> >But learning to calculate base 10, or base > >2, or base 60, will not help in learning the concepts. > > I heartily disagree here. Everything that I have witnessed as a > teacher tells me that there is a very strong correlation between good > arithmetic skills and the ability to proceed further in mathematics.
I agree with Herman! I agree with Thomas!
If a student finds arithmetic easy, they will almost certainly have the ability to proceed futher in mathematics (so I agree with Thomas!).
If a student struggles with arithmetic, but eventually learns the techniques, well, what they have learned are the techniques, but almost certainly not the concepts (so I agree with Herman!).
On the whole, though, I agree with Herman. Good arithmetic skills are necessary for proceeding further in mathematics (a la Thomas), but _not_ sufficient. Working hard with students who struggle with arithmetic is certainly beneficial for those students in terms of their arithmetical success, but it is not going to be particularly beneficial in improving their ability to do further mathematics.
As everyone knows, our brain consists of tubes - an arithmetic tube, an algebra tube, a complex number tube, even a poetry tube. All of the tubes are clogged at birth. Good teaching can help unclog some of those tubes. But I reckon if the only way to unclog the arithmetic tube is to teach algorithms, then at the end of all that, the 'further mathematics tube' will unfortunately still be just as clogged.