Sunday, January 27, 2013
Over the last week or two, the discussions in my "A" section (the first half of the pre-calculus sequence) have been off task quite a bit, and after repeatedly pointing this out to the students to no avail, I asked them to devote part of their weekly journal entry to discussing why they thought this was happening and to proposing solutions. Student after student kept mentioning the same thing as far as what they see as being the problem: some of the questions are not challenging.
Currently, part of what we are covering is exponential and logarithmic functions to which the students were introduced last year, so they do have a level of familiarity with some of the material. (However, the way the worksheets have been structured, only two or so of the eight daily exercises are about exponents and logs.) Since the "rules" came back to them fairly quickly, the exercises that were intended to help them understand where the "rules" came from became the easy exercises for the day. I have a feeling that this may come back to haunt them on the test, as the questions there are intended to determine whether or not they truly understand the "rules", and are not just seeing if they can use the "rules". Regardless, the fact that the students saw these exercises as being easy was seen as the culprit for the amount of off-topic time, because the student presenting the problem at the board was being ignored by the other students at the table, believing that they didn't need to pay attention since they already understood the problem.
There were other times during the week, however, when the discussions went very well. The students mentioned this in their journals as well, commenting that they believed the discussions went better when they encountered a more difficult exercise, since the entire group was truly needed to successfully complete the exercise. This has led me to take a critical look at the exercises on the worksheets, since I firmly believe that the exponent and log problems are just as difficult as the other exercises. The conclusion to which I have come is that I am assuming the students will put forth the effort to truly understand the material rather than just relying on what they already know about a topic. Any math teacher who has had to lead students through exponents and logs is well aware that the first time students encounter them, memorization tends to trump understanding. The difficulty I'm having is that the memorization came back relatively quickly for the students this trimester, so the struggle of trying to solve the exercises didn't happen...they relied on their memorization, were successful at solving the problems, and let it go at that. For the record, the memorization did not return as easily last trimester, and therefore the discussions were more fruitful. So, I'm not convinced that it's the exercises that need to be changed (and by changed, I mean made more challenging). Perhaps the students actually do understand exponents and logs more that I'm giving them credit for, which would not really be a problem from a math standpoint, but rather from a class management standpoint: what do I need to have prepared when this happens in the future?
The other thing that the students consistently mentioned was that, regardless, not paying attention to the students at the board was disrespectful and rude. Of course, I agree with this completely, and I intend on allowing the students to take their own admonition to heart and make the necessary adjustments themselves: if they know what's wrong, then they should be able to make the corrections without me.
In the big picture, this is again a strength and an obstacle of running a truly Harkness classroom. Letting the students be responsible for their own education means more than guiding them through the discovery of the academic content of the course. It means letting them learn what it takes to have a meaningful discussion and what it takes for a group to succeed. It means letting them work through the difficulties, having them reflect on and uncover what the real cause of the difficulties is, and make the corrections themselves, rather than having the teacher impose a solution (which I did a couple weeks ago with the popsicle sticks...still deciding whether or not that was a good idea). It means stepping back and trusting that the students can and will make the necessary corrections, and after 22 years of stepping in instead, it's really difficult to have the patience needed to allow it to happen. I want every discussion to go well, to be as fruitful as it can be. When it doesn't happen, my instinct is to take over, get involved, "fix" it...which is not what Harkness is about. I need to constantly keep in mind that I am there to guide the students, not to do the hard work for them. I've been successful at doing this with the math. However, I still have some work to do when it comes to the actually dynamics of the discussions themselves. Fortunately, the students have provided a good road map for me (courtesy of their journals)...which is much more in line with the Harkness philosophy.