Quotations XXIV: Probability

Posted on by Denise Gaskins


[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

Free Online Math for Middle School and Up

Posted on by Denise Gaskins

alcumus

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.

— AoPS Alcumus information page

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

Continue reading Free Online Math for Middle School and Up

Math Club: Counting 101

Posted on by Denise Gaskins

[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:

Continue reading Math Club: Counting 101

Reading to Learn Math

Posted on by Denise Gaskins

[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?

Continue reading Reading to Learn Math

Puzzle: Random Blocks

Posted on by Denise Gaskins

Red block puzzle

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?

Continue reading Puzzle: Random Blocks

Confession: I Am Not Good at Math

Posted on by Denise Gaskins

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