More bad Election 2012 related math

I said in my skewering of the Romney campaign’s lack of understanding of Venn Diagrams and how they work that we should be equally harsh against any and all bad math and interpretations thereof during this election season. And, lo and behold, Maddow and Moore give us a great example of the murky area of causation and correlation.

While I don’t know much about Florida or Florida voting laws, I’m betting that

a) the trend would be similar whether or not the new laws were in place, and

b) a similar trend is happening in many states.

Incumbents don’t get new voters registered. Florida is getting older. Republicans have done a great job at ginning up the base. This is to say nothing of the importance of contested primaries for U.S. president, Senate, House, etc.

The data warrants deeper digging. I’m not ready to reject the null hypothesis just yet.

I’m betting I was was the only person on campus unknowingly carrying around marbles in his backpack this week

I’ve mentioned my son a couple times before on this blog. I’m mesmerized by him and his mode of learning and ways of being. He’s like no person, child or adult, that I’ve ever met. He breaks all molds.

I started classes this past week, my first baby steps toward a PhD. I sit down in my Statistics class, surrounded mostly by 22- or 23- year olds, open up my backpack to fetch a pen and find these.

Most kids make a card or a drawing, but that’s not really Jude’s style. He’s more of a marble and tower kind of guy. But he’s also incredibly affectionate.

Now, I’m sure he didn’t put these marbles in my backpack to say “have a great first day!” He probably just put them in my backpack because that’s the kind of thing he does when he’s deeply involved in marble tower-building and just likes the feel of marbles in his hands. Still, if you don’t mind I’ll go ahead and take it as a reminder of his presence.

Thanks for my good luck marbles, Jude. I’ll probably go ahead and keep them in my backpack for a while.

Do violent video games cause violence? One Social Studies teacher’s experience teaching Math

(A lot of people have heroes. Many of those heroes are athletes or celebrities. For others, they are cops, firefighters, and teachers. One of mine is Lee Fleming, a co-worker, friend, and inspiration. Lee has taught Social Studies and Spanish. A couple weeks ago, she added “Math” to that impressive resume, despite never being formally taught math ed. She wanted to get her and her neighborhood kids ready for mathematics for the year and took it upon herself to review some math before the school year started.

I feel like we have a lot to learn from her experience, which is posted here, in her words.)



My Math Experiment with Tweeners:

So you can get the context for my math below, here is the email that I sent out to my friends in the neighborhood:

Parents of x middle school students,

I am sure you know that the state of Utah will be implementing the Common Core Standards and the kids will be experiencing a new set of standards for the year.  No matter what math they had last year or how far along they are, it will be different and [redacted] middle school has re-sequenced the math to align with the core.  Some of the skills are the same, but now it includes statistics and some more thinking-based processes instead of only computational-based standards so there will be new stuff not just for the kids but for the teachers too.  Since I have some pretty solid familiarity with the core from my work over the last couple of years in a national pilot with the math core, I decided it would be good to have my kids prepped a little so they won’t struggle as much with the changes and will be prepared to be more helpful to their peers and the teachers.

My girls were actually excited to do the math, but my son was less enthused so I had this really geeky idea that I would run him through a little math project aligned to the Common Core and see if anyone else is interested. It will be kind of a fun little project in which they look at graphs and charts to try to understand how statistics works and get their math brains going again since summer is always tough to recover from anyway.  I think my son would like it more if it were done in a group so… here is my
proposal for you:

*FREE SUPER FUN MATH PROJECT sessions in the Fleming’s Fancy Basement

– I will do two 90 minutes sessions, one for each of the next two Saturdays from 9:30-11:00 (August 11th and 18th)
– You can send your kid(s) to one or both of the sessions
– I am going to collect a $5 deposit upon entrance that I will *return *to the kids at the end of the session if they either master the math principles of the session or if they can prove they tried.  That way you and I both know that they got something out of it and if they don’t care, I get 5 bucks for my time and effort trying to keep them interested.
*Not including deposit

As I was planning the course I decided on this standard for 8th grade:

Investigate patterns of association in bivariate data.

