Friday, April 9, 2010

Math problems of the week: traditional algebra vs. CPM

1. The final factoring problems in McDougel Litell's Algebra I, a contemporary, traditional algebra text (p 773):

x2 + 6x + 8

x2 - 24x - 112

3x2 + 17x - 6

4x2 + 12x + 9

x2 + 10x + 25

x2 - 14x + 49

2. The only factoring problems in all of College Preparatory Math's Foundations for Algebra Year 2, a Reform Math algebra text (p. 159; p. 195):

2x + 20

5x + 35

3x - 15

5x - 60

8x + 12

9x + 6

-2x - 4

3. Extra Credit:

Why is factoring second degree expressions more traditional than only factoring first degree expressions?


lgm said...

Here's an excerpt from the final section on factoring in a 1997Dolciani & Brown - Algebra : Structure and Method Book 1. It's a later edition of the text that everyone (app. 60% of the cohort) who took Alg. I in my rural high school used in the 70s. It was used by JHU for talent search participants until they went with Thinkwell, and it's still used by Univ of Mo for their distance learning Alg course. The NROC also uses this text as part of their free online Algebra I course:

Chapter 5 Sect 11 Using Several Methods of Factoring

Factor Completely
A.(easy difficulty)
7. 5a2+10ab+5b2
29. p2-1-4q2-4q
B. (moderate difficulty)
31. 100+4x2-16y2-40x
33. a4-b4
C. (challenge)
49. x2(x+2)-x(x+2)-12(x+2)
54. (u2-v2)2-w2(u+v)2
58. Factor x4+x2+1 by writing it as (x4+2x2+1)-x2, a difference of squares

After this section, one goes on to solve equations and solve problems using factoring.

In NY, Integrated Algebra I students do have know how to factor ax2+bx+c.

kcab said...

That set of examples from the reform text is dismaying. That surely isn't typical in Algebra I, is it? I've been complaining about the low expectations of my daughter's algebra course but I may have to revise them in light of this example.

lgm said...

From cpm's website, it looks like the Foundations book is a pre-algebra text meant for preparing students to go on to Algebra.

Is your district using this for a high school Algebra I course?

Katharine Beals said...

lgm--Thanks for pointing this out. My copy of "Foundations for Algebra Year 2" own is stamped "Hockinson High School." No indication anywhere in the front matter however, what grade level this book is intended for--a peculiarity that seems particular to Reform Math books.

On the CPM website, one does indeed find an Algebra 1 and an Algebra 2 book that come after this Foundations for Algebra, Year 2 book, as well as Geometry, Analysis and Calculus. There are 7 books in all. To fit them in you'd have to start in 6th grade, making Foundations for Algebra Year 2 a 7th grade book. On the other hand, Hockinson High School starts in 9th grade, so perhaps there's some tracking involved.

The book's front matter does state that it was written not just to prepare students for future algebra courses, but "to consolidate the core ideas of previous mathematics courses, so that it will serve students of varied mathematics backgrounds." That's about as unambiguous as they get.