It is a simple fact that every worksheet must have a some number of exercises, be it 5 or 50. On the worksheets that the other honors pre-calculus teacher and I wrote to implement Harkness this year, the number of exercises per worksheet is 8.
It is also a fact that regardless of the number of exercises on a worksheet, the students will take completing the worksheet as the "goal for the day". This has been the prevailing attitude in my classes, and it occurred to me recently that this attitude has been getting in the way. You see, in the race to the end of the worksheet, the students were rushing through some of the exercises, at the expense of having the good, in-depth discussions. The reality is that even the "easy" exercises should be discussed thoroughly to make sure that the understanding the students think they have actually goes beyond the superficial and mechanical to a true, concept-driven understanding. However, if the goal is to finish the discussion of the current worksheet by the end of the class, then the easy stuff gets pushed aside and if the difficult stuff starts taking too long, it gets shorted as well.
This prevailing attitude came to an end late last week, when I explicitly reminded the students that having the in-depth discussion of the exercises was the goal, and that getting to the end of the worksheet was not. That day, we did not finish the worksheet and I did not freak out about it (I'm fairly certain the students were expecting me to panic at least a little bit). In planning this trimester, we made 30 worksheets for the 60 days...clearly, even with review days and test days figured in, we were expecting the worksheets to take longer than one day apiece. Somewhere along the way both the students and I lost sight of this, and the discussions were suffering as a result. Since the reminder and the subsequent refocus by the students, the discussions have been going much better...and actually, that's an understatement. So many of the students mentioned that the more deliberate pace and the lack of pressure to get to the end of the worksheet has improved the discussions and the understanding on the current worksheets...I honestly lost count how many students said this and thanked me for it.
That being said, I also realize that there is a balancing act here. We still have a certain amount of material we need to cover, so the students and I need to find the fine line between too slow and too fast, get to that line quickly every day, and do everything we can to not stray from it. Hmmm...life lesson? I think so.