This is a reprint of an address given at the Christmas National Council of Teachers of Mathematics (NCTM) meeting in 1958. It provides a critique of elementary instruction and discusses the changes necessary. It calls for fundamental change in the concept of mathematics teaching. (PDD)

Shares an experience from a mathematics methods course for elementary teachers that used concrete materials to teach the concept of rounding in different bases. Discusses how this experience modeled recommendations by the NCTM "Professional Teaching Standards" in creating classroom climate and conducting discussion. (MDH)

Included are activities and guidelines which suggest ways to use large numbers in relative terms so that they can become more meaningful for elementary mathematics students. Several spreadsheet projects illustrate the incorporation of the recommendations from the NCTM Standards dealing with number sense. (JJK)

Suggestions for using a computer disc containing unprotected programs are given. The Fibonacci sequence, prime factorization, sum puzzlers, and other examples are described. (MNS)