Algebra skills and learning physics

Followup to earlier comments on college readiness:

My earlier comments ended up centered on reading, with algebra left as an afterthought towards the end. But my boldfaced comment about algebra, which is that most students do not comprehend the very concept of prerequisites, and thus underestimate the importance of fluency in algebra to their careers, got reinforced this weekend during a conversation with a professor of engineering at Wannabe Flagship U.


First, my example. Simply ask your students to solve a simple log equation on one of the first few days of the semester. No warning, no review, straight out of the blue, no calculators or cell phones. And I do mean simple, something like "8 = log_10(2x), solve for x". My experience at a CC is that the majority cannot do it. They can do it just fine if shown an example or prompted to review it, but they do not know how to do it. This after "passing" college algebra and pre-calc classes that each spent a week or more on that topic along with application problems. Is it any wonder they are strung out in calculus when the get to the log integral? Or when we simply assume they can follow some simple algebra steps in class?

The corollary is that most think "prerequisite" means they need to have "taken" a course, not that they will be expected to know everything they were taught in it. [Again, a question about what we mean when we say that trig or calculus is a prerequisite for our class can make an interesting quiz.] Is it any wonder that they treat trig like a random history class from high school, or the high-stakes test they crammed for back in 10th grade? Take it, cram for it, pass it, and forget it. After all, next semester there will be several weeks of review of anything they need to know from that class. Except there won't be any review. That was then, this is college.

The conversation that reminded me of this was about the failure rate of students in the prof's third-year "dynamics" class, and a general remark that no student should go into engineering unless they had a solid HS background in algebra and were ready to start in calculus as freshmen. (Clearly alluding to weakness in math, particularly algebra, as a signal for future failure in the engineering curriculum.)

But, I protested, that leaves out lots of students, including essentially all of mine. (And not just the returning, adult students who almost always start back in HS-level classes.) And lots of mine have done very well in his program. Oh, that's different, as long as they come in from ICC with all of their physics and calculus complete. They will be a year behind, but they can do it if they really know what they are doing.

He also made a general comment, about abject ignorance of math and physics being the main reason that 20% of his students don't have a chance, but then amended it to say that the failures had usually started at WFU. My ICC alumni did OK. So what was the difference? Well, they seem to know their basic physics and math. Most of the WFU kids also know it, but some don't have a clue, despite spending thousands of someone's money on "taking" physics and calculus. He attributed most of it to a really weak math department at WFU, and social promotion in the calculus classes.

I'd be shocked, but I know that most of those classes are taught by grad student adjuncts or one-time assigned faculty -- not "regulars" like at ICC. (See regular discussions over at Dean Dad's forum for that topic, and concerns that adjuncts and new faculty grade easily to get good evaluations.)

But I also know that one of my weekly goals is to tell my students where calculus concepts they are working on that week (particularly from calc II, which they never have to apply in "anger" in my physics class) fit into what we are doing now, and what they will do next year. Ditto for key physics concepts, such as learning to draw a free-body diagram. The multiple-choice tests at WFU can't test this, but my exams require it. Perhaps more importantly, I tell them why I require it, and sometimes my alumni drop by and tell them the same thing, student to student.

And the most important part might be that last one. Student to student. I cannot take credit for their learning. They have to do that. I'm not even sure I can take credit for convincing them of its importance, because my alumni are a big part of that, although I do try to lay the groundwork.