Learning to Value Systematized Ways of Thinking

How should students come to see the value of systematized ways of thinking and approaching problems? I’m not exactly sure, but I’d prefer it look more like this:

As soon as I saw it disappearing from the bottom I thought, “Why didn’t I draw the light rays in my initial sketch?” In fact, I wrote that in my journal, if I would have drawn the light rays, how I have been drawing them, with the “cross action”, I would have made a more accurate prediction. Because I didn’t draw the rays as we discussed in class, I went back to basic thinking–like shining a flashlight on a wall and covering it with my hand. I didn’t really take into account the path the light takes when it passes through a small opening.

Then any of this:


or this

or this

or this

or this

or this

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