Sawyer's "Prelude to Math" is a book I keep trying to discard (I just have toooo many books. I'm a bookaholic!) but I start to look at it again and I always say--well, maybe not yett. And the edition I have is an old Penguin paperback published in 1960--when they still sowed paperbacks together with thread!
Another famous mathematician very concerned with the teaching of math was Felix Klein of Klein Bottle fame: "Elementary Mathematics from an Advanced Standpoint: Arithmetic, algebra, analysis"--1924;
--and of course Agustus De Morgan, way back in 1831: "On the Study and Difficulties of Mathematics"--written for English Public School boys.
More recently, Jerry King has written "Mathematics in 10 Lessons" attempting to approach the subject via Sets and Logic (2009), promoting the idea of the art or poetry of math. Well, that's OK for pure mathematicians: Theorem A/Proof, Theorem B/Proof, etc. but it takes a certain type of mind, I think (which, alas, I don't have much of) to appreciate and pursue math that way. It requires the ability to pile abstraction upon abstraction upon abstraction and not lose track of what you are doing. Not the sort of ability very many of us have--including engineers and scientists. Sawyer, Klein, and De Morgan--among others (Polya comes to mind) have attempted to get beyond the Theorem/Proof paradigm of math. Daniel Solow, I might add, has even attempted to elucidate to mathematical duffers like myself the mechanisms behind the Theorem/Proof approach to math in his 1982 book: "How to Read and do Proofs".
I used to fear and dislike math when I was younger altho I managed to struggle through First Semester Engineering Calculus and halfway through the Second Semester but I crashed and burned when I got to Hyperbolic Functions! Now I consider math a hobby, having retired several years ago, and could devote more time to pursuing the subject. I'm still not much of a mathematician, but now I prefer mathematical study to crossword puzzles or Sudoku.
Sawyer's "Prelude to Math" is a book I keep trying to discard (I just have toooo many books. I'm a bookaholic!) but I start to look at it again and I always say--well, maybe not yett. And the edition I have is an old Penguin paperback published in 1960--when they still sowed paperbacks together with thread!
Another famous mathematician very concerned with the teaching of math was Felix Klein of Klein Bottle fame: "Elementary Mathematics from an Advanced Standpoint: Arithmetic, algebra, analysis"--1924;
--and of course Agustus De Morgan, way back in 1831: "On the Study and Difficulties of Mathematics"--written for English Public School boys.
More recently, Jerry King has written "Mathematics in 10 Lessons" attempting to approach the subject via Sets and Logic (2009), promoting the idea of the art or poetry of math. Well, that's OK for pure mathematicians: Theorem A/Proof, Theorem B/Proof, etc. but it takes a certain type of mind, I think (which, alas, I don't have much of) to appreciate and pursue math that way. It requires the ability to pile abstraction upon abstraction upon abstraction and not lose track of what you are doing. Not the sort of ability very many of us have--including engineers and scientists. Sawyer, Klein, and De Morgan--among others (Polya comes to mind) have attempted to get beyond the Theorem/Proof paradigm of math. Daniel Solow, I might add, has even attempted to elucidate to mathematical duffers like myself the mechanisms behind the Theorem/Proof approach to math in his 1982 book: "How to Read and do Proofs".
I used to fear and dislike math when I was younger altho I managed to struggle through First Semester Engineering Calculus and halfway through the Second Semester but I crashed and burned when I got to Hyperbolic Functions! Now I consider math a hobby, having retired several years ago, and could devote more time to pursuing the subject. I'm still not much of a mathematician, but now I prefer mathematical study to crossword puzzles or Sudoku.