Show me your worst

Using Magnets as Metaphors for Goal-setting

Q What happens when you use a magnet to pick up small pieces of iron?

A It depends on how close the magnet is to the iron pieces. If it is too far away, the pieces of iron will remain where they are.

Q What happens when you use a magnet to move small pieces of iron - without getting them stuck to the magnet?

A For a start, you can only pull at the pieces of iron. You cannot push them (without them getting stuck). Not much will happen until the magnet is ‘close enough’. The distance depends on the size and composition of the iron pieces - small pure pieces will respond at a greater distance than large impure pieces.

It’s useful to bear in mind when you are setting goals for a class of students. You cannot push, only pull. The purer, smaller students will rise to the challenge first; the less pure, larger ones will only move when the goal is close enough.

Show me your worst

The young man at the Study Center, let’s call him Jim, was about ten or eleven years old. He had come to do his Maths homework but was not quite ready to get on with it. He was faced with a new visitor to the Center - me.

Jim needed to find out what I was like as a Maths Tutor. So he challenged me,

“What’s the most difficult Maths you can do?”

I pulled out a sheet of paper and a pen. And drew the symbols for the integral of e to the power x

He studied it for a moment.

“What’s e?” he asked.

“Oh that was from College maths. Too hard?” I suggested.

From the expression of his eyebrows I guessed that he had never seen such things before.

“Let’s try something from the last year of Secondary school,” I suggested and wrote the symbols for the sum of ? to the power n, from 1 to 4.

“What’s that mean?” Jim asked, pointing at the exponent.

“It means that we have to find the sum of a half raised to different powers”

Jim’s eyebrows raised together.

“Sum, means add up,” I began, “and what we have to add up is a half, half squared, half cubed and,” I paused but he didn’t respond, “half to the power four.”

I wrote down ?, and said, “the next term is half of half,” and waited.

“Half of half?” Jim started counting in his head.

I drew a rectangle and shaded half, then half of the half.

“A quarter,” he tested.

“Yes,” I wrote ? next to the ?.

“And the next term is half of that quarter,” I waited. Then I began to shade half of the quarter of the rectangle.

“An eighth,” Jim said.

“Yes, and the last term is a sixteenth, of course.”

So now we had the terms 1/2 , 1/4 , 1/8 , 1/16 on the paper.

“All we have to do is add them up,” I told Jim, but the look on his face told me that such fractions were beyond his experience.?

I related what I was going to do, and paused for Jim’s help here and there.

“It’s best to use 16ths, I think.”

“Half is eight sixteenths”

“A quarter is four sixteenths”

“An eighth is two sixteenths”

“And there’s one sixteenth here,” I said pointing at the final term.

On the paper we had 8 + 4 + 2 + 1 sixteenths.

“What do you get when you add eight, four, two more and one more?

Jim told me, “15”

So, “the answer we are looking for - the sum of a half raised to different powers - is fifteen sixteenths,” I told Jim.

He looked pleased at the result.

I think I passed his test.

As Jim got up to fetch his homework, I said, “Hmm, that was Maths from your last year in this school. You can tell your teachers you can already do it. Got any brothers or sisters in that year? Other family? You can tell them that you can already do it.”

The thing is, Jim already half believes it.