Monday, January 4, 2016

normal probability cumulative density function

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If the title of this post seems awkward, imagine my feelings when I found it on page 36 of New York State's Algebra II Fall Sampler from Fall 2015.

I encourage you to look at that link, and keep in mind that just a few minutes ago I Googled that phrase (in quotes) and got 3 results, with the Fall Sampler being the second in the list. Here it is. ( I clicked the "If you like" at the bottom, and picked up one more link.)

The area under a curve is a whole subject in and of itself (part of Calculus), and its discovery (or invention?) generally begins with rectangle approximations, trapezoidal approximations, limits, continuity, etc. Are these all part of Algebra II? I know that the process of approximation of the area of a portion of the Cartesian plane bounded above and below by continuous functions of x is very highly programmable. A lot of mathematics is involved in creating such a program. Expecting high school students to use such a program while remaining ignorant of the mathematics involved in its creation seems to be a disservice to those students.

The whole business about Common Core seemed predicated on understanding mathematics. Does someone who has mastered the art of pushing buttons on a calculator understand this concept? And whose idea was it to base a high school sample question on "normal probability cumulative density function".

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