Friday, October 28, 2005

Algebra Problems

Long-time readers might note a certain lack of complaining about students in this space. This semester I have the best students that I have ever had: these are the students that people assume enroll in college. Unlike some classes in prior semesters, my students are well-behaved, polite, and respectful. Sure, the calculus class is a bit lacking in self-discipline and self-motivation, but beyond that I have ideal students. Their only problems are strictly mathematical.

Allow me to point out out that almost all of the calculus students can do algebra; their mathematical problems are fairly minor. Some may have to work at it more than they should, and we have had some parentheses issues, but, overall, the calculus students can use the distributive law and do not do stupid things with radicals and exponents. They are wary of rational expressions and a bit shaky on trig identities, but they are as skillful and well prepared as any students that one might recall from some mythical glory days back when freshmen could do algebra. Heck, only one has applied the "freshman's dream" so far.

Unfortunately for my gen-ed class, many of them can not do algebra at all. Again, these students are bright and interested. Good students; they seem to like the class. Almost all of them hard-working and with excellent attitudes. Again, the type of students that one would hope typified college students. (And in sharp contrast to some of my colleagues' classes -- several instructors have had to program the phone numbers for Campus Security and the Student Conduct Board into their cell phones.) If these students were as serious about their high school educations as they are about their college educations, their lack of algebra skills can not be entirely their faults.

And yet, the most missed question on the test (tripping up between a quarter and a third of the class) was missed because of algebra. They can set up the equation, but they can't solve for x. Here are four typical responses to the same test question.