Still Relevant After All These Years

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 What was formerly a dull way of teaching mathematics by rote, so goes the myth, has suddenly been replaced by a marvelous new technique that is achieving miraculous results throughout the nation’s public schools.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:

Quotable: Math is a Game

I don’t love math nearly as much as I pretend I do when I’m teaching it or blogging about it or trying to enthuse my kids.

I just believe — ever since an eye-opening university-level Mathematics in Perspective course — that math is taught VERY badly, bumbled and fumbled and as a result we have this societal fear of what is, essentially, a great big GAME.

Jennifer in MamaLand
Spotted (myself!) around the Web…

See related post — Quotations XXV: Math is a Game

Quotable: What to Do When You’re Stuck

When a kid is feeling bad about being stuck with a problem, or just very anxious, I sometimes ask him to make as many mistakes as he can, and as outrageous as he can. Laughter happens (which is valuable by itself, and not only for the mood — deep breathing brings oxygen to the brain). Then the kid starts making mistakes. In the process, features of the problem become much clearer, and in many cases a way to a solution presents itself.

Maria Droujkova
Natural Math discussion of math club activities

Does It Work?

While I was collecting entries for the Math Teachers at Play #35 blog carnival, I ran across this post by Dave Lanovaz:

Quotable: Math Programs

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.

Quotations XXV: Math is a Game

Mathematics is a game played according to certain simple rules with meaningless marks on paper.

David Hilbert
quoted by Nicholas Rose, Mathematical Maxims and Minims

It’s like asking why Beethoven’s Ninth symphony is beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.

Paul Erdös

Continue reading Quotations XXV: Math is a Game

Quotable: Bad at Math

There’s a tendency for adults to label the math that they can do (such as identifying patterns, choosing between competing offers in a supermarket, and challenging statistics published by the government) as “common sense” and labeling everything they can’t do as “math” — so that being bad at math becomes a self-fulfilling prophecy.

Rob Eastaway, Mike Askew
Old Dogs, New Math: Homework Help for Puzzled Parents

Still a couple of slots left in Sol’s book giveaway. I’ll be hosting a giveaway soon, too — so watch this spot!

How to Start an Argument: The Monty Hall Problem


[Photo by MontyPython.]

You can get a good argument going in almost any group of people with the infamous Monty Hall problem:

Imagine you are on a TV game show, and the host lets you choose between three closed doors. One of the doors hides a fancy sports car, and if you pick that door, you win the car.

You pick door #1.

The host opens door #3 to reveal a goat. Then he gives you a chance to switch your door for the unopened door #2.

Should you switch?

What if you say you’re going to switch, and then the host offers to give you $5,000 instead of whatever is behind door #2?

Try the game for yourself at the Stay or Switch website.

Continue reading How to Start an Argument: The Monty Hall Problem

Math History Tidbits: The Battling Bernoullis

July 27th is Alex’s birthday. She shares it with Johann Bernoulli, an irascible mathematician from the late 17th century. This coincidence intrigued her enough that she wrote a research paper on Johann and his mathematical brother, titled “Jeering Jacob and Jealous Johann.”

Of course, to make the alliteration work, she had to mispronounce Johann’s name — but she figured he kinda deserved that. Read the historical tidbits below to find out why one writer said the Bernoulli brothers were “the kind of people who give arrogance a bad name.”*

Continue reading Math History Tidbits: The Battling Bernoullis

Quotations XXIV: Probability


[Photo by Micah Sittig.]

I used to fill the margins of my math newsletter with quotations and tidbits of math history. Here are some quotes from the July/August 1999 issue on probability, along with a few others I’ve stumbled on while browsing the internet.

No knowledge of probabilities helps us to know what conclusions are true. There is no direct relation between the truth of a proposition and its probability.

John Maynard Keynes

The 50-50-90 rule: Anytime you have a 50-50 chance of getting something right, there’s a 90% probability you’ll get it wrong.

Andy Rooney

Continue reading Quotations XXIV: Probability