Colbert, Causation and Correlation

Interesting problems on correlation and causation are not easy to find. Perhaps I am not looking in the right places, but when I start to search, this is what I find:

Source: http://www.regentsprep.org/regents/math/algebra/practicetests/MCTest1.htm

This problem offers a nice contrast between causation and correlation, but it feels manufactured. There is nothing compelling about it. Nothing that shows why the causation-correlation contrast is worth thinking about. When we discuss the answer, students understand that the rooster doesn't cause the sun to rise. They know this is ridiculous and wonder, "why are we talking about this? No one thinks that a rooster causes the sun to rise." 

And this is where I am struggling. I want to use examples that show a meaningful contrast between correlation and causation, because I know I can find problems that reflect common assumptions about causation and thus spark a class debate. 

How many times do people assume that a correlation means causation? I know there are endless examples of this, but I need to start compiling them.  

I was watching Colbert this week and found one of my first examples. With some major editing, I am going to show this as my opening:

This clip captures answers a lot of the "so what" question as well as a hilarious example of correlation and causation:

I am now going to think about how to turn the autism and vaccine connection into a investigable lesson.

Enceladus Moon: Volume, Rate and Scientific Notation

It turns out that there might be a large volume of water beneath the Surface of Saturn's Enceladus Moon, about equal in volume to Lake Superior and 245 times the volume of Lake Garda in Italy.

I am going to use this next year in conjunction with Scientific Notation. We can analyze what it means to be "about equal" in volume or "245 times the volume" of Lake Garda.

As an extension we will analyze a question that utilizes the context of the scenario. Using different types of models, we can attempt to answer the question: "is it worth it to extract the water?"

Students can start with simple calculations: how long might the water last us? how many bottles would it fill? Then they can progress to bigger questions: based on current technology, how much would it take to get there and extract the water.

Comparing these costs and gains might make for a nice debate (we will also include the typical Neil deGrasse Tyson argument on the connection between space exploration and the future of the economy).


Article Link: http://www.bbc.com/news/science-environment-26872184

Bullets and Math

Found this on reddit: http://www.reddit.com/tb/23m702

I am wondering how many bullets on in this photo and think there might be a lesson in it.  I might never use the lesson (not sure that I am comfortable estimating something like bullets), but it certainly presents an interesting question. 

So I posted it onto 101 questions. See what other people are asking. 

Martial Arts and Math

Is mathematics useful?

Of course!

Do I expect all of my students to leave class and use the quadratic formula on their way home?

Certainly not!

That is because the quadratic formula, just like all of the other content we teach in mathematics, has value that goes beyond its application (even though its application is fantastic). I want society to stop placing value on the mathematics we learn and teach simply because we will or will not "use" an exact topic outside of the classroom. Instead, I hope we look more towards the habits of mind, which pretty sums up the reasons I teach mathematics.

Mathematics is more than the sum of its content, just as martial arts is more than a collection of kicks and punches:

Math Meme

I am hanging this in my classroom next year.

You can't say that you don't know how to solve a problem until you have tried something. Problem solving isn't just about what you know, its about what you do.

source:
http://img.pandawhale.com/82307-weve-tried-nothing-and-were-al-9vbA.png

Numbers Only on Google Forms

I am currently working on a version of Mean Paper Airplanes that I found on Julie Reulbach's blog and came across her comment to Dan Meyer about Google Form Functionality:

I was excited to find that Google has added this feature in its most significant form overhaul for education: data validation. Forms also now have the ability to post images and video, which is awesome (I am going to make interactive modules with videos and images of tables, graphs and patterns for questions). 

I wanted to show how Google Forms can be set to fix her issue.  

When writing the question, notice the "advanced settings" tab at the bottom:

Click "data validation" and selected the "number" option and specify "is number" so that only numbers can be entered. Then I select an error message to pop up if students type in something else, like the units of measurement. The message I chose was, "only enter the number of inches."

From the student's perspective, they would see this if they typed in units:

There is so much more that can be done with data validation. I can't wait to play around with it more this summer.

Thanks Julie for finding that lesson, it has been really fun so far!  (I will post my extensions to it as it is amazing and fits nicely with the 8th and 9th grade CCSS curriculum as well) 

If the Moon were only One Pixel

A student of mine found this site: http://joshworth.com/dev/pixelspace/pixelspace_solarsystem.html

This just screams proportional reasoning. I will be using it next year.