[gavinlit]

ok -I'll spell it out clearly for you. The manner in which calculators are introduced and utilised in the field of mathematics is open to debate. Stating that the use of calculators somehow renders people incapable of mathematical thought is absurd. There is no causal link between calculator use and lack of mathematical understanding. Feel free to point out any study that contradicts my last sentence. Or you can always go for the straw man and throw out some meaningless labels. Suit yourself.

Please explain to me how 'being able to manipulate numbers in your head' is 'less than abstract'. I would imagine that thinking of anything is an abstract process but again feel free to correct me.

Manipulating numbers does not necessarily lead to anything. If you're trying to infer a link between mental number computation and algebraic manipulation then (once again) your inferring a causal relationship that just isn't there. Sure, the capacity to perform mental arithmetic is integral to using algebraic structures but it's not in itself sufficient.

I agree that if you use a calculator to bypass any understanding of numbers is detrimental. I do not think this means that calculators are bad or to be avoided. I do not see how this has anything to do with a particular system of education or yours or my political leanings. (EDIT) How is this related to political science?

I'm glad that you can 'smell' I'm a leftist. Clearly one of your artistic talents. Now if you'd like to actually make a considered point I'm happy to go along. The reason I entered this thread is that it's related to my main field of work & thought it might be free of name slinging and childish comments. Give it a try - you just might enjoy it.