Chapter 1

G.1 It is stated in the text that "Mathematics is alive and constantly changing. As we complete the last decade of this century, we stand on the threshold of major changes in the mathematics curriculum in the United States." Report on some of these recent changes.

References

Lynn Steen, Everybody Counts: A Report to the Nation on the Future of Mathematics Education (Washington, D.C.: National Academy Press, 1989).
See also, Curriculum and Evaluation Standards for School Mathematics from the National Council of Teachers of Mathematics (Reston, VA: NCTM, 1989).

G.2 Do some research on Pascal's triangle, and see how many properties you can discover. You might begin by answering these questions:

1. What are the successive powers of 11?
2. Where are the natural numbers found in Pascal's triangle?
3. What are triangular numbers and how are they found in Pascal's triangle?
4. What are the tetrahedral numbers and how are they found in Pascal's triangle?
5. What relationships do the patterns in Figure G.1 have to Pascal's triangle?


Figure G.1 Patterns in Pascal's triangle

References

James N. Boyd, "Pascal's Triangle," Mathematics Teacher, November 1983, pp. 559-560.
Dale Seymour, Visual Patterns in Pascal's Triangle, (Palo Alto, CA: Dale Seymour Publications, 1986)
Karl J. Smith, "Pascal's Triangle," Two-Year College Mathematics Journal, Volume 4 (Winter 1973).