Mathematical thinking and the 'special' mind

June 4, 8:17 PMInformal Education ExaminerLisa Jo Rudy

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Courtesy Stock X Change

Today I took Tom back to the Big Cheese Math Specialist.  I'd been trying to follow his instructions, but we didn't seem to be moving forward as I'd hoped. 

The specialist used Cuisenaire rods.

"Make a staircase," he told Tom.  Tom quickly lined up the rods according to height and color.

"Can you hand me a 5?"  Tom complied.

"A 3?"  No problem.

"How about 15?"  Tom handed him a one and a five. 

I was actually embarrassed.  How could a reasonably well-educated twelve year old mistake six for fifteen?

"You see?"  said the math specialist, smiling at me.  "This is the result of working with counting instead of real math concepts.  He's matching the digits, but not the number." 

Then he wrote the number 15.  A one and a five. 

Tom had handed him a one and a five. 

He had matched the digits.

But he clearly didn't understand that fifteen is really ten plus five.

Over the next hour, I watched as Tom started to actually grasp the numerical concepts behind the written figures.  By the end of the hour, he appeared to understand that ten is the same thing as 3 + 7, 7 + 3, 5 + 5, 2 + 8, 8 + 2...   He could distinguish 30 from 3, and handed the specialist two fives when asked for ten.

Of course, I don't know how well the lesson will stick.  But I do know that, all this time, I've misunderstood what Tom was seeing.  One and five make fifteen.  Of course!

How could I be so dense?!

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