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:
Me: Seven times two is…
… 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.
Pryor, K. (1999). Don’t shoot the dog. New York: Bantam.