Hi all, thanks for the comments (writing from a train using a kindle so forgive lack of links) google "better explained math intuition" which is an article on

Hi all, thanks for the comments (writing from a train using a kindle so forgive lack of links) google "better explained math intuition" which is an article on developing the four common definitons of e. the problem with saying "e is the function which is its own derivative" is the same as saying "a circle is the set of points where x squared plus y squared equals radius squared". i asks too much of a beginner and imo is best shown after they have an idea of the basics. ie, here is a round shape. we call it a circle. look at this neat property where every point is the same from the middle! lets write an equation for that... with e. what is growth? it is like interest on your bank account. why do we wait till the end of the year? month? second? intant? how can we write this as an equation? (in algebra, in calculus) the other reason to avoid calculus definitions is that 2% of students will bother asking for clarification/more details but most high schoolers can at least follow the algebra of compounded interest.i still don't get limits/infinitesimals to the level i like despite writing about them. anyway thanks for the comments, i love seeing what explanations work for people!