Thursday, January 20, 2011

Math problems of the week: 1990's vs. CPM algebra

I. The last two problems in the "Simple Equations" chapter of Wentworth's New School Algebra (published in 1898), p. 32:

A man bought 10 yards of calico and 20 yards of cloth for $30.60. The cloth cost as many quarters per yard as the calico cost cents per yard. Find the price of each per yard.


A man has a certain number of dollars, half-dollars, and quarters. The number of quarters is twice the number of half-dollars and four times the number of dollars. If he has $15, how many coins of each kind has he?

II. The last two problems in the "The Math Club: Solving Equations" chapter of College Preparatory Mathematics Foundations for Algebra: Year 2, pp. 202-203:

Tom is buying new computers for his writing team. He can buy the first five at a dealer discount. The other fifteen will be purchased for an extra $50 each. The cost of the computers comes to a grand total of $11,750. Find out how much each of the discounted computers cost. A Guess and Check table might be useful. Write an equation.


Below is a list of Tool Kit entries from this chapter.

MC-8 Equations
MC-119 Mixed Numbers

Review all the entries and read the notes you made in your Tool Kit. Make a list of any questions, terms, or notes you do not understand. Ask your partner or study team members for help. If anything is still unclear, ask your teacher.

III. Extra Credit

Approximately what percentage of CPM students will be able to solve the Wentworth problems, assuming they are armed with Guess and Check tables and Tool Kits?

Approximately what percentage of CPM students would have to list the Wentworth problems under things they "do not understand"? Approximately what percentage would find that the solutions are "still unclear" after talking to their "partner or study team members" and therefore have to ask their teacher?


Barry Garelick said...

The problems in Wentworth are viewed by today's math reformers as not being relevant, who cares about coins, etc. Never mind that such problems provide much better preparation for solving many kinds of math problems than the CPM and other texts.

Deirdre Mundy said...

Why on earth would an Algebra 2 student need a "guess and check" table to set up a simple equation?

If it was REQUIRED the simplest thing to do would be to solve the problem, and then make several FAKE guesses that culminated in the correct one......(Like the old trick of writing an outline for the report AFTER you've wriiten it...) Sigh.

CLEARLY the Wentworth problem isn't relevant--- noone sells Calico for 6 cents a yard!

Anonymous said...

Not that I am a big CPM fan (I'm not), but the FFA2 book is the 2nd year of Pre-Algebra, and contains what many traditional Algebra 1 books have in their first three chapters (integers, solving 2- and 3-step equations, graphing from an x-y table) plus some basic Geometry. The FFA2 book is reasonable in comparison to the CPM Algebra or CPM Algebra Connections. Go there if you want to find something truly worthy of criticism.

The problem with CPM is that they don't teach to mastery, they expect it to come over time. For many, it doesn't. So part of Algebra 1 have to be remediated in Geometry and Algebra 2, and parts of Algebra 2 have to be remediated in Pre-Calc/Trig.

In the hands of a teacher who is not a constructivist groupie, and one who will supplement, the books can be salvaged. But if your child's teacher is a true-believer in the "CPM way", your kid loses in the long run.

Katharine Beals said...

Anonymous, thanks for your feedback. Another thing that complicates these comparisons is that, to my knowledge, "pre-algebra" courses--particularly of the two-year-long variety--are a relatively recent development. As far as I can tell, Wentworth's algebra assumes no background in "pre-algebra", but, rather, comes right after arithmetic.