I was recently helping my daughter with her Math homework. She had the following problem. There are 320 rods in a mile.
How much of a mile is one rod?
How much of a mile are forty rods?
How much of a mile are sixty rods?
Can you solve it? Wait, there’s the catch – you can’t use division or a calculator.
I puzzled over this for quite a while. How can I help her answer the question if she isn’t allowed to use the basic tools required to answer it? I tried thinking of all sorts of convoluted way to get her to do division without doing division. My ideas became increasingly complex while her chances of understanding became increasingly more remote.
Then, out of the blue, the answer finally hit me. I couldn’t believe I didn’t see it sooner.
How much of a mile is one rod? 1/320
How much of a mile is forty rods? 40/320
How much of a mile is sixty rods? 60/320
There was no need to go any further. No need to use division. No need for a calculator. Those answers are all exactly right and are consistent with what one might expect of a third grader.
So simple, so obvious. Well, so obvious to a beginner whose mind was not clouded with a lot of more complex ways of thinking about the problem.
As leaders and problem solvers, sometimes we have to let go of the complexity and everything we know, in order to see things more clearly. Einstein called this the beginner’s mind. Looking at things from a simple and basic perspective. It’s what enabled him to develop the theory of relativity. While the people around him were trying to justify the presesence of certain forces, Einstein said, “What if they just aren’t there?” The beginner’s mind – one that doesn’t see and try to account for what is not there.
Maybe my paradigms are to rigid, but my first thought was 1/320.
But, then I told myself that it was not allowed because it is a representation of division.
I guess I got stuck on “use” vs. “represent”
Then I thought that maybe it should have been phrased as, “you can not do any calculations”, but then I may have still gotten stuck on “do” vs. “represent”. 😉
I think that I am making your point.
Another point is that many people live within rules that they make or misrepresent for themselves.
This greatly cripples their capabilities in life.
Fun stuff, regardless.
Thanks for your comment! I think the “use” versus “represent” is a great example. The beginner doesn’t know enough to make such distinctions so they actually have an easier time making sense of the problem.
I do like your other point as well regarding people making their own rules that get in their way. I’ve seen that happy so many times in big organizations.
Thanks for your comments!