“A dozen boys and girls, aged nine to twelve.  A week earlier, they had asked me to teach them arithmetic.  They wanted to learn to add, subtract, multiply divide, and all the rest.”    1

“Class began  — on time.  That was part of the deal.”  “If you are five minutes late, no class.  If you blow two classes – no more teaching.  “It’s a deal,” they had said, with a glint of pleasure in their eyes.”

“Basic addition took two classesThey learned to add everything–long thin columns, short fat columns, long fat columns,.  They did dozens of exercises.  Subtraction took another two classes.  It might have taken one, but “borrowing” needed some extra explanation.”

“On to multiplication and the tables.  Everyone had to memorize the tables.  Each person was quizzed again and again in class.  Then the rules.  Then the practice.”

“They were high, all of them.   Sailing along, mastering all the techniques and algorithms, they could feel the material entering their bones.  Hundreds and hundreds of exercises, class quizzes, oral tests, pounded the material into their heads.” 

“Still they continued to come.  They helped each other when they had to, to keep the class moving.  The twelve year olds and the nine year olds, the lions and the lambs, sat peacefully together in harmonious cooperation – no teasing, no shame.” 

“Division —  long division. Fractions.  Decimals.  Percentages.  Square roots.”

“In twenty weeks, after twenty contact hours, they had covered it all.  Six years’ worth.  Every one of them knew the material cold.”    2

“..I talked to Alan White, who had been an elementary math specialist for years in the public schools and knew all the latest and best pedagogical methods.”

“I told him the story of my class.”

“He was not surprised.”

“Why not? I asked, amazed at his response.  I was still reeling from the pace and thoroughness with which my “dirty dozen” had learned.”

“Because everyone knows” he answered, “ that the subject matter itself isn’t hard.  What’s hard, virtually impossible, is beating it into the heads of youngsters who hate every step.  The only way we have a ghost of a chance is to hammer away at the stuff bit by bit every day for years. Even then it does not work.  Most of the sixth graders are mathematical illiterates.  Give me a kid who wants to learn the stuff–well twenty hours or so makes sense.”

“I guess it does. It’s never taken much more than that ever since.”   3

For more information please call 732-557-0354



1.  Free at Last, The Sudbury Valley School.  by Dan Greenberg.  1995.  Sudbury Valley School Press.  pg 15.

2.  Free at Last, The Sudbury Valley School.  by Dan Greenberg.  1995.  Sudbury Valley School Press.  pgs 16-17.

3.  Free at Last, The Sudbury Valley School.  by Dan Greenberg.  1995.  Sudbury Valley School Press.  pgs 17-18.


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