Math Is Cool, Again and Still

Nancy Staples contributes a second guest entry to Math Hub.

You've probably seen the YouTube video of the mind-boggling "mathemagician" Arthur Benjamin, professor of math at Harvey Mudd College. It's an old video, but getting new play now that the gentleman has written a book. To the extent that he reveals his secret or that any mortal could actually apply it, it relies on storing and retrieving each number as a word, like "cookie" or "fission".

Of course, what Benjamin does isn't really "magic", and we don't want kids seeing math as something magical. Certainly, a robust working memory in combination with a warehouse of accessible stored information plays an important role. Most important, though, is a keen understanding of how numbers work, ways they can be composed, decomposed, and rearranged to make complex computations much simpler. Once you learn the system, mathematical tricks don't seem so magical. That's where we want our kids to be. If Benjamin's video helps motivate kids to learn to unlock that system, I'll take it.

By the way, if you want to talk about getting into some big numbers, Benjamin later turned up on Stephen Colbert's show, and that's a nice seven-digit audience to reach with a positive message about math.

 

Photo credit: http://www.math.hmc.edu/~benjamin/mathemagics.htm

Got Rocks in Your Head? Maybe You Should

Nancy Staples, a friend and former employee of Tom Snyder Productions, contributes a guest entry to Math Hub.

Got rocks in your head? Maybe you should. At least when it comes to math. So says Steven Strogatz, opining in last week's New York Times. Strogatz, professor of applied math at Cornell, says that each and every one of us would fare better with math (and have more fun) if we visualized numbers as objects - rocks, for example. He then walks us through a rock-strewn depiction of the cool properties of even, odd, and prime numbers.

The fact that math goes over better when made "concrete" is not news to math educators. But I loved the fact that this article appeared in the New York Times, the Grey Lady herself, rather than in an educational journal. Even more than that, I loved that it came complete with little drawings, so you could follow along. And clearly it struck a chord - it was on the NYT's most-emailed list for several days now. This means that more than a few people have a secret desire to play with numbers, and to get their friends to play, too.

So go ahead, fill your students' heads with rocks. Let them play with numbers and mess around with them in all sorts of ways. The numbers are always up for the game.

Cognitive science meets math fluency

 

Here at the Math Hub, we talk quite a bit about developing math facts and fraction fluency, but a recent Boston Globe article reminded us that cognitive fluency is an adaptive shortcut for so many other life facets.

Cognitive fluency is simply a measure of how easy it is to think about something, and it turns out that people prefer things that are easy to think about to those that are hard. On the face of it, it's a rather intuitive idea. But psychologists are only beginning to uncover the surprising extent to which fluency guides our thinking, and in situations where we have no idea it is at work. 

Research shows that companies with easy-to-pronounce names (Apple, anyone?) fair better in the stock market. When given two identical recipes, folks rate the one with a clearer font as being easier than its less legible counterpart. And familiarity, which eases our mental processing effort, is also often preferred:

Psychologists have identified what they call the "beauty-in-averageness" effect - when asked to identify the most attractive example of something, people tend to choose the most prototypical option. For example, when asked to identify the most appealing of a group of human faces, people choose the one that is a composite of all the others. Some psychologists suggest that much of what we perceive as beauty is just the fact that the most prototypical faces... are the easiest to process, because they share the most with all the other faces... that we've seen and stored in our perceptual inventory.

We’ve known some of this for a while, but it’s a good reminder. For math fluency products such as our very own FASTT Math and Fraction Nation, this natural affinity for fluency is happy news!

Graphic credit: boston.com

"Is It True That Some People Just Can't Do Math?"

Cognitive scientist Daniel Willingham tackled that question in the most recent issue of American Educator. Drawing on research with populations as young as infants, he shows why scientists believe that humans are born to understand numbers. He explains the importance of committing basic math facts to long-term memory to free working memory for more involved procedures. And taking a bit of a controversial twist, he explains how manipulatives may impede learning. However, he gives a thumbs-up to math analogies done right and shares four research-based principles that have been shown to make analogies especially effective in cultivating conceptual knowledge.

Download and read the full article online. 

What are your thoughts on what the research says about teaching conceptual knowledge of math?

Adding humor (and Red Sox boxers!) to math instruction

A comedy club performer turned math teacher just won a huge $200,000+ teaching award. My favorite part of a feature article on the winner, Edward Burger, was insight on how the Williams College professor combined humor and math instruction:

“In a creative approach to teaching, Burger sometimes uses humor to excite his students and is not afraid of taking risks. During a Parents' Weekend lecture early in his career at Williams, Burger posed a provocative conundrum from topology (the mathematical study that generalizes geometry — where shapes can be stretched, bent, and twisted, but not cut). He asked a packed auditorium of students, parents and colleagues: "If your ankles were tied together with a rope, is it possible to remove your pants and put them back on without cutting that rope?

He then proceeded to jump on a table and demonstrated the topological feat — wearing, of course, Williams boxer shorts tastefully adorned with purple cows. Years later at an address at the Boston Public Library, "I was donned in Red Sox boxers," he said.”

Any guesses on how he managed this feat? Please enlighten us by commenting below!

Of further interest, Burger recently worked with NBC on a “Mathletes” segment about the math behind the Olympic games, according to the article. “The Science of the Olympic Winter Games,” including “Mathletes,” can be accessed online.

Photo credit: http://www.williams.edu/go/math/eburger/