A graphing calculator, whatever that is, is not mandatory, according to our son's new 9th-grade math teacher. But kids who've gone through 9th-grade math told us it sure helps. In fact, they urged my son to buy one in the summer so he could learn how to use it in time for school. We bought it. It cost $129 on sale.

This is not going to be an old fuddy-duddy rant about how when I was a kid candy bars cost 5 cents (they didn't) and how we didn't have calculators (we did). Calculators then didn't make graphs, construct geometric figures, and have the periodic table stored on them, however.

Forking over for this powerful electronic tool made me realize that my kids, now both young teens, are part of a fairly new, third wave of education. The first wave involved teaching children how to do things manually - how to hunt, how to skin an animal, how to make a fire. This wave lasted for eons. Then the second wave arrived: a single century when knowledge held sway. As a result of the Industrial Revolution, key skills included knowing how to run factories, establish supply chains, and manage capital investments.

Today we don't really have to know how to make anything, thanks to dirt-cheap commodities, and we don't consider ourselves responsible for even basic knowledge. If you need to know a specific skill or bit of data, you can find it easily using the right tool. This tool is typically a computer of some sort - a laptop or Blackberry or graphing calculator or GPS. If all else fails, the ubiquity of cell phones ensures that you can call someone who might have the info.

So though properly educating a child of the third wave may still involve drilling them on the multiplication tables and quizzing them on world capitals, what they really need is killer apps and the devices that run them - search engines, Google Earth, GPS, fancy calculators, and other things I don't know about yet (and probably can't afford).

Growing up today is like fast-forwarding through all three education waves. As a toddler, you're a manual laborer, spending your days stacking blocks, poking sticks into the ground, blowing bubbles. When you begin to talk you move into the knowledge era, when every new discovery raises a question. Why is the sky blue, how do turtles scratch their backs, will there be a volcano here?

It doesn't take long, however, before a modern child's questions outstrip a parent's desire (and ability) to answer them. Enter the third wave. When my kids reached this point, I led their curious minds right to the web. Anything to stanch the flow of difficult questions.

The downside: children assume there will always be a computer around that will provide the answers. Kids are fact-hungry anteaters, probing their long digital tongues into computers to find data, devour the tiny morsels, and move on. But what if you can't afford all these devices? The only thing worse than being a fact-hungry anteater is not being able to be one. As devices multiply and prices don't come down quick enough, the digital divide is growing. Though our school system offers electronics to kids who don't own them, it can be a real hassle.

But that's not the only reason we bought the graphing calculator. A third-wave side-effect is that we've become driven by the fear that we won't measure up. That somehow, by missing this computer or that device, our kid will be left behind. And that is one expensive concern.

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