Rough calculations
Time for some quick arithmetic: Is 3600 x 4.4 x 104 x 32 larger or smaller than 3 x 109? Finding the right answer, says Sanjoy Mahajan, associate director for teaching initiatives at MIT’s Teaching and Learning Laboratory, does not require crafting a long, tedious calculation. Instead, the key to solving this problem — and many others — lies in having informal tools on hand that let us attack the problem. Though the result may not be perfectly precise, he believes, intuitive mathematical reasoning is often sufficient for our needs. “That’s not to say exact answers aren’t useful,” says Mahajan, “but if looking for them is your only approach, you may never get any answer at all. Sometimes it’s better to start with something rough.”So while conventional math teaching is often a highly formal affair, with an emphasis on definitions, theorems, and proofs, Mahajan believes we should learn practical math...