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Scientists take another look at how mathematics is learned and stumble upon some provocative findings

We have all at one point or another learned some variation of a mathematical formula involving trains and their timetables. For example: if a train leaves Boston for New York at 7am and travels at 60mph, will it beat a train leaving Providence at 6am traveling 45mph? The idea behind this kind of “story” problem is to engage a student with a real-world example to which they can relate. The thinking follows that that engagement will solidify the mathematical concept. It’s one of those conceits that has hung around for seemingly as long as math has been taught. And it may very well be completely wrong.

Researchers at Ohio State University have set out to determine whether or not these kinds of examples reinforce the math behind them. They conducted a study in which college students were taught a simple but unfamiliar system. Some learned it through abstract symbols and some learned it through concrete examples. They were then tested on what they were told was a children’s game, the rules of which used the same math as they were just taught.

Those who had learned the system through symbols did well in figuring out the game; those who had learned through examples did no better than if they were completely guessing. The experiment proved the researcher’s hypothesis that real-world examples tend to distract from the math and that students are likely to have difficulty transferring their knowledge to new problems without a purely abstract foundation. They are now turning their attention to younger learners to see just how pervasive the effect can be.

Via NY Times

Why a grizzly gets you shivering—but not global warming

In my Science Confirms the Obvious post today, I discussed the first psychological proof (so say the authors) that humans can indeed experience emotions without immediately knowing why. We do this, they say, because we evolved that way. True, scientists love that explanation, but here it’s quite intriguing.

Say you’re walking through the woods and encounter a grizzly bear. You see it and freeze that instant—even before your stomach drops with fear. “After all, you are likely to live longer if you immediately stop moving at the sight of a growling grizzly bear,� write researchers Kirsten Ruys and Diederik Stapel of The Netherlands’ Tilburg University, “and do not need full awareness for such a response to be instigated.� Given the flood of unexpected stimuli we face moment to moment, quick reactions make sense for survival.

You, that bear, and other animals experience emotions such as fear, anger, or disgust. But only a few species are aware of their emotions. This ability helps humans judge and respond to the behavior of others in order to navigate social situations and, ultimately, grease the wheels of complex society.

The study got me thinking about a talk given by Harvard psychologist Dan Gilbert at last October’s Pop!Tech conference. He expounded on why humans are so savvy at grasping immediate threats like grizzly bears or baseballs hurtling at our heads but suck at grasping abstract, slowly approaching ones like global warming. According to Gilbert, a “very large part� of our brains is devoted to dealing with immediate threats, but a “very small part� is concerned about planning for the future.

Humans, apparently, are still in the early stages of evolving extended response mechanisms. But it seems likely that by the time we portion more of our brain to long-term dangers, there will be few grizzly bears around to worry about, and a whole lotta global warming.

MIT professor awarded for his innovative, human-powered irrigation pump

The Super MoneyMaker Pump—yes, that’s the real name—sucks up water from sources as many as 30 feet below the ground, can spray it up to 40 feet high, and can even push it through 1,000 feet of hose to cover a larger section of land. In all, the pump can irrigate two acres of land, and costs only around $100.

MIT professor Martin Fisher and his team at KickStart, a nonprofit, invented the pump for small-scale farmers. Since it’s human-powered and easy to use, it allows them to irrigate crops all year round, instead of just waiting for the rainy season.

And no, it’s not really about money-making in the American sense. It’s designed to help farmers start small businesses. At this point, the pump’s users are generating an average of $1,000 extra profit each year. A smaller, less expensive version is helping farmers clear $650 extra per year. The work is a reminder that great new technology doesn’t always have a chip at its core.

Via MIT