We have an interesting discussion going in the comments on The Problem with Manipulatives. I mentioned a vague memory of a quotation. Now I’ve found the source.
Originally published in 1970:
The continuing hullabaloo about the “new math” has given many a parent a false impression. What was formerly a dull way of teaching mathematics by rote, so goes the myth, has suddenly been replaced by a marvelous new technique that is achieving miraculous results throughout the nation’s public schools.
I wish it were true — even if only to the extent implied by entertainer (and math teacher) Tom Lehrer in his delightfully whimsical recording on “The New Math”:
“In the new approach, as you know, the important thing is to understand what you’re doing, rather than to get the right answer.”
… Indeed, there is something to be said for the old math when taught by a poorly trained teacher. He can, at least, get across the fundamental rules of calculation without too much confusion. The same teacher trying to teach new math is apt to get across nothing at all…
— Martin Gardner
Foreword to Harold Jacobs’ Mathematics: A Human Endeavor
Unfortunately, I can’t embed the Tom Lehrer song Gardner mentioned, due to copyright restrictions, but here’s a link to YouTube:
You may have seen this video making the edu-blog rounds:
Continue reading The Problem with Manipulatives
Recognize that every math program, whether more traditionally skill-based or reform-oriented (more problem-solving, projects, less drill) has its merits and its weaknesses. Whether you believe there is too much emphasis on basic facts (less likely!), or not enough, you can supplement with the myriad of resources on the web.
— David Marain, MathNotations
Odds and Evens Week of 12-1-10
Click through to the original post for a counting puzzle, plenty of advice on helping with your child’s math homework, useful math links, and a couple of “cute 3-year-old” stories.
And remember that one of the best ways to supplement any math program is by playing games.
After a hectic couple of weeks, I finally found a little time to sit at the computer and browse — and boy, was I amazed to see what I had missed! If you have not yet read Dave‘s interview with Prof. Lynn Arthur Steen about the state of math education reform, click over and check it out: Part I here, and Part II here.
According to the intro, Prof. Steen “has been a driving force for the reform of school mathematics for many years and was on the development team that produced NCTM’s Curriculum and Evaluation Standards for School Mathematics. For the last few years, he has been involved in Achieve’s commitment to developing world-class mathematics standards for K-8 and ADP’s similar commitment to secondary mathematics.” He has some interesting things to say, although many of his statements are open to various interpretations, and at times he seems determined to provoke a hot-headed response. For instance:
Continue reading While I Was Distracted…
Well, the new year has come, and it’s time to start gathering up receipts and thinking about tax forms.
Would you like to know that our tax dollars are doing good in the world? The National Science Foundation has spent many millions developing and promoting “reform” math textbooks, with encouragement from the U.S. Department of Education. Surely our public schools will now rise out of the doldrums and surge ahead in mathematical achievement, right?
Try for yourself this problem from one of the more famous/infamous of the reform math textbooks:
Can you find the slope and y-intercept of this equation?
10 = x – 2.5
And then check out
this editorial[editorial has disappeared] at edspresso.com. You’ll be amazed at the answer!
Update: Checking on back-links, I discovered that this page had gone AWOL, so I’ll give you the “answer” from the teacher’s manual. The “slope” is 1 and the “y-intercept” is -2.5, according to Connected Math. Unfortunately, this equation actually describes a vertical line (undefined slope) at x=12.5 (never touches the y-axis).
Doesn’t bode well for “CMP helps students and teachers develop understanding of important mathematical concepts…”