In preparation for my teacher training which I will be
undertaking next year, I am currently volunteering in a local primary school. Recently
I have been supporting individual children in learning their times tables. The
class teacher asks me to sit with each child and we go through the times tables
that they struggle with the most.
Let’s say we are practising the seven times table. I will
ask the sequence like this:
Child: Seven
Me: Seven times two is…
Child: Fourteen
… and so on until we get to seven times twelve.
Some children can do this quite well, whereas others might
struggle. But what is most interesting is that occasionally, a child that can
answer the sequence perfectly all the way from seven times one to seven times
twelve, suddenly can’t answer correctly when I ask an individual question, out
of sequence. For example, later on in the session I might ask ‘seven times
eight is…?’ and the child cannot answer now that the question is not preceded
by the other questions in the sequence.
Often in this instance, the child will go back and quickly recount
that times table from seven times one until they get to the question they have
been asked. Or they will start back from an easily remembered sum such as seven
times five. When they do this, they can answer correctly again.
In Don’t Shoot the Dog by Karen Pryor (1999), the concept of
behaviour chains is explained. Behaviour chains are based on the principles of
operant conditioning i.e. the subject learns a response to a stimulus though
reinforcement. However, a behaviour chain refers to a sequence of such
behavioural responses, occurring one after another. Each individual behaviour
is learnt separately at first and then they become linked as each cue for the
next behaviour reinforces the previous behaviour. For example, all the children
in a class tuck their chairs under their desks and wait quietly. The teacher
then uses the cue ‘Let’s go to break time’ to signal the next behaviour (that
the children can leave the classroom) and to reinforce the previous
behaviour (waiting quietly).
Pryor also explains how the cue for a behaviour can actually
be the previous behaviour in itself. She gives the example of how when she moved
to a new house, she learnt all the contact information for both her new house
and her new office. However, when asked for only one part of this information, say
her zip code, for example, she could not say it unless she began by saying the
first part of the address. In this instance, saying the first part of the
address is the cue for saying the zip code. Therefore, Pryor suggests that you
should not learn something in the order in which it will be presented as you
will find the task becoming increasingly difficult, starting with the most
familiar information and ending with the most unfamiliar. This experience is ‘unreinforcing’
and does not enable effective learning.
Back to the example of the children learning their times
tables. The cue for answering seven times eight is saying the answer to seven
times seven, which is cued by saying the answer to seven times six, and so on.
When the children are asked an individual question out of this sequence, they cannot
answer it because the cue is not present.
The children have learnt the chain successfully but when
they are tested on their times tables, the questions will not necessarily be
presented in the times table sequence; they need to be able to answer
individual questions. Therefore, in future practice, I
will ask the children the questions in a randomised order to break the habit of
the children relying on answering the previous question in order to get the
current question correct.
References:
Pryor, K. (1999). Don’t shoot
the dog. New York: Bantam.
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