# PSYCH207 Lecture Notes - Lecture 4: Inclined Plane, Chessboard, Functional Fixedness

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22 Jul 2016
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10c | Blocks to Problem Solving
In the previous section, we covered a number of different problem solving
strategies. These st rategies are useful because many problems that we have to
solve can’t be solved in a single step. In addition, many problems have barriers
that hinder us from successfully solving a problem. What we’re going to talk about
now are some of the classic bloc ks, some of the classic things that hinder us from
successfully solving a problem. Before we do this, I’m going to present to you a
couple problems that highlight this phenomenon. When I present you with the
problem, what I want you to do is press pause on the module, so that you can work
on it a little bit before you move on to see the actual solution. The first two
problems I want you to try are called the nine dot and the six matches problem. So,
first, take a look at the nine dot problem. So, what you see here are a series of
dots, and what the task is, is to draw four straight lines that pass through each
of the nine dots, without removing your pencil from the paper. The six matches
problem is a similar type of task, and what this task requires yo u to do is to
arrange the six matches so that they form four triangles will all sides equal to
the length of one match. So, press pause now, and try to work on this problem for a
couple of minutes, and then resume play so that you can see what the solutio ns
are.
Welcome back. Now, take a look at the solution to those two problems. First, take
a look at the nine - dot problem on the left. As you can see, the problem is easily
solvable, as long as you draw the lines outside of the box. Most people aren’t able
to solve this problem, because they make the faulty assumption that the four lines
must st ay within the borders of the dots . So, literally, in this example, you
have to think outside the box in order to solve the problem. Now, look at the
matchstic k problem. As you can see, the solution to this problem requires that you
think in three dimensions, and create a three - dimensional object. Most people,
however, constrain themselves to creating the four triangles in a two - dimensional
plane, and thus, ca nnot solve this problem. Both of these problems illustrate how
peop le typically go into a problem – or often go into a problem, any way s – with
faulty assumptions, and these faulty assumptions, of faulty rules about the
problem, hinder successful problem s olving. There are a couple other examples in
the textbook: the string problem, and the candle problem, which I’d also recommend
you try out. These blocks to problem solving highlight what is called “mental set.”
Now, mental set is the tendency to adopt a certain framework, strategy, or
procedure, or, more generally, to see things in a certain way instead of in
another, equally plausible way. It can be induced by short amounts of practice, and
it causes people to make certain unwarranted assumptions, wit hout being aware of
making them. So, for example, when you look at the matchstick problem, by looking
at that original picture, where all the matches are sitting in a two - dimensional
space, people typically make the unwarranted assumption that the final o bject, or
the final image that they create, must also be in two dimensions. However, this is
not stated at all anywhere in the rule. Mental set can also be induced by what is
called functional fixedness. Now, here, this is an adoption of a rigid mental set
towards an object. If you looked at the string problem in the textbook, what you’d
find is a perfect example of functional fixedness. To solve that problem, what
you’d need to do is to attach the screwdriver to one of
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the strings to swing it like a p endulum. People typically don’t discover that
solution because the fail to think that a screwdriver can have other functions
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