“What I know is rivaled only by what I do not know”: Elaine Fine writes about knowledge and humility. It’s a great post.
Elaine’s post makes me want to revise what I wrote in an earlier post about information and knowledge: competent people not only know stuff; they also know how much they don’t know.
Tuesday, November 20, 2012
Knowing and not knowing
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comments: 4
Hi Michael. I just read a post at Diary of a Singaporean Mind that reminded me of your topic here. Thought you might like it.
http://singaporemind.blogspot.com/2012/11/psle-question-to-set-you-thinking.html
Happy Thanksgiving (a day late).
I sat down this morning to try (again) to figure out the problem. The numbers seem to work, but the picture itself seems off — my first thought was that the proportions seemed all wrong. Using a ruler app, I measured the rectangle as 4.5 x 9, which does not scale to 6 x 15.
Happy Thanksgiving to you too (several days late).
Wow... I didn't mean to make you work. The paragraph that reminded me of your post was this: Our education system trains people to answer questions and find solutions to problems. We forget that very often finding the correct questions and the problems to solve is actually more important. Even before you rush to answer the question...do you have the right question?
After you said you sat down to figure out the problem, I felt bad for skipping over that part. So I drew the rectangle in AutoCAD and looked again at Singaporean's picture. Right away I noticed that the one triangle has four times the area of the other. This means I should be able to fit four copies of the little triangle inside the big one.
After I looked at it some more, I figured out how to do that: On the big triangle, put a dot in the middle of each of its three sides. Then connect the dots. Done! We have just drawn one little triangle that defines the four little triangles in the one big one.
Sounds irrelevant, right? But notice that two of the little triangles we just created occupy the whole length of side XQ (the hypotenuse of the big triangle). In other words, the hypotenuse of the big triangle is exactly twice as long as the hypotenuse of the little triangle.
That means I know where point X is. If I can divide the diagonal SQ of the rectangle into three equal parts, point X is exactly at the point where two of those three parts meet. So now, now I could draw the thing in AutoCAD. (Victory!)
Conveniently, AutoCAD has an AREA command. I used it and found out that the small triangle has area of 5 square centimeters, and the big triangle has an area of 20. (The proportions are the same as the 4 and 16 posed by the Test Question, but the numbers are wrong.)
Prob'ly got yer head spinnin now, huh. But, thanks. I'd never have taken another look at that rectangle if you didn't embarrass me into it :)
I tell my students that in the so-called real world people will expect them to be figure out the right questions, not choose correct answers, so I liked I liked the observation about asking questions. But I got caught up in the problem. I’m still not sure I understand the problem with the problem, but I didn’t mind working at it — I wanted to figure it out.
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