This article makes the point that the emphasis on getting students to “understand” by using alternatives to standard algorithms is a subterfuge. The purpose, the article contends, is to make students look smarter than they are. They reason as follows:
The problem is this: “number bonds” is a counterfeit of the way kids who are genuinely good at math act by the time they get into elementary. While the other kids are counting on their fingers, kids who’ve been playing with numbers in their heads since they were two or three have figured out all the relationships and will take numbers apart to make it easier to solve. Not something stupid like seven plus seven, of course. More something like 115 + 115.
Having figured out that number-gifted children will do this as 100+100=200, 15+15=30, so 115+115= 230. This is quite nifty for a first-grader, but the left thinks it can skip all the work getting there. If they just teach perfectly normal, average children to think in terms of taking numbers apart, voila! Everyone will be a math genius!
I don’t know that it’s “the left” who thinks this way–I have run across plenty of apolitical math reformers who seem to be on this wavelength– but I take the article’s point. The thinking amongst these reformers is that one indication of “understanding” is whether a student can solve a problem in multiple ways. Reformers then insist on having students come up with more than one way to solve a problem. In doing so, they are confusing cause and effect. Forcing students to think of multiple ways or using “number bonds” does not in and of itself cause understanding. They are in effect saying “If we can just get them to do things that LOOK like what we imagine a mathematician does … then they will be real mathematicians.”
Robert Craigen, a math professor at University of Manitoba sees this type of thinking as wrong-headed: “Mathematicians don’t think that the ephemeral truths of higher reasoning have any validity when disconnected from the basic, mechanical foundation on which they are built.”
Maybe if we call the traditional approach something that sounds more appealing, we can get on with teaching math properly. Something like “alternative math”. What that alternative is (and to what it is an alternative) will be our little secret.