Friday, November 26, 2010

Math problems of the week: Chicago Math Project vs. Traditional Algebra

I. Final factoring problems in the "Factoring" chapter of the University of Chicago School Mathematics Project Algebra: Integrated Mathematics textbook (published in 2002), p. 769:


Solve by factoring:

x2 - 2x = 0
z2 + 7z = -12
y2 -2y - 3 = 0
2r2 - 10r + 12 = 0
b2 - 48 = 2b
k2 = 9k - 14
0 = m2 - 16
9w2 + 12w = 0
6y2 + y = 2 = 0
0 = 16m2 - 8m + 1

II. Final factoring problems in the "Factors" chapter of Wentworth's New School Algebra, (published in 1898), p. 107:

Resolve into factors:

x4y - x2y3 - x3y2 - xy4
9a2 - 4b2 +3a + 2b
x3 - y3 - (x2 - y2) - (x - y)2
(x - y)2 - 1 - 2(x - y - 1)
a3 - 2a2c - a2 - 4a + 8c -4
a2 - b2 - c2 + 2bc + a + b - c
x3z2 - 8y8z2 - 4x3n2 - 32y8n2
5ac + 3bc + c +5ab + 3b2 + b
2ab - 2bc - ax + cx + 2b2 - bx
x4 - 2abx2 - a4 - a2b2 - b4

III. Extra Credit:

1. Which factoring exercises better prepare students for modern day higher-level mathematics?

a. Those from the end of the 7th chapter (out of 27 chapters total) of an introductory algebra text published in 1898.
b. Those from the end of the 12th chapter (out of 13 chapters total) of an introductory algebra text published in 2002.

2. Relate your above answer to the ubiquitous assumption that it's not the curriculum, but the teachers, the parents, the children, and/or society, that explains the decline in the mathematical preparedness of today's U.S. students.