*[Photo by Ella’s Dad.]*

Throughout history, around the world, people in every culture have enjoyed playing games of chance. Strangely, mathematicians did not begin to study chance and probability until the 17th century.

Skip to content
#
Probability

## Introduction to Probability

## Quotable: Politics

## Free Online Math for Middle School and Up

## Christmas Puzzle: The Grinch Bug

## Math Club: Counting 101

## Math Contest Tip Sheets

## Reading to Learn Math

## Puzzle: Random Blocks

## Confession: I Am Not Good at Math

## Math Quotes V: A Man Is Like a Fraction…

*[Photo by Ella’s Dad.]*

Throughout history, around the world, people in every culture have enjoyed playing games of chance. Strangely, mathematicians did not begin to study chance and probability until the 17th century.

“Let’s give the governor a break,” says Williams College mathematician Edward Burger. “If nothing else, he’s encouraging math education.”

— Carl Bialik

Coincidental Obscenity Deemed Extremely Dubious

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

The Art of Problem Solving people recently announced their new Alcumus program, which provides online lessons on assorted math topics, including probability and combinatorics, which most math textbooks do not cover well, if at all.

Update October 2011:Alcumus currently complements our Introduction to Algebra, Introduction to Counting & Probability, Introduction to Number Theory, and Prealgebra textbooks, as well as our Algebra 1, Algebra 2, Introduction to Counting & Probability, Introduction to Number Theory, and Prealgebra 1 online courses. We expect to continue to expand topics in Alcumus.

I am signing up all my MathCounts students. If you’re a homeschooler, we would love to have you join us!

*[Photo by theogeo.]*

Christmas afternoon is a slow time at our house. How shall we while away the hours until the turkey is done? With math, of course!

Check out this puzzle from Blinkdagger.

*[Fature photo above by ThunderChild tm.]*

The last couple of weeks, in Math Club, we’ve been learning to count. My new set of MathCounts students have never heard of combinatorics, so we started at the very beginning:

- Counting and Probability I by Keone Hon
- Counting and Probability by Jason Batterson

Most of our math contest preparation consists of working lots and lots of old test problems. Occasionally, however, I put together a tip sheet summarizing a topic that my students have trouble remembering.

*[Photo by Betsssssy.]*

Do you ever take your kids’ math tests? It helps me remember what it is like to be a student. I push myself to work quickly, trying to finish in about 1/3 the allotted time, to mimic the pressure students feel. And whenever I do this, I find myself prone to the same stupid mistakes that students make.

Even teachers are human.

In this case, it was a multi-step word problem, a barrage of information to stumble through. In the middle of it all sat this statement:

…and there were 3/4 as many dragons as gryphons…

My eyes saw the words, but my mind heard it this way:

…and 3/4 of them were dragons…

What do you think — did I get the answer right? Of course not! Every little word in a math problem is important, and misreading even the smallest word can lead a student astray. My mental glitch encompassed several words, and my final tally of mythological creatures was correspondingly screwy.

But here is the more important question: *Can you explain the difference between these two statements?*

In the first section of George Lenchner’s Creative Problem Solving in School Mathematics, right after his obligatory obeisance to George Polya (see the third quote here), Lechner poses this problem. If you have seen it before, be patient — his point was much more than simply counting blocks.

A wooden cube that measures 3 cm along each edge is painted red. The painted cube is then cut into 1-cm cubes as shown above. How many of the 1-cm cubes do not have red paint on any face?

And then he challenges us as teachers:

Do you have any ideas for extending the problem?

If so, then jot them down.

This is strategically placed at the end of a right-hand page, and I was able to resist turning to read on. I came up with a list of 15 other questions that could have been asked — some of which will be used in future Alexandria Jones stories. Lechner wrote only seven elementary-level problems, and yet his list had at least two questions that I had not considered. How many can you come up with?

I want to tell you a story. Everyone likes a story, right? But at the heart of my story lies a confession that I am afraid will shock many readers. People assume that because I teach math, blog about math, give advice about math on internet forums, and present workshops about teaching math — because I do all this, I must be good at math.

Apply logic to that statement. The conclusion simply isn’t valid. …

**Update:** This post has moved.

Click here to read the new, expanded version

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

[Rescued from my old blog.]

The blackboard quotes for my math class have been a bit more philosophical the last few weeks:

A good problem should be more than a mere exercise; it should be challenging and not too easily solved by the student, and it should require some “dreaming” time.

—Howard Eves

An Introduction to the History of Mathematics