Behaviourism 1: Skinner's 'reinforcement' and 'conditioning' theories
In this scenario, we discuss the use of Skinner's ideas on conditioning and on reinforcing learning, as outline din the main body of the chapter. These ideas are applied to the context of a basic skills class for adults. In the class, there are two weekly sessions, one of which deals with basic literacy and the other with basic numeracy. You have been given the lead on delivering numeracy sessions to the clients. The learners in the group vary in age from late teens to retirement age, and have diverse backgrounds and life experiences. They also have different reasons for attending: for some, this is facing up to a long-held sense of inadequacy; for others, a practical means of getting support with reading, writing, and the everyday use of numbers.
This week's session involves basic multiplication. Online testing done for diagnostic purposes at the start of the course has indicated that this is an area where many of the learners struggle. There is a curriculum and a practical need to have this mind of basic maths-related understanding.
Task: Drawing on behaviourist ideas, what strategies might be useful in supporting engagement with multiplication in this situation?
An approach to begin with might be to discuss with the group their previous experiences of learning, and of maths in particular, in the past. It is often the case that such experiences will have been negative, that the subject will have been delivered in a boring manner, and that the learners might not have seen the relevance of the subject to them. Often such discussions can also yield useful information and insight into the learners, as well as into their perceptions of their learning needs and where they struggle in their everyday lives; it may well be that this gives the key to approaching multiplication for these students.
If the contexts of the learning are meaningful, then this not only supports engagement with the skills in their own right, but this can also support the contextualisation of what might otherwise be dull or confusing material to learn. Many learners might have memories of times tables, with charts on their classroom wall of tables up to 20 x 20; older learners may even recall chanting en masse the times tables in sequence to the teacher's satisfaction! One way of making multiplication meaningful is to think in terms of money, and to build up from everyday competencies which may not be understood as mathematical in themselves. Cash-handling is one, as is telling the time, and using both distance and weights and measures.
Money offers the use of relatively simple everyday transactions to be used as the basis for multiplication operations, and of multiples of coins or notes to find out larger amounts: a sample question might be along the lines of "If I have four five-pound notes, then how much money do I have?" Four fives are twenty, no matter what. If learners are having difficulty with times tables, then a workaround can be to show learners that they can add forwards to get the same result (five plus five is ten, plus five is fifteen, plus five is twenty). Part of the reinforcement comes from the practical usefulness of relating mathematics back to such everyday activities; it rewards knowledge and experience that the learner already has, and in addition provides a vocabulary for those same skills.
In this way, everyday skills might be related to a series of times tables, and so there can be contextualisation given to a range of mathematical calculations rather than their being imprinted through rote memorisation alone. In practice, you might find that a person's multiplication knowledge is a mix of ability and memory, and that both sets of competencies are drawn on as a consequence.
Learners can be challenged to use these skills in real-world contexts; it is easy to avoid engaging in numbers at times, through relying on others, through trusting people to give you the correct change, through guesswork, and through reliance on card payments and on calculators, for example. One way to show the usefulness of having these mathematical skills available is to get learners to try them out and so demonstrate additional independence and confidence in such situations. This can be done under controlled situations, such as in role-play exercises between class members. Success in such interactions, as well as praise and recognition of such developing competencies - whether they come from peers or from you as the instructor - can be useful as reinforcement over and above the learner's sense of achievement and their new-found abilities.
While explicitly, behaviourist teaching methods may not be wholly suitable to more advanced mathematics (such as long multiplication) they can give confidence and a bedrock of knowledge upon which to develop, and so there may well be a combination of knowledge gained through behaviourist teaching and learning as well as from the contribution of other paradigms in any learner's growing mathematics abilities. Not least where lack of confidence, and avoidance of engaging with mathematics in the past might well have been a significant issue for some learners, the ability to draw on some memorised information can offer both security and universality. As noted above, four fives are always twenty, no matter what is being counted.
The learning can be augmented through online and computer programs which give instant feedback through grading as well as affirmation of progress through the giving of points or similar tokens in the gameplay scenarios often used in such software. These kinds of support can be useful, but need to be aimed at an appropriately adult audience so that the materials are both respectful and meaningful; repurposed educational software written for children would not be appropriate in this context.
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