Speed...For Good or For Bad
On e-bay recently, someone named Cliff Petrak has been selling his book Don't Slow Me Down With That Calculator. The cost is $15 plus postage.
Based on his 40-years of experience as a high school mathematics teacher, Petrak claims that he can share a "multitude of little-known, super-shortcut techniques involving addition, subtraction, fractions, squaring and multiplication." Furthermore, students armed with this new knowledge (rather than a calculator) will leave their "computer-dependent friends in the dust."
The thing that bothers me about this book and its title is that mathematics is not a competition and the situation is not either-or! We should help students develop the necessary skills to do mental mathematics, pencil-and-paper mathematics, and calculator-based mathematics...which requires that we engage them to situations where they need to choose which tool--mind, pencil, or calculator--is the appropriate one to use (or combinations thereof).
And "speed" is not as important of a factor as most people (including teachers) think it is. Above the element of speed, I stress creativity, reflectivity, openness, deep understanding, perseverance, and willingness to look back.