Thursday, September 23, 2010

Math problems of the week: Traditional algebra vs. CPM Algebra

I. From the first and last assignments of the first chapter ("Definitions and Notation") of Wentworth's New School Algebra text (published in 1898), p. 9 and p. 14:

If a = 1, b = 2, c = 3, d = 4, x = 5, y = 6, z = 0, find the numerical value of:

1. 15x
2. 3ab
3. 7by
4. 5bd
5. 9y2
...

Perform the indicated operations, and find the numerical value of each expression, if a = 8, b = 4, c = 3:

1. (b + c) ÷ c
2. (a + b) ÷ b
...
10. (b2 - c2) ÷ b
11. (a2 - c2) ÷ c2
12. (a2 - b2) ÷ b2

II. The first and last assignments of the first chapter ("Getting Started: Working in Teams") of the College Preparatory Mathematics Algebra text, p. 4 and p. 17:

With your team, find at least three of the main ideas the authors wanted you to know about this course. You can find these ideas in the "Welcome Note" you just read. Make a list of them. Be sure that you put a copy in your algebra notebook.

Reflect on the study team activities you experienced the last few days. Which activities were your favorites? Why? What about your team makes you feel comfortable? What makes an effective team member?

III. Extra Credit:

Which problems better prepare students for 21st century mathematics?

4 comments:

Barry Garelick said...

The quote from CPM is downright inspirational. It's hard to find anything that insults not only students' intelligence but teachers and parents alike.

This reminds me in a strange sort of way, of the email dialogue I had with Sherry Fraser, one of the movers and shakers behind IMP, a math program developed at San Francisco State U via a grant from NSF, that is an integrated math program. She made the following statement at a meeting of the National Math Advisory Panel in November, 2006:

"How many of you remember your high school algebra? Close your eyes and imagine your algebra class. Do you see students sitting in rows, listening to a teacher at the front of the room, writing on the chalkboard and demonstrating
how to solve problems? Do you remember how boring and mindless it was? Research has shown this type of instruction to be largely ineffective. Too many mathematics classes have not prepared students to use mathematics, to be real
problem-solvers, both in the math classroom and beyond as critical analyzers of their world."


I wrote her an email regarding that quote and asked her to
provide me with the cites of the research that she claimed shows this type of instruction to be ineffective since I was writing an article on the type of math instruction that prevailed in teh 40's through the 60's. She replied as follows:

"I'm a firm believer in people doing their own research. I'm sure you won't have any trouble finding a number of sources to confirm this. I certainly didn't. I'd be interested in reading your paper when you've completed it. I'm familiar with math instruction in the 1950's and 60's but am now wondering whether the world war during the 40's had any impact on math instruction in that decade."

The paper showed among other things that from the 40's to the mid 60's ITBS math scores in the state of Iowa during that period for grades K-8 increased substantially. By the mid-60's a decline presented itself that continued on into the 80's as it did in other states. There are some remarkable coincidences that go along with the decline of test scores. Among them was the increase in student-centered classrooms and other educational fads.

Mrs. H said...

I'm a high school math teacher in Texas. The CPM assignment made me laugh out loud. Who dreams crap like this up?? What in the world do "feelings" have to do with learning math????

If I only learned the things I felt like learning, I'd never go to another inservice as long as I lived.

Barry Garelick said...

This whole thing brings to mind a quote from Sherry Fraser, co-director of a high school math text/curricula called IMP, (developed through grants from the NSF in the early 90's to San Francisco State University, totaling $11.6 million). IMP is an integrated math program for high school, probably comparable in idiocy to CPM. Fraser made a public statement on Nov. 6, 2006 before the National Mathematics Advisory Panel” a Presidential appointed panel charged with drafting recommendations on how best to prepare students for algebra.

How many of you remember your high school algebra? Close your eyes and imagine your algebra class. Do you see students sitting in rows, listening to a teacher at the front of the room, writing on the chalkboard and demonstrating how to solve problems? Do you remember how boring and mindless it was? Research has shown this type of instruction to be largely ineffective.

I wrote to Ms Fraser and told her I was writing an article on math instruction that prevailed in the 40's through the 60's. I asked her to provide the cites of the research that she claimed shows the type of instruction she described to be ineffective.

Her reply:
I'm a firm believer in people doing their own research. I'm sure you won't have any trouble finding a number of sources to confirm this. I certainly didn't. I'd be interested in reading your paper when you've completed it. I'm familiar with math instruction in the 1950's and 60's but am now wondering whether the world war during the 40's had any impact on math instruction in that decade.

I followed her advice and did my own research. I wrote it up in a three part article, which unfortunately has become a bit corrupted due to technical glitches but it is still mostly readable. Comments from readers are equally informative.

The three parts are here, here, and here.

Anonymous said...

The sad thing is our taxes paid for someone to dream this crap up.