Hiding Bad Things And Mistakes From Customers

Throughout his career, Schoenfeld has videotaped countless students as they tackled math problems. But Renee's video was one of his favorites precisely because it so beautifully illustrated what he considered the secret to learning mathematics. Twenty-two minutes passed from the moment Renee started testing the computer program to the moment she said, "Ah. Now it means something." That's a long time. "This is eighth grade math," Schoenfeld said. "If I put a typical eighth grader in the exact same position as Renee, I guess after the first few tries, they would say, 'I don't understand. I want you to explain it to me.'' Schoenfeld once asked a group of high school students how long they would struggle with a homework question before concluding that it was too difficult to solve. can decide. Their answers ranged from thirty seconds to five minutes, and the average answer was two minutes.

But Renee persevered. She experimented. She returned to the same problem over and over again. She spoke her thoughts out loud. She tried and tried. She simply did not give up. On some dim level she knew that there was something wrong with her theory of how to draw a vertical line, and she didn't stop until she was absolutely sure she had got it right. It.

Renee is not a math genius. Complex concepts like "slope" and "infinity" clearly did not come easily to her. But she made a strong impression on Schoenfeld.

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