## Tuesday, August 21, 2012

### R squared equals one

Do you have a friend or colleague who always has the perfect analogy for any situation? I do. My friend, Clark, can come up with perfect analogies for any situation in a second. And they're always clever. I have another friend who comes up with analogies equally quickly; however, they never seem to make sense. To her, the analogy is perfectly clear. To the rest of us? Clear as mud!

The analogy of my blog's name is perfectly clear to me. The danger with sharing the analogy with you is that you might read it and respond, "Clear as mud!"  :)

The coefficient of determination (r squared):
•  is a measure that allows us to determine how certain one can be in making predictions from a certain model/graph.
• represents the percent of the data that is the closest to the line of best fit
• is a measure that assesses how well a model explains and predicts future outcomes
• is expressed as a value between 0 and 1. A value of one indicates a perfect fit and therefore a very reliable model for future forecasts. A value of 0 would indicate that the model fails to accurately model the dataset.
Every day we put our "model" on the line and we test it, hoping for an r squared of one.  We design (what we think is) the perfect lesson with just the right learning target and just the right set of activities to get our students there, and then we go for it. While we are teaching, we check for outliers, for students that wander near the line of best fit, for students that are right on the line, and students who don't even make our graph. A reflective teacher then tries to account for as much of the variability as we can, hoping to get close to that perfect value of 1.

That is what I try to do every day. Achieve a one.  Sometimes I get close. A few times, I've been near 0 and had to start all over the next day. Every once in a while, I "score" a one. And we all know how wonderful that feels! To me, those 1's come with the synergy created between the art of teaching and the science of teaching. They are hard-won. And they feed me (professionally) like little else does.

I hope to share my 1's with you, as well as my 0's and all that falls between. I hope to hear about yours as well. We'll rejoice in our 1's while sharing our strategies, activities and thoughts and we'll analyze the 0's so that - the next time - our outcome will be different.

Looking forward to the journey...

1. So insightful. Strive for the 1 and be okay with some days of getting a 0.75 or even a 0.5! You can totally do it!

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