Final Exams

Well, we've reached the end of the first trimester, which means we've reached the first round of final exams.  One of the things the other honors pre-calculus teacher and I decided over the summer was that we would not change the format of the final exam or of the review we gave for it.  We did this for the obvious reason: we wanted an objective measure of whether or not the students were doing better this year.  As in the past, we spent two days on the review exercises.  The results were not surprising.

First, the review itself was easier.  The students came in better prepared and had far fewer questions than in the past.  And on the exercises with which they initially had trouble, they were more willing to at least try something than students in the past.  And on the day of the exam there were far less last-minutes questions than there have been in the past, and overall there seemed to be less anxiety about the test (either that, or the students this year are remarkably good actors).

Then came the test itself.  From a grading standpoint, this year was more difficult, but for all the right reasons.  The mistakes that the students made were more "calculation" than they were "content".  Content mistakes are easy to grade, since it is immediately obvious that the student does not know how to solve the problem.  Finding calculation mistakes in an otherwise correct solution, however, is far more difficult and far more time-consuming.  Don't get me wrong, I'm very happy for the change.  Grading the paper of a student who at least knows what they're doing but (like me) has occasional difficulties with 1+1=2 is much more enjoyable than the alternative.  As I've said previously, I would much prefer that the emphasis in education were placed on how much the student has learned rather than on the grade they have earned, and as such when the test indicates that the students have learned the material, the rest is worth it.

Now, admittedly, the mathematician side of me knows that the scores on one set of exams is not enough to definitively indicate that one method of teaching is better than another.  But this was about more than just the numbers.  The way the students were able to review more independently, the variety of methods they used to solve the some of the exercises, and the overall tenor of the classroom over the last few days all have their source in one place: Harkness.  The students are less dependent on me for the initial attempt at a problem and have less anxiety when it comes to solving multi-step exercises, and having seen the progress the students have made in both of these areas as the trimester progressed (and having not seen the same kind of progress in previous years) tells me it's working.  

And despite the initial resistance, the vast majority of the students have acknowledged their progress as well.  In all fairness, there are still a few students who would prefer to be spoon-fed and then regurgitate the method they were shown rather than figuring things out on their own.   After all, mimicking the teacher has worked for them for the last 11 years, and at this point, it's easier for them.  But looking at what will be better for them long-term, I know that mimicking others is not the way to go.  Those who can mimic are plentiful; those who can problem solve are rare.  And those who are willing to make the effort to at least attempt to solve any problem set in front of them are the ones the colleges and employers keep saying they want.  By the looks of it, Harkness-trained students are what they're looking for.  And one trimester in, I'm more than willing to provide.