By Coles, Alf
Mathematics Teaching , No. 193
"People often say: 'I teach them but they don't learn'. Well, if you know that, stop teaching. Not resign from your job: stop teaching in the way that doesn't reach people, and try to understand what there is to do for you to become daily more skilled in helping these youngsters furnish their minds with things which are so elementary that, where they take five years today, I can do them in 18 months, sometimes less." (Gattegno, 1988, p 12)
It is almost twenty years since Caleb Gattegno, a co-founder of ATM, published The science of education, a final account of his life's work in the study of teaching and learning. There has been little movement in the UK in the direction of the radical and remarkable vision he painted in that book; he was perhaps ahead of his time. If by the end of reading this short and inadequate summary of a fraction of his ideas any teachers feel some relevance now to their classroom and would like to form a collaborative group to work on issues or questions arising from Gattegno's writing then please get in touch via email (firstname.lastname@example.org).
1) The Science of Education Part 1, Theoretical considerations
Here I set out my interpretation of some of the themes of the extraordinary Theoretical considerations which form Part 1 (now out of print) of Gattegno's The Science of Education . It is in this book that Gattegno describes his blueprint for the transformation of education. In editing a whole book down to a few paragraphs I have tried to give a flavour of as many of the themes Gattegno pursues as I can. This has resulted in a slightly disjointed text and ideas that are not pursued - many of these ideas can be followed up further in the ATM's A Gattegno anthology .
The birth of a new science
In a 'common sense' attitude towards our experience we tend to imagine ourselves as somehow 'in here' and everything else as 'out there' and that we have more or less unproblematic access to what is 'out there'. Yet on reflection it seems clear that all our dialogues with what we think of as the outside world are in fact dialogues with ourselves, e.g. "Is it my dog I see there?" is a question about whether I have inner evidence that the dog I see is the same as the one I can recall as being my dog. There is no reality which is not human - reality is a construct. This is not to say that we cannot agree about our realities and create criteria for the truth of statements, but ultimately everything we see or say is stamped by our own interpretation. All we can know and work on are the contents of our awareness.
Individual sciences work on specific aspects of our awareness. Optics deals with and 'explains' our awareness of impacts on the eye; acoustics our awareness of impacts on the ear. The Science of Education is in this tradition but it is apart from all other sciences in that it will not be looking at some aspect of what we are aware of but looking at looking. Put another way it is concerned with knowing about knowing or with our awareness of being aware (of something).
Like all sciences the Science of Education has methods and instruments. In this case there is a single method and that is our own watchfulness (or presence) and a single instrument which is to question. The only way we can study ways of looking or ways of knowing or our awareness of things is through watchful introspection as we deliberately put ourselves in situations, for example a classroom, where there are things that will catch our attention or awareness. The Science of Education is something every teacher needs to engage in personally. It will not provide 'answers' that can be applied but rather questions to be explored or experiments to be tried.
Awareness of awareness
Through watchfulness we can become aware that we have a number of ways of being aware of things. These are our 'ways of knowing' and they include: perception, action, analysis/synthesis, acquaintance, contemplation, intuition. …