Day 133 (of 188) mean median or mode. Are all averages equal? Thanks to #sblchat
Tonight was Wednesday and that means #sblchat. Always a lovely chat that always fires me up for the last part of the week. Tonight we had an interesting sidebar about taking Standards Based Learning (rubrics, performance standards) which often have descriptors that educators often then number in order to arrive at a (usually prescribed) letter grade or percent. As a late in life lover of math, I love opening awful discussion questions such as:
– is zero even a number? Can it rationally be used to calculate a ‘score’ (love the philosophical debate over what nothing is – or should that be isnt??)
– we categorize the learning style based on percentages above the number 50 – shouldn’t there be better descriptors for the learning below the ominous “50”? (ps just a coincidence that that was my number when I played football).
– can all 3s (next to learning outcomes) = a B in one subject, an A in another and a C+ in a third? (Yes in report cards I have seen!)
– for those that still like to take an ‘average’ of learning – which to pick. Mean median or mode? Just because many like the mean (add ’em all up and divide by how many you added) doesn’t mean it’s righter than other averages.
I’m gonna show some scores out of 4: 0, 4, 3, 4, 1, 2, 3 , 3, 4, 3,
The mean: 27/10 = 2.7
The median (middle) from lowest to highest: 0 1 2 3 3 3 3 4 4 4 = 3
The mode (repeated most) is a 3 (with a 4 pressing hard)!
I worry when we just ‘trust to the math’ without thinking about what the math means to the Learning. SBLchat has given me some great confidence to feel more confident to ask the tougher questions and stay focused more on what the learning is about (descriptive feedback) than what the numbers may or may not say.
This can be especially true when the numbers get bigger (quizzes tests and other tasks & the subjective ‘weighting’ of these tasks without considering ‘why’ there may be outlier marks) as can be seen seen in the highly influential Ken O’Connor from his fabulous book 15 Fixes for Grading:
Don’t let numbers distract you from the learning that is (or is not) occurring. Know the why.