ESRC Mathematical Relationships: identities and participation
Edinburgh seminar: The Curriculum
Jenny Shaw
Jenny Shaw taught Sociology at the University of Sussex for over thirty years and is the author of Education Gender and Anxiety. Now retired, she remains associated with the University as a Senior Research Fellow and is writing a book on Shopping: Social and Cultural Perspectives
Outline
This talk starts with Howard Becker’s reverse engineering point – What, if we wanted to produce maths disaffection might we go about it? Possibly, by giving lots of tests and using impersonal marking (digital) systems. Though not all testing is counterproductive it evokes anxiety and other subjects suffering ‘flight’ like languages are also ones which rely heavily on testing. There is connection between testing and the content of maths and I want to talk about the feeling of maths as a subject, the feelings and unconscious associations it evokes and stereotypes of the people drawn to it. As a field maths is reputed to have an ‘awesome’ power, and it certainly has a mean vocabulary which is full of negatives, negative numbers, cancelling and taking away and a hidden morality as in ‘right’ and ‘wrong’. This leads me to discuss how a subject (discipline) can serve as a container for feelings and thoughts, and to the prototype for the container/contained motif which is the mother/infant relationship.
The nature of relationships is the key to much psychodynamic thinking, and feeding/ ingestion the prototype experience for much learning and teaching. The relationship with the one who feeds is especially important and, critically, much more than milk is ingested. The first anxiety-inducing performancemothers’ feelings and her anxieties are part of the environment to which the infants adapts. The term psychoanalyst Wilfrid Bion uses for the circuit of feelings which flow between mother and infant,‘reverie’. In the best case scenario an infant is left alone with its pain, and has a mother who is not too frightened herself, who remainsemotionally in touch,and processes some of the feelings afflicting the child, and then returns them in a more tolerable form. In this case the child can bear the learning process, and press on. But there is another scenario where the mother is frightened, does not accept the projections of anger, fear and panic,or return them in a more tolerable understood form, but bats them away with the consequence that they lose all meaning and become a ‘nameless dread’. The infant still projectively identifies with the mother, but instead of having a sense of her as a receptive and understanding person, is presented with a wilfully misunderstanding ‘object’. In this situation, non-meaning dominates, and unmet needs are responded to with envy and hostility –as I think was illustrated by some of Tamara’s transcripts from the last seminar.The relationship with maths (the object) had gone bad and ‘pleasure’ came only from reviling/attacking both it and the person teaching it- who was viewed with envy and hostility.
The importance of relationship to understanding is the basis of Bion’s concept of thinking, his –K and K mentioned in the last seminar. But it is not only the hierarchical parent/child or teacher/student relationship which is critical, but the horizontal ‘sibling’ relationship too and I think we should be considering the stereotypes/projections about those who are good or not at maths. Maths sits at the top of the hierarchy of prestige of subjects and it is not easy for those who can’t ‘do’ maths to understand what it takes to be ‘good at it’, so I think we need to explore how these ‘others’ are viewed- as a different species, as Gods? There are many ways of helping childrenand we all come to schools and to subjects with different emotional baggage. But one thing teachers of maths might find useful is child psychotherapist Margot Waddell’s three ways of relating to another person: adhesive, projective and introjective, and her example of the three different ways a mother might help her child with a jigsaw puzzle. Generally speaking, the psychodynamic take on learning is that it cannot be imposed, but can be supported; and that children can only learn from their own real experiences. There is some scope for re-thinking the order in which maths is taught – the latency period for example with its characteristic joy in amassing facts, and enjoying being tested on them. The key to the Sauvy’s success teaching topology to primary school childrenmay have been its basis in relationships. So the challenge, I think, for maths educators is how to bridge or link to the unconscious and primitive understanding of relationships in ways which foster their more abstract representations. In the paper on thinking where Bion advances a schema for how thought develops from a preconception which meets/mates with a realization to make a conception and produces satisfaction (a harvest of self-sensations) he writes that the ‘crux lies in the decision between modification or evasion of frustration’, and illustrates this with an example drawn from mathematics: ‘Mathematical elements, namely straight lines, points, circles and something corresponding to what later becomes known by the names of numbers derive from realisations of two-ness as in breast and infant, two eyes, two feet and so on….’ He stresses that thought is ‘the modification of the experience of frustration’, and that the development of mathematical elements is ‘analogous to the development of conceptions’.
Bion Wilfrid (1967) Second Thoughts. Selected Papers on Psychoanalysis, London, William Heinemann Medical Books
Bion, Wilfrid (1970) ‘The Container and Contained’ in Attention and Interpretation: a scientific approach to insight in psychoanalysis an groups’London, Tavistock Publications.
Becker, Howard (1988) Tricks of the Trade; how to think about your research while you’re doing it, Chicago, University of Chicago Press.
Jean and Simonne Sauvy (1974) The Child’s Discovery of Space, Harmomdsworth, Penguin Education,
Waddell Margot, (1998) Inside Lives.Psychoanalysis and the Growth of Personality, London, Karnac.