What the heck is this??  Why can’t they just say something like two variables?

So I thought if I were a teacher trying to get kids to understand multiple variables and scatter plots, I would like for kids to have some general literacy about what bivariate data looks like and what it means.  I also thought that the stats leading up to this standard (I checked out the lower grades too) included binomials, understanding population sampling, and general understanding of stats and graphs.   I also thought that it would be important for kids to understand what the data is NOT saying just as much as they should try to learn something from it.

So… I decided to pick a topic of interest to the kids and pose a question to investigate:

Part I:

Pose question of the day:

What is the relationship between video games and violent behavior?

I had the kids pose a hypothesis.

On these cool white boards I had cut at Lowe’s (2’x2’):

Part II: Walk around the room and look at data in conjunction with a series of statements:

1)      Video games have gotten more violent.  What makes this statement true or false?

2)      Video games have caused an increase in violent crime.  What makes this statement true or false?

  1. Girls who play video games have worse behavior than girls who do not.  What makes this true or false?

  1. Boys who play video games are more likely to have behavior problems than boys who do not.  What makes this statement true or false?

  1. As the use of video games has increased, so has bullying and teenage violence.  What makes this statement true or false?

I gave each student a color and for each statement they had to write what made the statement true or false.  I gave them a choice of pairing up or working alone and I had a mixture of both.  Some kids would write alone and then gravitate to another team.  Some wanted to work with a partner the whole time and some kids wanted to be alone the whole time, it seemed to be a good strategy.

As I was walking around, I found that the questions they had the hardest time with were the tables about violent behaviors for the gamers.  I had semi-anticipated this based on the fact that it was not only complicated but the question asked them about data that was NOT on the chart—the overall incidence rate of behaviors is listed, but it does not disaggregate non-gamers.  It was really interesting to hear the dialogue and it was also a great opportunity to demonstrate the value of a good graphical summary of data.

Part III Discuss findings

Once they came back together, we went through each of the boards and had them clarify any comments, explaining their proof from the data that their statements were accurate.

I also asked them if their original hypothesis had changed after looking at the data.  I was surprised how much the kids understood about the data but what was even more interesting was their interpretation of the data.  Many assumptions came up, but the two predominate conclusions that came up were:

  • Video games have caused a decrease in violence because kids can take out their violent aggression through games instead of people
  • M-rated games cause violence

Are video games the ONLY explanation for violence decreasing?  Are you sure?  Where does it tell you in the data that video games made a difference in violent crime?  What if we looked in a place in the world where there was no electricity and we noticed that violence was decreasing too—what would you say the cause would be there?

I asked them to then draw a picture of an experiment they could run to prove that video games really did decrease violence.  Each team struggled for a bit but then one team had drawn a picture of two houses:

Then another group chimed in with “but it would have to be 100 houses!” and then a third said “I think all the houses would have to be people who never played video games before and see if their violence changed.”

So we collectively talked about independence of variables.  Pretty cool, right?  I also had them define correlation vs. causation, I don’t honestly know if those are math standards but seemed relevant to the conversation.

Finally, I had them take the charts that they struggled with and asked them to draw a graphic representation.   This was super fascinating!  The one girl in the group,  younger than the other kids by two years, generated this chart.  She got the idea of key, x and y-axis, and did not hesitate to jump right in:

The boys, who up until this point had really understood the data even more than her, produced stuff like this:

And even that was only after looking at her work.

Finally, I had them leave with an exit ticket of explaining the difference between causation and correlation, and then giving them an assignment to look at a minimum of one chart or graph and decide what the graph IS saying vs. what it is NOT.    We have part II tomorrow morning, I hope they retained what we discussed last week!

