Monday, August 18, 2014

Keep the Mystery

A few years ago, my husband told me he thought he saw a wolf running across our dirt road. At the time I said no, but maybe he was right. The creature he could have seen is a so-called coywolf, a coyote+wolf+dog that has allegedly established itself in the forests and neighborhoods of New England.

Yesterday, I was reading about the coywolf in the New York Times and was reminded of the incredible nuance, mystery, and ambiguity of the study of genetics and evolution. “Should You Fear the Pizzly Bear?” by Moises Velasquez-Manoff is an article about the effects of climate change on speciation.

“The dirty secret of biology is that the fundamental unit of science - i.e. species - in fact can’t be adequately defined,” said a Monterey Bay Aquarium scientist.

Even Charles Darwin saw the difficulty in the notion of species. From the Velasuez-Manoff article, “...[Darwin] was vague on how to define species, referring to ‘the vain search for the undiscovered and undiscoverable essence of the term.’”

As a child and then a teenager in school, science was presented as something that was unambiguous, and something that smart scientists in labs somewhere were doing with precision and finality. I was shocked when I began studying evolutionary biology in college. The taxonomic system of classification, a construct created by humans, prompted more questions than answers, its tree model seeming too simplistic to adequately explain the breadth and nuance of life on Earth.

Science became interesting to me at that point. I realized that everything wasn’t figured out already and people like me could join the conversation.

My learning about epigenetics in college caused me to question some of what I’d been taught about genes and heredity. Today, there is growing evidence and acceptance of the idea that traits can be inherited that are not written in one’s actual DNA. This directly contradicts what I was taught in high school biology.

As an educator who creates or curates units and lesson plans, often the temptation is to simplify things for students (and teachers). Another temptation is to rely on knowledge of a subject from my own (increasingly distant) school days. Do we present science in all its bizarre, unknowable complexity? How can teachers challenge even young students with unanswerable questions?

Friday, August 1, 2014

Summer Gems

Here are two articles you shouldn’t miss this summer, and they make a nice pair.

Why Do Americans Stink at Math?” by Elizabeth Green, July 23, New York Times, and “Most Math Problems Do Not Have a Unique Right Answer” by Keith Devlin, August 1, 2014, Devlin’s Angle.

I’ve come to the conclusion that our old ideas and stereotypes about math and education are hard to shake. It really means reading articles like these as they come out every month or so, in order to truly change our minds and our practice.

To whet your appetite, here are a few quotes:

One of the first math classes he observed gave him such a jolt that he assumed there must have been some kind of mistake. The class looked exactly like his own memories of school. “I thought, Well, that’s only this class,” Takahashi said. But the next class looked like the first, and so did the next and the one after that. The Americans might have invented the world’s best methods for teaching math to children, but it was difficult to find anyone actually using them. - from “Why Do Americans Stink at Math?”

Having earned my living as a mathematician for over 40 years, I can assure you that the belief is false. In addition to my university research, I have done mathematical work for the U. S. Intelligence Community, the U.S. Army, private defense contractors, and a number of for-profit companies. In not one of those projects was I paid to find "the right answer." No one thought for one moment that there could be such a thing. - from “Most Math Problems Do Not Have a Unique Right Answer”

The last summer gem is this youcubed video about using Number Talks in math class. How would you solve 18 x 5 mentally?