Comments on: Final Exam Question #51

By: uberVU - social comments

uberVU - social comments — Sun, 21 Feb 2010 03:24:10 +0000

Social comments and analytics for this post…

This post was mentioned on Twitter by bfchirpy: It is a feature not a bug that Mike and Dan can draw their own self-serving conclusions from the same set of numbers. http://bit.ly/ddfF25…

By: bmc456

bmc456 — Wed, 17 Feb 2010 02:15:28 +0000

I had never heard of this game and it intrigued me to try download it and try it. Now that I know a little more about it, the question posed here makes more sense.

I like that students can argue their reasoning for who they think is the better doodle jumper!

By: Sean Sweeney

Sean Sweeney — Thu, 04 Feb 2010 18:54:47 +0000

Here comes a new challenger!

Sean:

http://picasaweb.google.com/SeanWSweeney/BloggerPictures?authkey=Gv1sRgCMSWrc_91azOuAE#5434462898374349074

For fairness sake, I did play 1.5 hours total on kids’ phones beating their high scores first.

By: Megan

Megan — Fri, 29 Jan 2010 14:31:15 +0000

I know what I would have answered if I were taking this test… and it would have been something seemingly close to what David Cox said. I wish you luck in beating your friend :)

By: Mr. Sweeney

Mr. Sweeney — Wed, 27 Jan 2010 03:45:26 +0000

In my experience with doodle jump, Dan is clearly better. It is pretty difficult to pass the mid 50,000 barrier. Mike has never done it. Dan’s done it (at least) twice. It’s possible Mike will be better when he’s played as many games as Dan has, but right now my money’s on Dan.

By: Alex

Alex — Mon, 25 Jan 2010 14:14:30 +0000

Beautiful question.

I agree you want to know standard deviation but definitely do not give the students the standard deviation. Often when results are quoted in the news you are only told averages or extreme values and you are not told standard deviation. Of course this is ridiculous but students won’t learn that it’s ridiculous unless you put them in a setting where they can argue for either side being the “winner” because of missing information or because “winner” can have different definitions.

By: cornwalker

cornwalker — Mon, 25 Jan 2010 01:07:30 +0000

What is clear is that based on Dan’s lower average it appears Mike is a quicker study. Dan’s high score may also be a simple anomaly or he may just be wildly inconsistent.

I wouldn’t redefine the problem though – the lack of decisive information is precisely what invites speculation and perhaps even requests for data that might provide a clearer answer to the problem. Since it’s a remedial Algebra class I doubt you’ll see requests for standard deviation, but perhaps a bright student or two will notice (and maybe even graph) the rate of improvement and see that Mike will soon put the hurt on Dan.

By: David Cox

David Cox — Sun, 24 Jan 2010 23:59:27 +0000

I’d love to think one of your students may answer something like:
You’re better Mr. Meyer by a long shot. Your average may be down because you stunk when you started playing. However your most recent score is closer to the high score. New learning replaces old. Q.E.D.

By: Dan Meyer

Dan Meyer — Sun, 24 Jan 2010 23:55:06 +0000

I don’t know how seriously to take this. The imprecision you cite as reason to remove or redefine the problem is the exact reason this problem exists. This is what we do. On Wednesday, they’ll see the same problem. Team Dan will make its case and Team Mike will rebut with the same arguments you’ve made. They’ll reverse roles and repeat.

I could have explicitly defined “better.” I could have defined a standard deviation. I could have forced an objective answer to the question and graded it on a scantron. But that’s the kind of teaching I’ve tried to fix in my rear-view mirror for the last six years.

If anyone else wants to take up this kind of intellectual grandstanding, they’re welcome to it. I feel silly discussing pedagogy with anonymous commenters whose credentials in this field are a bit mysterious.

By: Zeno

Zeno — Sun, 24 Jan 2010 20:18:00 +0000

What about: (3) Dan is better because his last game score is higher. (You’re only as good as your last game.)

(1) is not a good answer because the high scores may be due to luck more than skill. (2) is not a good answer because the averages may include games that do not reflect the players’ current skill levels.

But I think the correct answer is: the question cannot be answered in a meaningful way because the meaning of “better” is not specified. If “better” means “has the higher high score”, then (1) would be the answer. If “better” means “has the higher average score”, then (2) would be the answer. If “better” means “has the higher last score”, then (3) would be the answer. But these answers are all really a matter of semantics, not mathematics.

If “better” means “more likely to get the higher score on the next game”, then a plausible mathematical analysis might be possible in principle. But I’d agree with cornwalker that the information provided isn’t sufficient to permit a reasonable answer.