*(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.)*

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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 8^{th} 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?

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

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

- 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

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*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.*

So much goodness here. The are two pieces that stuck out to me.

1) The initial hypothesizing. I love it when students have their own preconceived notions and are asked to publicly display or announce them. This certainly “raises the stakes” for their investigation.

2) The advanced experiment design toward the end. “there would have to be like 100 houses” and “you’d have to get people who never played video games before.” This is such a critical element of mathematics that is pretty much neglected in most traditional course sequences. Math teachers often leave it up to the science teachers to discuss things like control groups and experimental design, but it’s as much a mathematical skill as a scientific one.

I wonder if a next step might be (have been?) to come up with a few follow-up scenarios to their experiments. i.e. let’s say the experiment shows a *slight* increase in violent behavior in a few households, a *slight decrease, or none at all. What does that mean? What kind of conclusions can we draw? How can we draw a stronger conclusion? This might be a more advanced topic of hypothesis testing but I’d love to hear their thoughts on what kinds of conclusions we can draw based on a single experiment of, say, 100 households.

Great stuff Lee!

I’m with Geoff and his comments. I would just add that any time we can get kids discussing math – not just solving problems – there will be a benefit to each of those kids involved in the discussion. I like to point out to my students that for my Master’s in Engineering I had some bad data. But I was able to argue against my hypothesis based upon the data – only to find out (as I was waiting for the Dean to sign off on it ) that my data was wrong and my hypothesis had been correct. I then turned around and defended my hypothesis based upon the new results. Lesson learned – your hypothesis is either affirmed or not based upon your data and just because your hypothesis is wrong doesn’t mean you change your argument.

Oh, and I think Lee’s pretty great too!

I really like that it brought out the difference between causation and correlation. As a social studies teacher I know that this is not a simple concept even for high schoolers. I also think a follow up could be for them to design an experiment/survey/etc. to try to prove whether it is causation or correlation. Even if they don’t actually do the experiment, designing it and thinking about how to “prove” it would be both motivating and valuable thinking in my opinion.

Finally where does Lee live so I can send my kids over to join in 🙂