The Gallup 12

It's natural for lovers of numbers to enjoy the results of the latest Gallup poll. One of my friends just shared a Gallup list that was new to me. The Gallup Q12 is a list of 12 crucial indicators of employee and workgroup performance.

I don't know if there's any research supporting this, but I have a hunch that we could re-write these 12  statements to talk about student and staff fulfillment in schools.

Isn't this what students seek when they come to class?

And it's an elegant summary of the encouragement we crave as educators, the fuel that keeps us in the game.

In reflection, I owe a huge thank you to my mentors in GISD. Thanks for looking out for me and always giving me that next push.

Correlation Coefficients - A Graphic Organizer for Your Students

Just a simple graphic that might bring clarity to the idea of correlation coefficients. A.4A

Quadratic Transformations - Tying it together

A.7C offers a new twist on an old idea.

Parabolas still move up and down, but they also move left and right now.

They still get narrower and wider, but we also describe those changes as compressions and stretches. And while the old standards only included vertical stretches and compressions, the new standards discuss horizontal stretches and compressions.

Distinguishing between horizontal compressions and vertical stretches is tricky. Take a look at this example:

Horizontal Compression: f(x) = (2x)^2  

Vertical Stretch: f(x) = 2x^2

Both of these transformations will result in a graph that is narrower than the parent function. An important difference to notice is that the narrowing effect of the horizontal compression will be stronger than that of the vertical stretch since the "a" coefficient of the compression is squared.

One more point to keep in mind: a horizontal compression of f(x) = (2x)^2 is equivalent to a vertical stretch of f(x) = 4x^2! The effect on the graph of the parabola will be exactly the same; we can only distinguish between the two when we look at the value and placement of the coefficient in the equation.

Fun with images in Google Slides

So I just learned this new trick that you can use to make your images in Google Slides look even better. Watch this one-minute tutorial to learn how to mask images.

Before

After

You could mask the images using circles...

Or alternating trapezoids...

Or thought bubbles...

Choose from dozens of different shapes!

Have fun!

Danger averted! Is it dangerous to swim after watching a Nicholas Cage film?

Texas is adding a few new standards to the algebra I EOC test this year, three of which deal with correlations between real-world sets of data.

• A.4A - Calculate the correlation coefficient using technology
• A.4B - Compare and contrast association and causation in real-world problems
• A.4C - Write linear functions the provide a reasonable fit to data to make predictions

My favorite is A.4B because it's so great for discussion. For example, the number of films with Nicholas Cage correlates closely with the number of people drowned by falling into a pool.

Image from http://www.tylervigen.com/spurious-correlations 

So should we close down swimming pools during years when Nicholas Cage makes a lot of movies?

 --> ?

Understanding causation is crucial because it guides our decisions and policies. Stats with Cats identifies 6 key purposes for studying causation.

"For example, if you can figure out what causes a condition or event, you can:

• Promote the relationship to reap benefits, such as between agricultural methods and crop production or pharmaceuticals and recovery from illnesses.

• Prevent the cause to avoid harmful consequences, such as airline crashes and manufacturing defects.

• Prepare for unavoidable harmful consequences, such as natural disasters, like floods.

• Prosecute the perpetrator of the cause, as in law, or lay blame, as in politics.

• Pontificate about what might happen in the future if the same relationship occurs, such as in economics.

• Probe for knowledge based on nothing more than curiosity, such as how cats purr."

But since correlation doesn't prove causation, how can we tell whether two variables are correlated due to a third factor or due to a genuine causal relationship?

LearnAndTeachStatstics lists 9 criteria identified in Chance Encounters by Wild and Saber.

1. Strong relationship: For example illness is four times as likely among people exposed to a possible cause as it is for those who are not exposed.
2. Strong research design
3. Temporal relationship: The cause must precede the effect.
4. Dose-response relationship: Higher exposure leads to a higher proportion of people affected.
5. Reversible association: Removal of the cause reduces the incidence of the effect.
6. Consistency: Multiple studies in different locations producing similar effects
7. Biological plausibility: there is a supportable biological mechanism
8. Coherence with known facts.

Is there a strong relationship between Nicholas Cage and drowning deaths? Did we conduct an experiment with strong research design? Would removing Nicholas Cage from the film industry keep us safer? Importantly, is our observation coherent with known facts?

Check out this collection of Spurious Correlations from Tyler Vigen. But preview the charts first before sharing them with your students, since a few are for too mature for school.

Surviving Rotations without Patty Paper

Patty paper is an awesome tool for doing rotations on the coordinate plane. But what if you need to graph a rotation and there is no patty paper available???

The 8th grade team at Jackson Technology Center recommends first turning the paper to see what your image will look like. Students can use this method to graph rotations without using coordinate rules OR patty paper. (Thanks Amber, Sandy, Emmanuel and Tommy!)

Here's how. 

Independent and Dependent - Like the Back of Your Hand

Students struggle to remember which axis on a coordinate plane is independent and which is dependent. Here's a simple trick from the 6th grade teachers at Jackson Technology Center.

Just look at your hand! When you  hold your hand in front of you, your thumb is independent of your other four fingers. Those four fingers tend to hangout together - you might even call them dependent. 

Just like in the coordinate plane, dependent is vertical and independent is horizontal. 

Thank you, Brenda, Megan and Katie for this "handy" trick. ;)