Thursday, 10 January 2013

So what are the origins of our Maths Anxieties?


Firstly, A brief history about the origins of modern Math Phobia and Anxiety.

Rene Descarte’s (1596 - 1650) “mathematically deduced method”,  ( you may know 'I think, therefore I am') drew from a Rationalist  Socratic/Platonist  view, in which numbers are proof of facts beyond what humans can claim to ‘know’ by our sensations alone. In other words, numbers are true and impossible to deny, whether you like it or not. This Rationalist epistemology  sought to establish ‘what can I know?’  inferred that if 'God is in the details',  a God-sanctioned morality logically exists as well.  

This is the 'dominant' view.

However, a contrary empiricist ‘Fallibilist’ tradition  which  suggests started with Xenophanes of Colophon,  also ran parallel to the Socratic one, (perhaps even predating it by two hundred years):

Certain truth [about God or the world] has not and cannot be attained by any man; for even if he should fully succeed in saying what is true, he himself could not know it was so (Xenophanes, Fragment 34: (Glaserfield,1998. p.26).

This view indicates that 'truth' is not God-given, but is man-made according to how we perceive the world. That means that morality is not fixed, but is manufactured, and changeable.

The dominant view of maths represents it as  decontextualised abstractions which are 'neutral' and 'above' everyday 'manufactured' ideas.. In adult education this ‘neutral’ mathematics education and discourse continues to affect student and educator  identity. Some would argue it does so in a negative 'alienating' way.

Descarte’s  Method  was just one of the Enlightenment’s contribution to modern mathematics.  It is  considered that his  tradition of scientism  continued into the late Nineteenth Century. Educators employed the kinds of  ‘alienating’ pedagogies that were considered suitable for to educating the masses.  The so-called  'Absolutist'  tradition was further codified. As Traidaffilos (1998) states:

Platonism, on one hand, dissociated mathematics from its profane origins. Formalism, on             the other, alienated mathematicians from their cultural attachment to the socio-historical process, since they claimed exclusive custody of mathematical culture and its becoming (p. 23).

Although later in the twentieth century Behaviourism, cognitivism and Social Learning Theories cultivated interactivism, sociolinguistic theory and constructivism  even under the “New Maths’ system, mathematics education remained deeply invested in scientism and ‘reification‘ (ie making knowledge obscure to the uninitiated).

Mathematics as a discipline emerged in isolation from other curriculum areas, and this affected learner identities, but in particular in their views about how 'good' they were at mathematics. Consequently, many adult learners  consider mathematics as a commodified and isolating 'discipline', having little to do with their personal lives or having much relevance to the social practices they engage in.

When an adult learner engages in mathematics, ie at the ATM, parking the car, doing tax-returns, calculating discounts, doing DIY, etc, they don't see that as 'Maths'.  They can do 'Maths' but don't see it as such. Adults have been brainwashed into thinking that 'Maths'  exists only in the classroom, and is something that ordinary folk are barred from participating in.

If that sounds anything like you, and your relationship with maths - you can see how it all began, generations before you were born!

Saturday, 5 January 2013

Neoumeracy - The Origins of Math Culture


Is it reasonable to suggest that adult mathematics education has always been a cultural activity that involves relationships between the ideological views of both ‘educator’ and ‘educated’? If so, it would be worthwhile to investigate the nature of the culture and conversations we use in contemporary mathematics education, and how we got here. 

Evaluations of mathematics parallel historical development describe how Absolutism evolved to inform ‘Modern’ mathematics  alongside Fallibilism which informed a Radical Constructivist Tradition. From the latter emerged Post-modernism,  and Poststructuralism

By considering the epistemological origins of these mathematics ‘cultures’, and by exploring how mathematics education has evolved, we can locate different theories and models  as they have emerged and often merged within and across paradigms, and how discourse has featured in them. While considering adult student and educator identity, and the enduring plasticity and power of ‘Mathematisation’ (Triadaffilidis, 1998) as a dialogic presence in contemporary adult education discourse, opportunities may arise to outline some impacts of these parallel traditions on educator and learner identity, as they influence adult mathematics education in contemporary settings.

Triadaffilidis, T. A. (1998). Dominant epistemologies in mathematics education: For the learning of mathematics, 18:2. 21-27.