Well, what the teacher should have said is, “That’s great you can do the work on a calculator—it’s a very important instrument—but you also need to develop an independent sense of number, or else those digits will never mean anything to you and you won’t be able to critique their use or effectively check whether you’ve made a mistake.”
Teachers: how many times have you had students submit an answer to a problem, say, on calculating the volume of a box, but their answer is negative? Or larger than the Earth?
Students: as above, the calculator is an important tool. But it’s just a tool. Your fourth grade teacher had some sense. Even when it comes to graphing, there are some things best left to computers, and some things for which nothing can replace the visceral sense of drawing by hand.
Yeah. About that.