Today I gave a cumulative final in my PreCalculus with Trigonometry class. A week ago I gave them a list of standards for what would be on the test, and I allowed them to make a 3×5 notecard with formulas and the kinds of things that we would have on public records (posters) in the classroom.

So far, it’s FAIL.

The test took me 25 minutes to take, fixing mistakes and changing a few problems along the way. Not a single student has finished in 100 minutes.

For many of the students, they can’t recall how to find the equation of a line from two points.

Systems of equations by elimination or substitution is just asking too much.

And expecting them to remember how to find sine, cosine and tangent without a calculator using special triangles is not going so well either.

I can take two lessons from watching my students struggle through this exam. I didn’t teach them how to study effectively and I didn’t think like a student when I was making this test.

On the first lesson, I’ve seen before that my students don’t know how to study effectively, but for some reason I assumed that this year was different. They seemed to do really well on all of the unit tests. My theory now is that all of the short quizzes I gave before each unit test were acting as their studying, and they didn’t need to retain information for more than a week or two. I need to write out how to effectively study for a math final, and begin modeling this at the beginning of the year.

Regarding not thinking like a student, when I made the final I made problems that require a relatively thorough understanding of the topic. I didn’t take the easiest questions from unit tests and put together a final. And I think I made it too long, in the hopes of refreshing some 1st semester skills. I should have started the test with the most recent topics and worked my way backwards through the year.

Well, next time it’ll be better. Constant, incremental improvement.