## Entanglement

The first two posts in this series (below) outlined the ‘massive entanglement’ that arises when overlapping non-mathematical and mathematical discourses, as described in Valerie Walkerdine's book The Mastery of Reason. This entanglement is the crucial issue facing teachers of mathematics.

How does this entanglement come about? Learning maths requires the reification of the abstract through the concrete, which is often achieved through a range of (linguistic) devices such as use of metaphor, or linking mathematics to non-mathematical contexts:

How does this entanglement come about? Learning maths requires the reification of the abstract through the concrete, which is often achieved through a range of (linguistic) devices such as use of metaphor, or linking mathematics to non-mathematical contexts:

… non-mathematics practices become school mathematics practices by a series of transformations, which retain the links between the two practices... but this requires a shift in the relations of signification involved in the transition from one discursive practice into another.

It is in these complex signifying chains, where terms interchangeably act as signifiers and signifieds, that mis-readings frequently occur. Which links in these chains are unnecessary, or unhelpful, to learning mathematics? To what extent are non-mathematical contexts useful or meaningful?

Conversely, is it really the case that mathematics is essential to non-mathematical practices? If mathematics is not necessary to describe the world around us, if it is not essential to our daily lives, then is it desirable, or necessary, to learn mathematics through these contexts? Is it necessary for us all to learn mathematics at all? If mathematics is not everywhere, as we are led to believe, then why does it hold such a place of importance in the school curriculum?

## The myths of school mathematics

In his book The Sociology of Mathematics Education, Paul Dowling describes some possible myths propagated by school mathematics. One of these is the 'Myth of Reference', in which (p.4, p.6):

Mathematics is mythologized as being, at least potentially, about something other than itself... It is as if the mathematician casts a knowing gaze up on the non-mathematical world and describes it in mathematical terms... the myth is that the resulting descriptions and commentaries are about that which they appear to describe...

Dowling's book gives numerous instances of this myth in school mathematics texts. You just have to pick up a textbook, or look at an exam paper, to see the myth in action for yourself. An example might be the value-for-money calculations we ask students to perform, often without a calculator - these questions are not about finding the cheapest toilet rolls, or whatever it might be, they are about doing mathematics.

So, is it, or is it not, the case that mathematics is an essential aspect of all of our day-to-day practices? Dowling suggests not, citing the example of research findings set up by the Cockcroft Committee into the use of mathematics in the work-place (p.5):

They found that a great many young employees – a ‘vast army of people’ – did not appear to require any formal mathematics, not even counting or recording numbers.

Clearly there are some of us who use mathematics more than others, but it is indeed hard to argue that many of us need the mathematics required to pass a GCSE exam with a grade C (particularly some of the calculations required in the non-calculator examination).

Dowling goes on to suggest a second myth, the 'Myth of Participation':

[The myth of participation is that] mathematics is not so much being constructed as potentiallyaboutsomething other than itself, rather, it isforsomething else. Mathematics justifies its existence on the school curriculum by virtue of its utility in optimizing the mundane activities of its students. [My emphasis]

If we subscribe to these two myths, they may suggest some reasons why students may find the application of the mathematical to the non-mathematical problematic. In what sense does 'real-life' mathematics have anything to do with the lives of our students? Is mathematics really 'everywhere', as we lead our students to believe?

## The mastery of reason

If mathematics is not relevant to the every-day lives of many people, why should it hold its current position of importance in the curriculum?

For me, mathematics is worth studying as a means to itself. We can learn mathematics in order to solve mathematical problems. This, for me, is where the value of mathematics lies - it has no more or no less value than other subjects - I do, and teach, mathematics because I enjoy solving mathematical problems, and wish to share this enjoyment with others.

However, the source of this enjoyment may, in fact, be the reason

However, the source of this enjoyment may, in fact, be the reason

*why*mathematics is considered so important; Walkerdine asks (p.189):What kind of pleasure is the pleasure afforded by mathematics?

I will talk more about the

*personal*'pleasure afforded by mathematics' in the final post. For now, I would like to focus on the source from which

*mathematics itself*gains its power:

...the co-called generalisability and context-free nature of mathematical discourse is achieved through the suppression of the metaphorical axis... That suppression is both painful and extremely powerful. That power is pleasurable. It is the power of the triumph of reason over emotion, the fictional power over the practices of everyday life.

Herein lies the central point of the book.

Walkerdine suggests that the symbols of mathematics have been created through a chain of signification leading to the suppression of meaning, creating a discourse which can then be read back onto

*anything*.

In this way, mathematics achieves its universality, and its statements have the appearance of statements of fact. This elevates the status of mathematics to the 'perfectly rational', with the power to describe and control our universe. This renders to the mathematician a powerful position, for s/he produces statements which are taken to be true.

This might go some way to explaining why mathematics holds the position of power it currently does. The question remains: Should mathematics hold this position of importance in our curriculum? What are the implications of the current nature of mathematics education on our children?

## Producing 'the child'

Mathematics and rationality have risen to prominence in their ability to 'describe' the universe and the human mind. Arithmetic is the fundamental tool of Capitalism, measurement and statistics are used to describe what is 'normal' in society.

The prevalence of mathematics is nowhere more apparent than in education, as Walkerdine explains:

It is my contention that the modern order is founded upon a rational, scientific, and calculating form of government... the calculating mind and calculating the child are as one.

Here government is being used in the wider sense; the government of education is based on calculating the child. The word

*calculating*is important here; this is not purely the

*measurement*of the child:

The practices provide not a point of description of the real, but a point ofproduction, of creation of signs. 'The child' as a sign... is not simply a description of the pre-existing child. The practices themselves, in their regulation, produce what itmeansto be a child: what behaviours, words, etc. are used... The truth of children are produced in classrooms.

There is no 'pre-existing child', only the child that is produced in the various discourses in which they are placed. This realisation has far-reaching implications.

What child are we producing in maths classrooms? In schools? At home? Is there a disconnect here, between the 'student' and the 'child'? How

*should*education contribute to the production of the child?