— Lee


I feel like there’s a lot to learn here. What were your takeaways as an educator? Likes? Wonders? Clarifying questions? Next Steps? Let’s hear them in the comments! And thank you, Lee, for providing us a really nice case study.

Sprinklers, Circles, Sectors and such (my first real foray into Geogebratubing)

First off, I basically stole this from @NatBanting. And when I say “basically”, I mean “entirely.” Here’s the original blog post where you can see his frustratingly boob-shaped backyard. I tried to video my backyard but I didn’t have a good ladder to get a good vantage point. And my roof is terrifyingly steep. And I’m scared of heights. So I let him do the grunt work and I sat back and tried to figure out Geogebra on the fly. I’ve used Geogebra before, but not quite in this capacity, and to this degree. Huge thanks to John Golden (@mathhombre) for his Geogebra session in Grand Rapids a few months ago for encouraging us to create and share. I created the shape of the yard using inkscape (

Now, I have a sprinkler system, rather than a hook-up-to-the-hose kind of sprinkler. So once you place them in the ground, you’re sort of stuck. Therefore, it’s much more imperative that you place your sprinkler heads correctly to minimize the amount of water overlap and the sprinkler cost and maximize the amount of water coverage. That’s what this task is intended to do.


Geogebratube: Sprinkler task


As for facilitating a task like this, I’d consider having students attempt this using paper and pencil first, make predictions, share their work, before giving them this Geogebra worksheet. In fact, you could start with Nat’s original post using a mobile sprinkler, then throw in the installation of the sprinkler system as an extension (or twist).

Also, you could easily modify this task with several different yard shapes (possibly by someone who isn’t afraid of heights). You could also scaffold nicely by starting off with just the 360 sprinklers and then slowly bringing in the sector sprinklers. If you want to go crazy, you could extend this into a project with PVC pipe distance and such.

How would you use or modify this task for your classroom? Let everyone know in the comments!


Epilogue: It Takes A Village (To Develop Curriculum)

This is curriculum-creation in the 21st Century: Nat created the task. John taught me how to better use Geogebra. I just took their stuff and ran with it. This may warrant an entire blog post, but for now, I just wanted to highlight this.

Why doesn’t Nike+ use math to encourage me to run?


The Nike+ app, which at the end of my run the other day, looked like this:

(editor’s note: yes, I’m slow. Thank you for noticing. Also, along with some encouragement in data format, I had Tim Tebow give me words of encouragement for bettering my pace.)

Now, there are a lot of numbers here, but I’m primarily interested in that last piece.

“You ran 0.10 mi more and 0’56″/mi faster than the average of your past 7 runs”

Why did Nike+ choose my past 7 runs? Was there some sort of algorithm to maximize how good I feel about myself?

Sadly, I think not. Witness my previous run:

So it looks like it just takes your past 7 runs and compares your mean distance and pace. That’s not very good motivation, now is it Nike+? Can we improve (at least, in my opinion it would be an improvement) Nike+’s distance and pace comparison to help the runner feel better about his or her progress?

Guiding Questions

  • Would a different measure of central tendency lead to a different, and perhaps more encouraging, data capture?
  • Would averaging a different number of past runs lead to a different, and perhaps more encouraging data capture?
  • Could we write an IF…THEN or other type of algorithm to encourage the runner?

Suggested Activities

  • Give some runner data (either fabricated or authentically generated; shoot, you can use my data if you want) and ask students to describe after each run “what should the app say in order to give the runner a sense of accomplishment?”
  • Once students have done that with individual data points, have students sketch out an algorithm or decision tree.
  • Test that algorithm or decision tree against a new set of runner data.

  • Compare decision trees and algorithms to see who’s is the “positivest”(?).
  • Turn into algebraic expressions if you want, presumably to help out the coders.

There are few things more discouraging than seeing that I’m actually running slower than my seven previous runs averaged out. At least package the data so I don’t feel like I’m out of shape.