My introduction in exponentials and logarithms was via growth rates. My dad used baby fish as an example and I grokked it in a fifteen minute ride. Perhaps not very suitable for the more advanced topics (changes in base rate, the why of e) but you can teach this any ten year old.
Somewhere now typing this I have a feeling that this goes to show I have a very partial understanding of logarithms in that they transform between numbers on an exponential curve and exponents where my exponent is something I think of as periods in a discrete process. So the point of OP of the distinction between syntactic and semantic thinking is very real.
Somewhere now typing this I have a feeling that this goes to show I have a very partial understanding of logarithms in that they transform between numbers on an exponential curve and exponents where my exponent is something I think of as periods in a discrete process. So the point of OP of the distinction between syntactic and semantic thinking is very real.