> On the other hand teaching a kid math has to at some level at some point revolve around taking some numbers and getting other numbers out...
Yes, but perhaps not the very first thing. To me, the first thing should be interesting, aesthetically pleasing patterns -- images -- that have mathematical meaning (http://arachnoid.com/mandelbrot_set/graphics/title_image.jpg). Then, when the student's curiosity has been aroused, we can "open the machine" and show its inner workings.
> I cant really see how one can do algebra without knowing arithematic.
But that's easy. I'm not necessarily recommending it, but one can easily have algebra without numbers. Remember that the most useful algebraic equations are those in which the numerical values are irrelevant.
Yes, but perhaps not the very first thing. To me, the first thing should be interesting, aesthetically pleasing patterns -- images -- that have mathematical meaning (http://arachnoid.com/mandelbrot_set/graphics/title_image.jpg). Then, when the student's curiosity has been aroused, we can "open the machine" and show its inner workings.
> I cant really see how one can do algebra without knowing arithematic.
But that's easy. I'm not necessarily recommending it, but one can easily have algebra without numbers. Remember that the most useful algebraic equations are those in which the numerical values are irrelevant.