The blog that has had the biggest impact on my teaching this
year has undoubtedly been by Pritesh Raichura on explaining a concept by going
from concrete to abstract. In simple terms, starting an explanation with an
example that pupils will be able to grasp easily and then when more abstract
terms are used, pupils have the anchor of this concrete example to give meaning
to the abstract term.
Instinctively most of us would start explaining a theory or
definition and then use an example to explain it rather than the other
way round. I’ve become convinced of the merits of going from abstract to
concrete, I think it’s especially helpful when teaching subjects like economics
and business where there are so much jargon that it can seem like we are
speaking a different language.
I first thought that this would be as straightforward as just
using an example before I explain an abstract concept, but when I first tried
to implement this into my instruction, there were 3 mistakes that I was making
that I needed to rectify.
Mistake 1: slipping into attempts at discovery-based
learning
I’ve long since been convinced by the work of Sweller et all
on the importance of direct instruction led by a teacher for novice learners
but I found it interesting how I would instinctively revert to a more
discovery-led approach when I started an explanation with a concrete example.
So when teaching the design mix to pupils (considerations
firms make when designing a product in the R+D phase) I would start with a
concrete example of why a computer manufacturer would want to ensure a new
laptop they design is attractive, works well and is relatively cheap to make.
So far, so concrete but I found I would slip into ‘guess
what’s in my head’ questions. So, after positing that they would want their laptop
to be attractive to look at I would start asking questions like ‘why is it
important that their laptop is attractive?’ and ‘what other factors would they
consider?’ rather than clearly explaining the example.
I have had to retrain my mind to be disciplined and explain
my concrete example fully. The best time for questioning is when you start to
get more abstract with explanations to check if pupils can appreciate the links
between the concrete and abstract topics.
Mistake 2: jumping too quickly from concrete to abstract
Once I gotten back into the habit of explicitly explaining
an example, the next area I fell down in was jumping too quickly a concrete
example to an abstract concept. So, having gone from my laptop example, I would
jump straight from this example into a complex abstract notion of the conflict
between aesthetic and economic manufacture.
The problem is that the leap was to big. Pritesh spoke about
pupils being able the concrete example giving meaning to the abstract but it was
so abstract that the meaning was lost. Donald Dewar once said that ‘devolution
is a process, not an event’ and I think the same is the case with going from
concrete to abstract.
Ideally, this would go Concrete -> a wee bit less
concrete -> more abstract -> abstract concept.
So when teaching the design mix, I start off by going through
my example of 3 factors that a computer manufacture would consider when
designing a new laptop. After explaining why these 3 factors would explain
(which doesn’t take long as the whole point is that it is an example pupils can
understand easily) I question on what I have already told them to ensure
the example makes sense.
Next, I make this slightly more abstract by discussing the
conflict between these features. So, I will say something like “but if I
want my laptop to look appealing by it being very thin, that means it has a
small battery and so it doesn’t last as long. So, making it look nice makes it
less good to use.”
I gradually add to my diagram showing all 3 conflicts using explanations
like this.
This is only a small increase in the abstractness of the
concept, so pupils can use the example to make sense of the concept. At this
point, in questioning I would cover up the whiteboard and make sure pupils can
remember and explain these 3 factors and the conflicts between them to make sure they are still with me.
If they are I can then take this a step further on the
concrete – abstract journey by replacing these terms with business terminology
and introducing the term ‘the design mix’ for the first time.
Now I can question pupils on what these terms mean and the
conflicts between each one, checking if pupils have made the journey with me
from the concrete to this more abstract notion.
Then finally, I can make it really abstract by explaining
the impact the target market and the economic climate has on what importance
manufacturers place on different elements of the design mix.
Mistake 3: Only using one example
At this point, my explanations, questioning and feedback
from their practice questions shows me that pupils have a strong understanding
of the design mix. Or so I think. A problem that could arise (and has arisen)
is that for some pupils, they really understand the considerations of a laptop
manufacturer but that is where their understanding ends.
My intention isn’t for
them to leave my class with an in depth understanding of the computer
manufacturing industry but to understand the concept of a design mix and apply
it to any industry.
So at this point what I need to do is to introduce other
examples and show how the design mix impacts their decisions. Some of this will
be the same to highlight the similarities in the concept. This is also an opportunity
to highlight the differences, so I pick an example where economic manufacture
is more important than aesthetics to reinforce the earlier explanation of how
different industries place different emphasis on different elements of the
design mix.
Some of this may seem obvious to you but for me it took a
bit of trial and error to understand how this process works for me, but as I
refine my concrete-abstract explanations, it is a real game-changer in
improving the clarity of my explanations.