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LINKS: ....Bird Flu Info ....Your Memory Enhancer ....Neurotech ....Success Tips ....Free The mathematical brainIn a recent book, 'The Mathematical Brain' by neuropsychologist Brian Butterworth argues for a brain that adapts based on interest and practice rather than innate predisposition. He also argues for an area of the brain that is present in both human and animals that deals with numerosity. Numerosity dealing with the numbering of collections and comparing the numerical size of more than one collection. Butterworth makes the distinction between numerosity and language; language as a ladder to using and extending the usefulness of of numerosity. He differentiates between awareness of size and numerosity, siting numerosity in the left hemisphere of the brain. He argues that representation of space is intimately bound up with brain representation of numbers. Body schema issues [the brains model of the body] have become linked to counting, through counting systems based on body parts, and with most emphasis on fingers. Fingers are so bound up with counting that he posits a link between representation of fingers and numerosity in the brain. He sites the parietal lobe as associated both with finger representation and numerosity. He argues that the use of fingers is a cultural tool that extends the innate (but limited) capacity to distinguish numerosity (he refers to the innate awareness of numerosity in terms of a specialised 'number module' in the brain). Fingers leading to other means of extension (tokens, symbols, operations). He further argues, after giving evidence that what you do leads to greater representation for that task in the brain (a braille readers reading finger is represented by more brain cells than other fingers), that interest and practice and good cultural tools, rather than heredity, determine your capacity to do and competence at anything. This is in turn is an argument for the importance of making mathematics interesting in an educational context. He sites evidence of prodigies who were not in fact spontaneously good, but worked extremely hard and received, effective teaching and cultural tools. He goes on to argue that given the importance of interest and practice, early success or failure can be crucial in the context of long term success or failure. Vicious circles can arise from an early inability to solve a problem leading to avoidance of that class of problem leading to a further inability to solve that kind of problem [and so on]. Virtuous circles can equally arise if early attempts are successful leading to further interest and therefore more practice and therefore more experience of success at a class of problem leading to more interest [and so on]. The implication is that if you are lucky enough to get a foot on the ladder and not slip you keep going and if the step is for whatever reason placed to high for you you abandon the ladder. He goes on to emphasise the role of continuous argument in a subject like mathematics, if you miss out a chunk of mathematics in the middle of a continuous argument the following steps won't make sense, and all mathematics is a continuous argument, there's no point in starting to learn calculus if you haven't grasped the mathematical concept that lead up to it. The point being that intelligence is not enough you need to have seen the pieces in the right order and see how they fit together. He also rails against rigid classroom environments where there is 1). A failure to work with the concepts children may have picked up elsewhere that work but do not fit into the formal system as taught by the teacher. 2). The failure to emphasise understanding over rote learning. 3). The natural tendency to seek the greater good of the whole group and follow a pace set by the curriculum timetable, both at the expense of the pace of the individual 4). The failure to realise that anxiety (which is note identically equivalent to incapacity) is a genuine impediment to performance. I conclude from this that it can be useful to differentiate between personal mathematics and school mathematics, and to try and persue them seperately (while allowing each to benefit the other). HOME...... Brain Food LINKS: ....Medical Dictionary ....Stress Management ....Allergy Info |