Sunday, October 08, 2006

Standards Coverage

In a comment in the previous post, Darren says:

I find the Algebra 2 standards to be fairly "aggressive", like drinking water from a fire hose. How you find time to add in topics that are not in the standards, I don't know but would be most interested in learning.

(I think it is worth starting a new post to answer this... I'm interested, as always, to hear people's thoughts.)

Well, you're right. We are not able to adequately cover all the standards as they are written, especially since our students start so far behind the curve. What we've done is to strand out the standards over the 4 years. We leave some things out of Algebra 1, and push them into Algebra 2. Some of the Algebra 2 standards we then move into Pre-Calc. And some, we decide not to do at all.

When deciding what to cover (and in what depth) in Algebra 2 Honors, I look not just at the list of state standards, but at the blueprint for the standardized test (i.e. what are the key standards that comprise the bulk of the test), at what will be covered in Geometry and Pre-Calc, and at what will be most useful for students moving in a trajectory toward Calculus.

I know we can't do it all, so my goal is to balance the required coverage with a strong scaffolding for success in Calculus - all with an eye to who our target student is.

For example, though I think conic sections is a great topic, a thorough unit would take my students many lessons to master - yet there is only one single question on the test. So we leave it for Pre-Calc.

The same is true for combinations, permutations, probability and stats, mathematical induction, series - all together these topics comprise just about 20% of the test. I choose to focus on the rest, and go deeper by including relevant scaffolding, math analysis components, word problems, and so forth.

With our students, I believe this actually yields higher test scores than covering everything more shallowly would.

There is discussion of this going on at Darren's site if you are interested.


Anonymous said...

Okay, that makes sense, but what do you do about pre-calc, since you move part of algebra 2 into it? Was it already short on content, or do you have to them move something out of pre-calc?

Dan Wekselgreene said...

Pre-calculus is different than the other math classes in that there are no defined standards for the class. Our pre-cal students take the Summative Math standardized test, which is essentially a summary of Algebra 1, 2, and Geometry concepts.

There are standards defined for trigonometry and math analysis, and, as far as I understand it, there is a wide variety between schools as to what is actually covered in a pre-calc class.

Our pre-calc class is being redeveloped this year, so it will include a few Algebra 2 topics, lots of the trig topics, and a few math analysis topics. Since there are no specific requirements, we are free to choose what we think will be most helpful for our students. I'm not designing the curriculum - just consulting with the teacher who is, so I can't say right now what it will look like exactly.

Darren said...

You're right that "pre-calc" is an amalgamation course, but the state math standards explicitly state that trig and math analysis can be combined into one "pre-calculus" class. In fact, that's what's done in our district, and I'm teaching the course for the 4th year in a row.

Even combining the standards for those two topics, the pace is not near as fast as the pace required for algebra courses. In fact, I usually reach all the standards by about the first week in May. At that time I review some of the topics that the calculus teachers tell me are critical--logarithms and graphing functions and rational equations (both algebra 2 standards).

Darren said...
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