Common Core Question: What is included and excluded in high school mathematics?

Question

I took pre-calculus in high school, and I did not get to learn about matrices, and conic sections, vectors law of sines and cosines, and etc. I took geometry as well and found that matrices were also covered in the textbook, yet we did not cover it in class.

Why is there some material that does not get covered, yet it is very important to learn, or much yet be exposed to?

I know some students in other high schools in New Jersey who do not get exposed to matrices, and other material.

So is the common core really something normalized for everybody, yet, there is a difference in what is being learned? Sometimes it feels like others have advantages over others based on what is being taught, so what is really the common core doing?

(In my opinion its like a foot race where we all have the same finish line, but have different places to start, some closer to the finish line then others.)

Answer 1

The Common Core State Standards for Mathematics can be found here:

http://www.corestandards.org/Math/

Besides the mathematical standards, see also about the standards, what parents should know, and whatever other parts of the site that may be of interest. From the about section's FAQ:

As to your [edited] post, you write:

So is the common core really something normalized for everybody, yet, there is a difference in what is being learned?

The Common Core is normalized in the sense that the standards are freely available; they are in the first link above, and they can be searched through quite easily using the site. For example, here is a search through the Math Standards for the word 'matrix' to show where and how it appears.

It seems to me that the issue you are describing is around curriculum; note that in the first excerpt above, it says (emphasis in original) that, "Education standards, like Common Core are not a curriculum." Curricular concerns -- picking one, adhering to one, supplementing one, etc -- are major issues facing mathematics teachers.

In just the past couple weeks, Matt Larson (current NCTM President) put out a post on curricular coherence in the age of open educational resources; see also the response from Dan Meyer (link) who has a pointer to another post by (former student of mine! -- though I take no credit -- and occasional contributor to this site, MESE) Tyler Auer (link).

So, concerns like yours are prominent right now among math educators -- including but not limited to math teachers and curriculum writers. Succinctly, to respond to another excerpt from your post:

Why is there some material that does not get covered, yet it is very important to learn, or much yet be exposed to?

One response is, there is more "important to learn" material than could possibly be covered. But another response is, if the Common Core Standards for Mathematics were properly addressed within a curriculum (but whose responsibility is this?) then you would see, for example, matrices and conic sections. The discrepancy in how to meet the Standards' learning goals is an important area of contemporary consideration.

Finally, a digital resource: For a nice online "Common Core Curriculum" to address both the ELA and Mathematics Standards, you might check out the materials freely available at $\text{engage}^\text{ny}$ (link).

Answer 2

Your teacher decided it was not as important to learn as the topics they chose. Textbooks publishers put in everything the teacher might possibly want to use.

If you never learn matrices until a Linear Algebra course, you'll still be fine. You will learn matrices there. They are a tool for solving systems of equations, among other things.