a hard problem. When I do this in groups with professors, people
with terminal degrees, they struggle to come to consensus on this, and it takes
them, actually, significant time. But I am a big believer in redemption and second
chance, so I usually give them a second problem to work on to see how they do on that one. So let’s look at the second problem. We still have cards with things on
both sides, except in this case, these cards in this green problem are
stand-ins for students, for people. And on one side, we have their age, and on the other side we have
the drink that they’re drinking. And there is a rule in this situation. The rule is if that they’re drinking
alcohol, they must be over 21. Again, we’re concerned that some students are
violating the rule, and so we want to ID them, and we also want to be efficient. So what is the minimum number of
students that we must ID to verify that the rule is being followed and which ones? Now, this is a much easier problem. Most people can easily immediately see
that we are concerned about the minor 16 and the person who’s drinking alcohol,
to check whether they are at least 21. And so people do much better on this
problem than on the other problem, but if you think about it, these
two problems are very similar. They’re not identical, but they are isomorphic. There’s a mapping between letters and numbers,
vowels and consonants, and odd and even numbers, and age and drinks, and age above and below
21, and alcoholic and non-alcoholic drinks. And the rule also matches. So because they’re isomorphic, what that
means is that the mental operations required to solve the problems are the same. So how can it be that one is much
easier than the other, takes less time, and most people agree on the solution? People have different explanations for that,
but one of the interesting explanations is that we are very familiar with the rule of–
the drinking rules, in the U.S. at least. We use them all the time. They affect us. Maybe they affect our kids. Maybe they affect our students,
if we’re chaperoning an event. Maybe we’ve tended bar at some point, and
we’ve had to pay attention to these facts. The other problem is abstract
and does not rely on that rule. But here’s the interesting fact. When we go into a school and ask students
to solve the problems, predictably, they don’t as well on the blue
problem, the abstract logic problem, than they do on the green problem. But when we give them the green problem
first, and the blue problem second, but in between we tell them now
that you’re solving this problem, think about the problem you just solved. See if there’s anything there that helps you,
this one, then the percentage of students who can solve the more difficult
problem goes way up, and it’s statistically significant, actually. The reason for that is that the knowledge
needs to be activated in order to be useful, and that is the same for
you, if you think about it. You all had the knowledge of drinking rules,
if you are viewing this from the U.S., and it did not dawn on you that you could
use that little tidbit in your brain out of the millions of things that are in your
brain to help solve that abstract logic problem. So the moral of the story is that most of
our knowledge sits there doing nothing most of the time and that we need to
activate it before it can become useful. The good news is that the activation
is one of the easy things to do, just reminding students, like in that example. Think of the problem you just solved. Think about that thing you learned in calculus. See how that can apply to this psychics
problem or this engineering situation. That’s all that is needed for the activation, if
the knowledge is indeed in the students’ minds. [ Music ]