Final Exam Question #51

Who is better at Doodle Jump? Mike or Dan? Why?

The first semester ended, not with a bang, but with two days of canceled class… because you can’t be too careful with those Santa Cruz tornadoes. and two days of hasty final exams. My remedial Algebra class spent a lot of time this semester on what California calls computational fluency and what I would rather call the awesome descriptive power of numbers.

Which has meant, thus far, everything from times tables to proportions to infographics all leading to the motivation for the question above: when your friend is being kind of insufferable about how good he is at Doodle Jump, you can use numbers to shut him up!

It is a feature not a bug, in my opinion, that Mike and Dan can draw their own self-serving conclusions from the same set of numbers.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

1. Sean Sweeney

January 22, 2010 - 6:54 am -

Woah… That’s weird. I was just playing doodle jump. My policy is if I catch a kid playing games in class, I confiscate his game playing device until the end of the day and destroy his high score so that my name will remain at the top of the list forever.

2. Darren Draper

January 22, 2010 - 11:59 am -

I love these kinds of questions. They force the kids to look at the data, synthesize, rationalize, attempt to justify their responses and then throw their hands up in the air because “better” is in the eye of the beholder.

There are too many important times in life when there are no clear-cut, correct answers to not teach our kids how to deal with these kinds of questions from an early age.

Dan, I’m telling you, man: this blog is far from counterproductive. Thanks for your willingness to keep me in the math groove. There are some days, like today, that I really miss making the kids scratch their heads.

3. Elizabeth

January 22, 2010 - 4:52 pm -

@Sean – I love your strategy! What could be worse than being forced to see your reptilian-brained teacher’s high score atop the list every time you fire up Doodle Jump?

This is what makes you a true and worthy evil genius of a teacher. ;-)

4. Brian Cormier

January 22, 2010 - 7:25 pm -

Dan, this is unrelated but today was parent visitation day so I switched around the order a bit so the parents could see “Graphing Stories” instead of a day of practice with compound inequalities. The parents loved it and said, “Wow, what a great class.” I gave you full credit and it was ultra-engaging. Best way to re-introduce graphing in 2 variables. I pick and choose the vids, and when we’re done I show them an unlabeled speed vs. time graph of my journey home from classroom to front door for us to analyze and label. They do their own for HW. I know it’s one of your favorite and proudest lessons. Thanks to you, it has become mine as well.

5. Dan Meyer

January 23, 2010 - 6:22 pm -

Awhile back I spent some time sketching out all the different roles of a teacher I could think of at the time — the teacher as caregiver, scholar, etc. Sean makes the first truly convincing case I’ve seen for the teacher-as-evil-genius.

I won’t add it to the post, though.

Thanks for the affirmation, Darren, but I should quickly point out that blogging is still valuable to me as a professional development tool. The concern of that post was specific to WCYDWT, which I’m finding too technical to discuss anywhere asynchronously.

Brian, that’s cool to hear. And fun extension there.

Zeno, I’m willing to credit arguments that (1) my high score makes me better or that (2) Mike’s average score makes him better. But it’s a free-response question that I haven’t yet graded so I can’t say I won’t be convinced by other arguments.

6. cornwalker

January 24, 2010 - 10:58 am -

I say there’s not enough information. What’s the standard deviation? What was Dan’s average and high score at 359 games? I want graphs of all the scores (score vs. time and distribution curve) before I make my decision.

7. 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.

8. Dan Meyer

January 24, 2010 - 3:55 pm -

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.

9. David Cox

January 24, 2010 - 3:59 pm -

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.

10. cornwalker

January 24, 2010 - 5:07 pm -

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.

11. Alex

January 25, 2010 - 6:14 am -

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.

12. Mr. Sweeney

January 26, 2010 - 7:45 pm -

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.

13. Megan

January 29, 2010 - 6:31 am -

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 :)

14. bmc456

February 16, 2010 - 6:15 pm -

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!