I’m spending a lot of time these days thinking about multiplication. Keith Devlin, a Stanford mathematician, author, and NPR Math Guy, has created a swirling controversy through his Devlin’s Angle column on the Mathematical Association of America website (http://www.maa.org/devlin/devangle.html). Last summer Devlin sparked a debate by exhorting teachers to stop defining multiplication as repeated addition. His follow-up articles this summer fanned the flames and ignited a raging firestorm in the blogosphere. 4x3 can readily be rewritten by the repeated addition of 4+4+4. But what does repeated addition look like for, say, 3/4 * 5/8? It’s a challenge to articulate a definition that is both accessible to kids in elementary school and still true as the numbers become more complex.
I’ve enjoyed reading the unfolding arguments. It’s a healthy and important discussion, because determining what we should teach is essential before we decide how to teach it. Designing technology to more effectively instruct and engage students in a misconception or limited explanation shouldn’t be the plan. I fear that too much of the “innovation” and promise of technology doesn’t go deep enough into the roots of why our kids aren’t succeeding. It’s far too easy to take the existing curricular canon and put it into a glossy technological wrapper and be satisfied that kids “like” using it. We need to push ourselves further.
So, the search for a new way to define multiplication continues. When we have it, we can devise ways for technology to help visualize it, explore it, practice it at appropriate levels, and connect it to the content that came before and follows. It’s rigorous work, but if we get it right we can truly make a lasting and meaningful difference with kids’ understanding. It’s worth the extra effort.