Several years ago, a good friend of mine, who happens to be a junior college math professor (unrelated), described to me his “dump” theory. He said his brain had reached maximum capacity, and in order learn a new nugget of information, he had to “dump” or forget something else in order to make room for it. Of course, he was completely kidding. Nevertheless, I’ve seen evidence of his dump theory every year I’ve been teaching.
Many (most?) of my students seem to believe that math classes are entirely self-contained. That is to say, Algebra 2 is the equivalent of Home Economics. There is no prerequisite — anyone is eligible to sit the course. And there is no class which comes immediately after it — Home Ec 2?
They can’t seem to grasp the idea that they might need to be able to factor a polynomial to complete a Calculus problem or divide fractions to complete a Trigonometry problem. They must, must, believe that whatever is necessary to achieve maximum learning this year will be taught this year.
I graded the first Calculus tests of the year earlier tonight. I had to stop counting how many times my students factored . I never even tried to count how many BC students tried to cancel addends and minuends in a rational expression. My favorite is when they cancel the from with another from the denominator. What?!?
I know I’m probably preaching to the choir, and I apologize. I’m just tired of spending days reteaching fractions, properties of exponents/radicals, factoring, solving equations, the quadratic formula, the unit circle, function transformations, and a dozen other things in every single course I teach, no matter the level.
Who is to blame for the problem? Well, the students, duh! Right? I don’t know… I lean toward no. I think we, the teachers, are much to blame. How often do I ask my students to practice in May something they learned in October? If it doesn’t directly apply to the problem of the day, I can honestly say, I don’t. Not very often, at least. And I’ll guess I’m not alone in that boat. It’s not that practice makes perfect. It’s that practice negates the dump theory. If my students practice the old stuff often enough, they won’t have time to forget it all.
So what do I do? I remind my classes at the beginning of the year, at the end of each semester, quarter, unit, chapter, section, and day that this class is not Home Economics. You actually have to carry with you the skills you learn from day to day or you will fail. Fail. But words don’t always work.
This year, I’ve begun something else. I stopped making my tests self-contained. Every quiz and test I’ve given this year (not many, just yet) has incorporated old material. Without a solid basis of material for this year so far, I’m testing on what the students should know from their previous courses. The first quiz in Calculus was on function transformations. The first quiz in Trigonometry was on operations with fractions.
In my classes that are primarily Juniors and Seniors, I’m starting every day with 3 warm-up problems from an ACT practice test. And sometimes I’ll leave them on the board for the Freshmen to try. This is a great way to get a variety of topics incorporated on a daily basis.
If I want my students to understand that they can’t “dump” what they learned in math last year, then the standards I set for myself and for them need to be raised.