PROVING APPROXIMATION WITH PRECISION

The New York Times recently (Sep 16) published an interesting article – “Gut Instinct’s surprising role in Math”. The article shares an interesting view about human mind’s ability to instinctively solve math problems. It shows how the mind is wired to perform some seemingly complex math tasks with ease.

To quote it from the article “Whenever we choose a shorter grocery line over a longer one, or a bustling restaurant over an unpopular one, we rally our approximate number system, an ancient and intuitive sense that we are born with and that we share with many other animals. Rats, pigeons, monkeys, babies — all can tell more from fewer, abundant from stingy. An approximate number sense is essential to brute survival: how else can a bird find the best patch of berries, or two baboons know better than to pick a fight with a gang of six?” It’s interesting to know that not only the human brain works this way but even baboons’ and rodents’ work in the same manner.

In fact, research has shown that new born babies if found to be good at deciphering approximations with ease, will carry on the same trait when they grow up and have to deal with abstruse mathematical problems. NYT states: “One research team has found that how readily people rally their approximate number sense is linked over time to success in even the most advanced and abstruse mathematics courses. Other scientists have shown that preschool children are remarkably good at approximating the impact of adding to or subtracting from large groups of items but are poor at translating the approximate into the specific.” In fact, it goes further and suggests that Math teachers should emphasize on the power of approximation early on in the child’s education so he can hone this natural skills to an advantage. To quote “Taken together, the new research suggests that math teachers might do well to emphasize the power of the ballpark figure, to focus less on arithmetic precision and more on general reckoning.”

At LazyMaths.com, we precisely try to encourage our students to leverage these skills of approximation. We have found that with practice, the line between approximation and precision can be diluted if not fully erased. In the section of Don’t Solve, LazyMaths offers a large number of examples of a variety of Math problems attempted using the techniques of approximation.

If you are interested in checking out how good your natural approximation skills are, here’s a quick test.
http://www.nytimes.com/interactive/2008/09/15/science/20080915_NUMBER_SENSE_GRAPHIC.html

For more interesting articles visit: www.lazymaths.com/zlog