Glaring omissions to me, that is.

The obsession with Al Gebra and manipulations has used up loads of time which could have been spent on

1. Parameters.

The sudden appearance of the word “parameter” in High School :

*“Interpret expressions for functions in terms of the situation they model. 5. Interpret the parameters in a linear or exponential function in terms of a context.” *

The idea of a parameter is basic to the study of functions and relationships. At the start the equation y = mx + b has four letters in it. x and y are variables. What on earth are m and b? Numbers? Fixed numbers? Variable numbers, but not as variable as variables? No, they are parameters for the line. For a given line they are fixed, but for different lines one or both are different.

(When I was at school we, that is the kids, used to call them “variable constants”)

2. Parametric representation of curves and relationships.

For example a circle. With parameter θ a point (x,y) on the unit circle is described by x = cos(θ), y = sin(θ)

and a parabola, parameter a, point on curve given by x = a, y = a^{2}

and for a lot of curves the only neat way.

It also allows for ease in programming graphics of curves.

3. Polar coordinates. The ONLY mention of the word “polar” is with regard to representation of complex numbers. With no way of simple plotting them ?????

How about the function representation of a circle as r = 2 ??

There are others!

It was admitted at the time of development of the CCSSM that too much time was spent on K-8, and HS math was a rough job – so why can it not be modified ???????

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Even for algebra: I’ve been exploring some parabolic problems recently – specifically, I wanted to know how much elementary school teachers should prepare students in advance of the secondary standards – and I searched through CCSS-M for

parabolaandvertex(I tried the latter pluralized asvertices, too).The returns were so unimpressive that I think, surely I must’ve erred…

My reply is a new comment, lack of attention is today’s problem.

Well, they have to spend hours and hours on rational functions, division of a polynomial by x-a, rewriting them, but without the benefit of partial fractions. It looks to me as “CCSS High School math” would be better called “Pre-pre-calculus”, inspite of the fact that must students finish with math at this point. What a strange view of math they must end up with ! “What’s it for” they may well ask.

Excellent points. Your question about modification points directly at the problem with standards. Teachers need a suggested curriculum and a background in mathematics and pedagogy. Then trust the professional to do the job. Good education cannot be a top down authoritarian activity. That will always lead to distortion and omission.

“constants aren’t; variables don’t”.

i quite like “y = Mx + B” (etc.; Capitalize

“Constants”) and used to encourage it

in students (back when i had students).

i’d *sure* like to see it in a lot more *texts*.