## H Wu says teach Q not R in school

http://math.berkeley.edu/~wu/Lisbon2010_2.pdf

The Mathematics School
Teachers Should Know
Lisbon, Portugal
January 29, 2010
H. Wu

See page 6.  Also he is implying teach Peano Axioms as well.

==Page 7

(2) A university mathematician once described to me how he
had been presenting \fractions from the eld axioms point of
view” to teachers from grades 6{8.
Thus, beginning with the axioms that the rational numbers Q
satisfy the associative, commutative, and distributive laws with
respect to + and , and that every nonzero number has a
multiplicative inverse, he derived all the usual properties of Q.
This knowledge will not help teachers to teach 12-year olds about
fractions, because 12-year olds don’t care about axioms of a eld.
They have no idea what a eld is or what axioms are good for.

==

This bad idea is what Keith Devlin advocates.  Devlin opposes teaching the Peano Axioms or recursion in school, even though he admits in effect at one point the recursive nature of elementary math.

http://math.berkeley.edu/~wu/Schoolmathematics1.pdf

(A) Whole numbers The basis of all mathematics is the whole numbers.
In particular, a complete understanding of the whole numbers and its arithmetic
operations is the core of the knowledge teachers need in K-3. What is often not
recognized is the fact that an adequate understanding of place value, the central
concept in discussions of whole numbers, only comes with an understanding of
how to count in the Hindu-Arabic numeral system.

Precisely, m is smaller than n, or in symbols, m < n,
if m comes before n in the counting process.