Abstraction

Sometimes, things do not go according to plan.

I had a great plan for today to have a concept quiz over Special Right Triangles. 

Between the flu knocking out half of the class, the first friday after break and the confused looks on their faces, I just could not go through with the quiz, so I thought it was going to be a “problem set, sit down and work quietly” kind of a day…

Abstraction had a better idea. Enter Ed.

Ed is a great kid, a great student and a great thinker. So Ed says, “how do we know that the square root of 2 times the leg is the hypotenuse?”

A great question. We had talked about it earlier this week by working through 6 examples and picking up the pattern and using it to abstract the rule. Apparently, that did not stick, but what happened next did. 

We did this together as a class:

 

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we went through the logic and the steps and they agreed with them. Then, I made a deal with them. 

The deal:

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Either a bunch of problems to practice, or a real thinking exercise. Surprisingly, a lot of kids tried it. Ed tried. He got this:

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Today was a great day. Ed did not do endless problems. Ed got the concept. Ed did something perplexing, hard and abstract. Ed was successful. It was a great day. 

Ed grew today. So did I. 

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