Multiple Means

Through school (and college), we learn that figuring out the answer (or guessing it) alone wasn’t good enough: it had to be arrived at by following the correct steps. The only exception to this is while answering multiple choice questions.

Richard Feynman described his experience in The Pleasure of Finding Things Out when he saw his cousin trying to solve algebraic equations:

“He says, “What do you know–2x + 7 is equal to 15,” he says “and you’re trying to find out what x is.” I say, “You mean 4.” He says, “Yeah, but you did it with arithmetic, you have to do it by algebra.”

His cousin was saying how you arrived at the answer mattered as much as the answer itself. Feynman did not buy that point:

“The whole idea was to find out what x was and it didn’t make any difference how you did it–there’s no such thing as, you know, you do it by arithmetic, you do it by algebra.”

But aren’t there certain advantages to knowing a technique to get to the answer? Like when the answer doesn’t leap to your mind. Or when the hit and trial method isn’t going anywhere.

Nowadays, schools that “people like us” send their kids to communicate common information and notifications via e-mails. Homework assignments for my 3 year old are sent as printed sheets (that makes sense: why have the teacher write the content?). Ok, but what does that have to the rest of this blog, you wonder.

Here’s the answer: once it is printed, software can “read” it, if not all the time, at least often enough to be useful. There are apps like PhotoMath that Wired describes as follows:

“(The app) just uses your phone’s camera to look at your math problem and BOOM. Problem solved.”

Obviously it’s not perfect, but it does solve many algebra problems!

I wonder what Feynman would feel about such apps? The obvious objection is that this is different from Feynman’s point because he did use some technique to solve algebra, just not the “approved” one whereas the app way means the kid doesn’t ever learn of any way to solve such problems. The counter-argument is that the “real world” always changes to make what the technology of the day offers as the new normal: in this case, perhaps tech makes knowing how to solve algebra problems a redundant skill just as the Internet has made remembering so many things redundant because everything is just a Google search away.

Wonder what our educators will think about such matters…