Forty years ago an Indiana electronics company brought a product to market that did more to change American K-12 education than almost anything else. The company, Bowmar Instruments, began selling the first handheld pocket calculator for a whopping $240! By 1976, the cost of the cheapest four-function device had dropped to a few dollars and calculators were available to children in virtually every home. And as a result, the way children learn and do math in the U.S. was forever changed.

Just the other day I was helping my eighth grade son with his algebra homework. He was solving a fairly complicated equation and got down to the last step 7x=42. He whipped out his calculator. I said, “Will, you know this. 7 times what number is 42?” He replied, “Uh, I really don’t know. Why does it matter? I’ll just use my calculator.” He proceeded to punch the numbers into his T1 84.

My son is a very good student, but his number sense is lacking. Like many students who have used calculators in class from day one, he does not have an intuitive sense of the relationship between numbers. Want to know if your child does? Just ask him or her to figure the tip on the check next time you’re out for dinner. Kids with number sense can mentally compute 10% and then add half of that to come up with 15% or double it for 20% and they can do it quickly.

There is a time and place for calculators, but their use should be coupled with instruction in critical thinking and number sense. Sometimes kids will arrive at an incorrect answer to a math problem because they put the wrong numbers into their calculator. When it spits out a wild answer, they have no idea it makes absolutely no sense. Far too often, they don’t analyze the answer and think to themselves, “Does this make sense?” Why? Because they have complete faith in their all-knowing calculator. Gadgets only get kids so far. In the end, they must have number sense.

Recently, message boards and blogs serving high school and college math and science teachers have been brimming with articles about how to use WolframAlpha, a free web-based service that goes far beyond simple searches by providing answers to complicated questions in math and science. Go to wolframalpha.com and type in 3x^2+4=31 and the solutions x=3, x=-3 come back. Type in “the number of molecules in 1.2 pounds of sugar” and the result “9.58 X 1024“ returns.

Wolfram Alpha now is offering apps for the IPhone at the iStore and on the Android market for $1.99. Nearly 100,000 paid copies have been downloaded on the Android Market alone. I worry that many will use Wolfram to avoid the pain of learning. “Best $1.99 I’ve ever spent. It helps me endure math class. I owe these people my first born child,” one student recently wrote about the Wolfram app in a user review on the Android Market.

I’m all for it if students are FIRST taught how to solve problems without the crutch of the latest app. Technology makes math easier, but it shouldn’t replace good old fashioned mental math and number sense.