Reading more about explicit instruction (and especially Adam
Boxer’s excellent guide) has had a
significant impact on my use of concrete examples when explaining a concept.
I have blogged before on how I have tried to implement
guidance on going from concrete to abstract but this takes this a step further:
which concrete examples do you use.
There is advice given sometimes about always sticking to the same one example in an explanation, but I now appreciate the need for several carefully chosen examples. This is how I used this research when teaching the concept of externalities do my pupils, a topic which often confuses pupils initially but a key threshold concept they need to understand to appreciate market failure and the effectiveness of government intervention:
Example 1: The shoe factory and the neighbours
My first example involved a firm producing shoes, a consumer
buying shoes and a local community being kept awake by the noise the shoe
factory makes when producing them. This will start pupils to understand the idea
of third parties to a transaction being impacted, but more examples are needed
before this becomes more abstract.
Non-Example: The shoe factory and the customer
Now I introduce a non-example, an example which is not an
externality. This time I explain a shoe factory but customers have to come in
to the factory to buy their shoes and are frustrated by the noise. This is not
an externality because no third party is affected by this.
The key is that the non-example is almost the exact same as
the example. This is an example of the set-up principle where examples
and non-examples share a lot of irrelevant features and pupils do not have
misconceptions about the difference, the only difference between the examples
is that for an externality a third party is affected but when it is not an
externality they are not. Pupils then extrapolate that if a minor difference stops this being an externality, so will larger differences so anything where a third party is not impacted is not an externality.
Example 2: Passive Smoking
However, we still have not established the boundaries of the
concept. At this point, pupils may think that an externality is only caused by
a firm and only involved a minor concern like interrupted sleep. The next
example of an externality to be explained is a consumer smoking, causing others
to become seriously ill from passive smoking.
This demonstrates that an externality can be caused by a
consumer or a producer and can be a minor concern or life and death. This is
the sameness principle. By seeing different extremes of a concept,
pupils infer that anything in between is also an externality, called interpolation.
Example 3: University
However, there are still unwanted similarities between the
examples and pupils may draw incorrect inferences. They may believe an
externality has to be a negative impact and must be about the health of a third
party.
The next example is that usually a higher proportion of
people going to university leads to more economic growth, leading to more
employment opportunities for all citizens. This allows me to focus on an
externality potentially being positive and that the benefit could be financial
or non-financial.
Usually I show all these on a diagram showing a buyer,
seller and third party. What is key is that the labelling and way it is explained
is the same and so the pupil is only considering the similarity or difference
in the example itself, this is the wording principle.
Testing Principle
At this point pupils will practice with many examples to assess
if they understand the concept. I will
give them a combination of new examples interlinked
with the examples I have used, and pupils will need to determine if there is an
externality or not and if so, what it is.
Gradually going more abstract
Now I can go more abstract by introducing pupils to the idea
of third parties to a transaction. After this, they can be introduced to
external and social costs and benefits, then how these are drawn in diagrams
and finally the market failure.
This is a gradual process and as the concept becomes more
abstract there is lots of questioning and practice to ensure pupils understand
and are thinking deeply about the concept before finally it is all brought
together.
This process does take time to consider what examples to use,
but in terms of effectiveness I find I get the most reward for my time and it makes
my explanations significantly clearer. If anyone wants to learn more about
this, I thoroughly recommend buying Adam’s book, a lot of what I mention above
is taken from Tom Needham’s chapter.