A Lack of Algebra Skills

My pre-calculus (trig/analysis) students finished a test Monday, and the results were positive only to manufacturers of red ink.  While over half of my students scored A's and B's, the most frequent grade was an F.  And some of those scores were such low F's that a better grade would be a G.

I guess I could take heart that many students, even when making a mistake in a problem, got the trigonometry correct.  They understood the use of sum and difference identities, half-angle formulas, and double-angle formulas.  No, too many of the errors are algebra errors, e.g.:

• (cos x + sin x)^2 is not cos^2 x + sin^2 x, and similar errors
• not knowing how to manipulate numbers under a radical sign
• not correctly manipulating numbers, especially fractions within a fraction
• not "seeing" simple substitutions that would lead to a solution

Four or five years ago my district switched from the so-called traditional Algebra 1-Geometry-Algebra 2 sequence to Integrated Math.  While I'm not fond of integrated math--I prefer focusing on a set of topics for a longer time for deeper understanding--I don't think it's the integrated math per se that's causing such a precipitous drop in Algebra skills.  I think it's the integrated math curriculum that our district has adopted.  While it's big on visualization of topics, it's weak on actual algebra.  There aren't large problem sets divided into easy, moderate, and difficult problems that a teacher can choose from and help differentiate for students of different abilities; no, there are only a small number of practice problems on each topic, and there's no differentiation for the teacher (or student) as they're pretty much all bland and of the same difficulty.

I guess our integrated math teachers could try to augment the curriculum, but teachers will recognize that that brings with it its own set of problems.  And honestly, our teachers aren't paid to create curriculum, they're paid to deliver the district-approved curriculum.  Our district recognizes that there's a problem but takes only half-measures in response, for example, adopting an "augmentation curriculum" for our Integrated Math 1 classes--after how many years?  and with only how many years left in this current adoption before we rush to buy a new round of crappy textbooks?

I try not to criticize my school or district on this blog, but when I see the obvious damage that's being done to students by the district, it bears pointing out.  Our textbook adoption process is broken because our district is broken.  There is no leadership at all; in fact, the response from the district is often "we're letting the schools experiment to see what works best"--and then, if something does work well at one school, the district won't mandate it, but rather will allow other schools to "try" it if they want to.

In the meantime, too many students are learning math at a superficial level and are not prepared for STEM majors after high school.  We've closed doors on them before they ever even knew the doors were there.

Update:  I've checked with other teachers who administered these chapter tests (in their many versions) and all are horrified by the algebra mistakes.