Even Easter Sunday finds me baffled at the complex dimensions of education in our country. What may seem obvious to many, assigning end of semester grades, confounds me at times.

However, since today is a holiday, this post is ultra-short.

I simply post the following graphic for your thoughts and comments. A draft post penned earlier awaits further editing in my drafts folder. Hopefully, I will post it in the next couple of weeks. In the meanwhile, what does the following figure evoke for you?

Happy Easter!

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## About Dave aka Mr. Math Teacher

Secondary math teacher teaching math intervention, algebra 1, honors precalculus, and AP Calculus AB. I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.

All three curves have value with some explanation:

1) Normal Distribution: Defines the range of outcomes expected with population in quintiles.

2) Honors Precalc: Defines the range of outcomes in quartiles with a biased midpoint.

3) Example HS: Defines the range of outcomes in quintiles. Does not intend to provide

any information about “best” performers. Better described as:

A) Exceeded requirements in most/all aspects.

B) Exceeded requirements in some/many aspects.

C) Met requirements.

D) Failed to meet minimum requirements in some/many aspects.

F) Failed to meet minimum requirements in most/all aspects.

Substantially flattens differentiation on the upper range of outcomes

especially if requirements are set low enough. Characterized by tests

that have 100% outcomes by a significant number of students.

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Thanks for your comments, Terence. As the distributions are not uniform per letter grade, quartiles & quintiles are not mathematically correct. However, your interpretation is insightful re: compression at high end, especially with the paucity of data and context to accompany my graphs. I’ll update everyone soon via an associated post.

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Perhaps some populations do not fit a normal distribution.

Consider http://www.businessinsider.com/google-policy-to-pay-unfairly-2015-4

The selection process for Honors Precalc may produce just such a set.

As a (former) manager of computer programmers I can assure you that productivity in this group of professionals does not follow a normal distribution.

Natural selection continuously eliminates members who fall on the left of the curve (“I don’t have to run faster than the bear, I just have to run faster than you run.”). Education has a similar responsibility. A very few cannot meet the academic requirements for elementary school. Some (again, only a few) don’t have the ability to meet reasonable requirements for high school (social promotion aside). At the college level it becomes clear that some will not succeed (despite the clamor for everyone to get a college degree). Certainly there should be no expectation that everyone is capable of perfomring at a level required to deserve and obtain an MS or PhD

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I agree with the Google article’s premise: power-law distribution versus normal distribution for compensation as well as your comments re: natural selection pruning the distribution. The two distributions I show in contrast to the normal distribution reflect grades where the N = 1,500 (example high school) in one case (honors precalculus) and N = 90 or so in the other. There is definitely a self-selection bias with honors precalculus versus the entire school population. More to follow in a post, and/or subsequent comments. Thanks for commenting.

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