This is a four-part review of the incredible book The Mastery of Reason by Valerie Walkerdine, written in 1988. The book contains a number of themes, from which I have drawn four, to be described in a series of four posts.
This post, the first, is about difference in relational dynamics at home and at school, and the effects of this for children's learning of maths.
[relational dynamics] are strongly emotive and the concept of the unconscious is necessary to understand that dynamic.
This idea lies at the heart of this book. The potential importance of the unconscious - that which we do not know about ourselves and which motivates our actions without our conscious knowledge - is becoming increasingly interesting to me. I feel that theories of the unconscious may have a lot to offer teachers in gaining a better understanding of their students.
By this I do not mean that we should seek to impose ready-made, half-baked psychological constructs on our students in an attempt to explain away their behaviour, but perhaps rather that we could aim to find out more about what may lie at the heart of their actions, by engaging with the work of psychologists and psycho-analysts. In this I follow Lacan, who suggested that the unconscious 'speaks' through language, and that we can learn about another's thoughts by listening carefully to what they have to say.
This is the approach taken by Walkerdine in this book, who analyses interactions at home - between children and parents - and at school - between children and teachers - with the aim of understanding how relational dynamics effect children's learning of mathematics.
More or less
An example of this approach is the analysis of the terms more and less, and other quantity relations, both at home and at school.
It is striking that almost all the examples of more from the corpus [of mother-child interactions] form part of practices where the regulation of consumption is the object... This presents a relational dynamic relating to power…
Walkerdine argues that the term more is first learned, and therefore has meaning that is inextricably linked, with power relations between mother and child:
Centrally implicated is an analysis of power: there are not two equal participants. Furthermore, the meanings created within such practices relate to the power and relationships inscribed within them
What are the implications of this for teaching the contrastive pair more and less in the maths classroom? Walkerdine gives detailed evidence from school discourse that children often understand the term more very well in tests, but do not appear to understand the term less, often confusing it with more. She explains why this might be the case:
Although more and less are assumed to be an important contrastive pair, it is often assumed that young children do not understand the meaning of less, and indeed, interpret questions involving less to mean more. This failure is taken to imply, and in some accounts to be caused by, a failure to understand quantity relations. In the analysis of the terms more and less in home practices, I argue that children have plenty of practice in activities involving quantity relations. However, the terms used to signify similar relations in the relevant practices do no appear to be the contrastive terms more and less. Other terms, such as a lot and a little are far more common. While there were in the corpus inspected many instances of more, and none of less, it is important to point out that the term more was not used in practices involved the contrast of quantity relations. More was used almost exclusively in the regulation of consumption by parents, and the children’s requests for extra helpings. In these practices, the opposite of more is not less, but something more like no more…
The term more signifies something very different at home than it does at school, and is linked to a powerful relationship between parent and child. Walkerdine suggests that we, as educators, should aim to become more aware these kinds differences in signification at home and at school. She goes on to suggest that:
…we cannot expect the inscription of such signifiers as more to be equivalent across class and culture. That is, more as a relation within these practices is lived.
Social class and culture are crucial dimensions of Walkerdine's work. In this article for the excellent journal For the Learning of Mathematics, she explains further the relation between the signifier more and social class:
For example, a mother might tell her daughter that she could have no more of a particularly expensive commodity or that she could not have more food until she had eaten what was on her plate... It will come as no surprise that such terms were used more frequently by mothers in working class families, so that such little girls would be more likely to understand their mothers as more regulative and to have very strong negative associations with the term more.
Maths for shopping
A second example of the difficulties in assuming signifiers to carry the same meaning across different discourses is explored in a number of examples of students simulating shopping exchanges in the classroom, and comparing them with children's shopping experiences at home.
In one shopping task, students are given 10 pence and asked to calculate the change after buying certain goods costing between 1 and 10 pence. The transcript of the lesson captures beautifully the difficulties in implementing this kind of activity in the classroom.
Again, Walkerdine suggests that the problem lies in the difference of signs in two separate practices - we can't just apply context and hope for transfer:
The two practices barely overlap. The pedagogy assumes that children learn about money only from the handling of small coins which leads to the real understanding of arithmetic processes, whereas the understanding of money on the part of the children [in her research] is one in which large sums of money are involved, these sums have important value attached to them, and are inserted in crucial domestic economic practices.
Walkerdine suggests that lifting a practice that has powerful meanings for students and placing it in the maths classroom is problematic:
The purpose here is not to purchase shopping, but to calculate a subtraction. In this sense, the practical format can be misleading and sometimes downright unhelpful... It is [the children’s] positioning within a practice which produces the possibility of the fantasy and of pleasure. This produces particular effects. They have a good time, certainly, but they do not get a lot of mathematics done.
These final sentences give some clue as to where Walkerdine thinks the problems within the maths classroom may lie; the themes of fantasy and pleasure are central themes which I will explore in subsequent posts.