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What is the Power Law?

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Q: What is the Power Law?

A: The Power Law is one of the Mastery Level Calculation options for Standards-Based Grading that calculates a current mastery level by fitting a power function to the scores for a particular standard.

Say What Now?

Let's say you have a student who has consistent scores on a standard.  The Power Law would fit a line to those scores like this:

Consistant Performance

consistent_performance.png

In this case, the fitted line is at 2.98 and that score will show up in your gradebook to represent the student's current mastery level.  

But now let's say that a student shows regular improvement over time like this:

Regular Improvement

Screen_Shot_2013-10-22_at_10.12.27_AM.png

After 4 assessments, the fitted line is at 3.44, and this score will be displayed in the gradebook to represent the student's mastery level of that standard.  Note that this is higher than any score the student has received, but, given the rate of improvement, is perhaps a reasonable representation of the student's current mastery level.

Finally, let's say a student shows irregular improvement, like this:

Irregular Improvement

Screen_Shot_2013-10-22_at_11.06.46_AM.png

Here the fitted line, and thus the current score in the gradebook, is at 2.68, drawn down by that drop at Score 2.  Depending on the situation, this may or may not be a reasonable score for that student.  Perhaps the assessments are wildly different or the student had a bad day resulting in Score 2.  On the other hand, perhaps the student doesn't have a firm grasp on the material yet and the 2.68 is a reasonable guess at his current mastery level.  Alas, it is the ongoing problem of representing knowledge in easily-consumable bits of data.

Robert Marzano talks about using a power function in Transforming Classroom Grading.  He specifically notes that it is best used on very specific skills.  If you have broad standards, this might not be the formula for you.  We recommend taking a look if you are curious about the research behind the recommendation!

Other Resources

How Do I Change the Mastery Level Calculation for my Domain

How Do I Enable and Manage Standards-Based Grading for my Domain

Transforming Classroom Grading by Robert Marzano

 

 

 

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