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A great, simple clicker question for showing the importance of student discussion
When using clickers to spark peer discussion to promote learning, sometimes it can be hard to demonstrate to students the importance of discussing the answer with their peers. My colleague Steve Pollock just shared this wonderful question with me.
Here’s the question. Think about it for a moment. Before you read the answers (below), submit your answer via the poll in the right-hand column of the blog. Just give us a quick response.
Don’t look for the answer before you put your response into the poll!
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Steve used this question at the beginning of the semester to make the point that discussion does have a purpose in the class.
When students voted silently, 34% of them got it right.
He didn’t show them the distribution, just asked them to talk to their neighbors. The next round of votes was 75% correct.
And the right answer? A. Did you get it right, or did your gut instinct lead you to the intuitive (but wrong) answer? That’s what happened to me — I got it wrong on my first guess. Peer discussion makes you stop and really reason through your answer!
Comments: (4)
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Categories: Classroom Response Systems, Peer Instruction
Read All Stephanie Chasteen
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November 23rd, 2010 at 6:06 pm
Could you explain the logic behind the answer to the question?
December 7th, 2010 at 11:24 am
Here’s the algebraic answer:
If price of balls = “B” and price of racket = “T” then:
T + B = 110
T = B + 100
Solve those two equations simultaneously:
T = 110 – B = 100 + B
110 – 100 = 2B
B = 5
The “intuitive” answer leads you to the answer “10″ because we generally don’t read the question carefully enough and instead solve the problem “If the balls and racket together cost $110 and the racket alone costs $100, then….” and come up with the answer “$10″ for the price of the balls. But the question states that the racket alone costs $100 *more* than the balls. If we take that into account properly, you’ll realize that $10″ is actually the cost of *2* cans of balls (as can be seen by the algebra above).
It’s not a hard question once you sit down and talk to someone about it, or pause to think about it, but on our own we often get stuck, so that’s why we think it’s a good question to show students the power of talking to someone about their answer.
December 7th, 2010 at 12:15 pm
Wouldn’t it just be that the single can of balls is $5 and the racket is $105? Thus the racket is $100 more then the can of balls, and they total $110? The equation above makes algebraic sense, but you cannot quantify the number 2 (for cans of balls) from the question itself. \Can\ is used in the singular tense throughout the question.
December 9th, 2010 at 10:52 am
Jessica,
That’s right, the can of balls is $5 and the racket is $105. That satisfies both equations above and is what I am saying. 2 cans of balls cost $10, so a single can of balls is $5. Note that we have to satisfy both T+B = 110 *and* T=B+100. The “2″ in my explanation above comes from solving those two equations simultaneously; not from the question itself.
T + B = 110 (The can of balls and the racket together cost $110)
T = B + 100 (The racket costs $100 more than the can of balls)
Solve both equations for T
The first equation becomes: T = 110 – B
The second equation is still: T = B + 100
Set the two sides equal to each other:
T = 110 – B = B + 100
Add B to both sides
110 = 2B + 100
so 2B = 10
So, the “2B” comes from the algebra, not directly from the wording of the question itself, which only refers to the price of a single can. You can certainly reason out the answer without the algrebra; I just used the algebra to nail it down.
Does that answer your question, or did I miss your point?