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?

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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. ;)

Is This a Math Test or a Reading Test?

Why Word Problems Stump Even Our Strongest Readers

For those of you with extra reading time, I'm enthusiastically, sincerely, and non-sarcastically recommending these two fantastic articles on literacy in the math classroom:

Attack Story Problems with the 3 Phases of Close Reading 

and 

Reading in the Mathematics Classroom

For those without a lot of extra reading time at the moment (Ahem, teachers in between the months of August and June!), let me skim them for you!

Part 1: 

Why is this a problem? Don't reading teachers teach kids how to read?

Yes, reading teachers teach students how to read. Reading to understand math problems, however, differs from reading to understand a literary passage in several ways:

• Word problems are written in a very compact style. The author of a math problem attempts to squeeze as much information as possible into each sentence with minimal redudancy 
• Word problems force your eyes to travel back and forth. Unlike information in reading passages which is generally laid out left-to-right, information in word problems forces the reader's eye to move back and forth and up and down repeatedly throughout the text.
• Word problems contain three different types of text: 
• The Problem Statement: How many apples does Joseph need for the Halloween carnival?
• Explanatory Information: Joseph estimates that one third of the 245 guests invited to the carnival will purchase a caramel apple.
• Supportive Prose: The student council at Joseph's school is planning a Halloween carnival to raise funds for an upcoming field trip.
• The key idea of a word problem is usually found at the end of the passage. This differs from reading passages, where the main information is usually found at the beginning of a paragraph. 
• Words used in daily language have different meanings in math class. For example, when I tell you that my Mom and I have similar hairstyles, I don't mean that you can write a proportion to describe the relationship between our haircuts.
• Small words make a huge difference. Finding 20% of your total bill is not the same as taking 20% off your total bill. (Metsisto, 2014). 

Part 2:

What can I do in my math class to build "word problem literacy?"

Model your thinking out loud.

As you read through a problem, "think out loud" about what you would do to approach the problem. Model the process of figuring out what the problem is asking, re-reading the text to discover a problem-solving approach, and re-reading again to pull together the important information. Talk about any difficulties, tricks," or extraneous information that you notice. As your students' mathematical literacy improves, ask them to model their own thinking.

Pre-Read. Read. Re-Read.

• Pre-Read
• Your goal with pre-reading is to get the gist of the problem. Ask your students to do this without holding a pencil in their hands so that they are not tempted to start marking up the problem yet.
• Read.
• Get out the pencils and read the problem a second time with the intention of marking specific details. Students may underline, circle or highlight the important information now that they know what they're looking for. Be sure to notice the small words!
• Re-Read.
• Work the problem with your pencil in your hand. Follow the mantra, "Read a little, do a little," working through the problem piece by piece as you re-read it. ("Attack Story Problems," 2014).

"Attack Story Problems with the 3 Phases of Close Reading." Attack Story Problems with the 3 Phases of Close Reading. Smekens Education Solutions, Inc., 22 Aug. 2014. Web. 10 Jan. 2017. <http://www.smekenseducation.com/Attack-Story-Problems-with-the-.html>.

Metsisto, Diana. "2. Reading in the Mathematics Classroom." Literacy Strategies for Improving Mathematics Instruction. By Joan M. Kenney. Alexandria, VA: Association for Supervision and Curriculum Development, 2005.  <http://www.ascd.org/publications/books/105137/chapters/Reading-in-the-Mathematics-Classroom.aspx >

Why and How to use TI Navigator?

You already use the TI Nspires every day without using Navigator... so why take the extra step? 

The Navigator software transforms your Nspires from a sophisticated calculator to a dynamic device that you can use to communicate with your students in real time, get instant feedback and simultaneously view all of your students' screens.

A few of the best features:

• Quick poll - send a poll to your students anytime. No advance planning needed. 


• (Examples: Warm-up problem, check for understanding, "What's your favorite soft drink?")
• Navigator Activities - Send your students a hands-on learning lab. Peruse dozens of TEKS aligned Navigator activities here. 
• Screen Capture - Instantly see all of your students' screens
• Student presenter - Choose one of your students to demonstrate calculations for the whole class. (Hint: You can also choose YOURSELF as the "student" presenter.)

So how do I do this?

Four minutes on Atomic Learning is all it takes. Click here for video tutorials on setting up your classes, sending polls and using screen capture.

Open Navigator by clicking this icon on your desktop.

Sample Class Rosters 

Dummy Class - Use this "dummy class" roster if you would like to use the same generic set of logins for every class. For example, your students will login as "A," "B," "C," and so on. This is a great option for classes with frequent transfers (Ex. AEC).

Example Class - Use this example roster as a model of how to create individual logins for each of your students. This option allows you to collect data from each of your students throughout the year.

How to "Gamify" Your Class in 4 Steps

What is Gamification?

Gamification refers to applying the elements and design techniques of great games in a non-game context.

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Gamification doesn't refer to playing actual games!

Gamification Examples:

• Starbucks Rewards - for coffee drinkers
• Frequent Flier programs - for travelers
• ChoreWars - for those of us who have chores to do
• ThinkThruMath - for math students
• Zombies, Run! - for joggers who want jogging to be less boring

Why Should I Gamify my Classroom?

• Gamers exhibit the characteristics we want to see in our students:
• Persistence
• Risk-taking
• Attention to detail
• Problem-solving
• And gaming communities foster values that we can harness to motivate our classes:
• Community
• Competition
• Achievement
• Status
• Altruism

Key Elements of Great Games

• Points
• Levels
• Quests
• Progression
• Avatars
• Badges
• Leaderboards

How to Gamify Your Class:

1. Figure out what you want students to do. For example, maybe you want your students to master the readiness TEKS for your course.
2. Identify a few BIG miles stones for your students to meet. A big milestone might be mastering an entire reporting category.
3. Identify several smaller sub-tasks. An example of a sub-task might be mastering one of the readiness TEKS.
4. Create a story and track student progress. In this example using the 8th grade readiness TEKS from Garland ISD's curriculum, students create a band, learn new songs each time they master one of the TEKS, grow in popularity each time they master a reporting category and "go platinum" when they complete all of the readiness TEKS.

For Inspiration:

The top 25 best examples of gamification in business

The Gamification of Education

Werbach, Kevin. (January 2017). Gamification [MOOC]. Retrieved from https://www.coursera.org/learn/gamification#