Willing to Try

There's not much to report this week.  We're all recovering from the two weeks of AP tests and trying to get back in to something that at least resembles normal for the remaining two weeks.  We took the fourth test of the trimester this week, and there were no major surprises, especially with the disruptions caused by the AP tests.  There has been a slight increase in the number of students who are coming to class unprepared, but again, nothing out of the ordinary for the end of the year.  So overall, a somewhat low-key week.

One thing that did hit me during the week was the struggle the kids were having with the review exercises we planted with the exercises that cover the current material. The second half of the course is dominated by trigonometry, with the conic sections thrown in for good measure.  The review questions, however, have included analyzing polynomial and rational functions and simple finding the area under a curve problems (without the shortcuts of calculus...it's all Riemann sums), for example.  These were things that the kids knew how to do close to the end of the first half of the course, but without consistent practice have forgotten.  If we're honest, we often forget how to do a good bit of the mathematics we've learned if we don't practice it very often, so it's not really a surprise that the kids have lost some of these  skills over the course of the intervening months.  I've thrown in similar types of review exercises near the end of the second half of the course in years past, and while the struggles were similar, there are a couple key differences this year: (1) a lot - as opposed to very few - of the kids were able to start the problems, and had the right idea but were shaky on the details; and (2) when someone who did remember how to do the exercise went to the board, the other students remembered the material much more easily than in years past.  My hope is that this carries over to next year when they encounter some of the algebraic gymnastics necessary to be successful in calculus, that while they may initially be shaky on the details of the manipulation necessary in an exercise, they will remember the details more easily with a slight nudge in the right direction.

More importantly from my vantage point, the kids are willing to dig into the exercises.  Even if they have forgotten how to do them, or in the case of the current material are unsure how to begin them, they at least try something.  And in that attempt, they at least have a place to start the discussion the following day.  In that attempt, they are trying to draw on the mathematics they have covered not just in my course but in previous courses.  In that attempt, they are showing a willingness to actively engage the exercise, understanding that even if they aren't successful at home, they are increasing their chances of understanding the point of the exercise when it is discussed in class.  And in that attempt, they are showing me they are ready not only for calculus next year, but for college the following year.

This is also why it is really obvious who has done the homework and who hasn't.  The kids who have done the preparation more easily participate in the discussion, whereas the kids who have not, even though they try to participate and try to do the problem at the board, well, there's just something about the way they do it that screams, "This is the first time I've even looked at this problem!"  Hopefully the kids who have let off the gas pedal the last couple days will get back to normal by Monday and finish the year as strong as they began it.  We'll find out soon enough...