Finishing Strong

It's been fun this week watching the kids work with the new material.  Struggle is probably the more accurate word.  We have been working with rotating conics, writing conics in parametric and polar forms, and finding powers and roots of complex numbers by using DeMoivre's theorem.  None of these topics is necessarily difficult, but all of them are new twists on old material, and the rotations in particular are long and tedious, requiring a fair amount of patience.  And with the inconsistencies in the schedule during this unit, the connections to the old material haven't come as easily.  Couple that with the fact that this unit has a greater percentage of new material than the others and it's made for more struggle than usual for the students.  However, that did not deter the vast majority of them.  Instead of backing down, they dug in.  Admittedly, I have honors level students, and it irritates them when they don't understand something, and yes, I understand that Harkness allows me to use that to my advantage.  However, the fact that they redoubled their efforts to come to grips with several bits of new material has been really fun to watch.

Even more, it has been great to see the progress the kids have made during the course of the year in terms of their willingness to take on the challenge themselves, coming to me for help as their second or third and not their first line of attack.  Most have truly taken responsibility for their own learning, and have learned to work together and rely on one another.  Most are willing to admit when they are lost...quite the accomplishment for an honors student.  The fact that they are not letting this deter them is another accomplishment, since often an honors student, who is so used to things coming easily to them, can actually give up faster than other students when confronted with an academic challenge.  Unfortunately, those who have not reached this point tend to slow down the conversation, trying to force an answer and an explanation out of themselves rather than working to discover or create a solution with the group.  And there are still a few kids that are not preparing for class; however, the other students did not allow that to slow down the discussions, essentially working around the fact that there was a bit of "dead weight" in the group, still including them in the conversation but not allowing them to dominate the group either with questions or with an explanation intended to cover up the fact that they are unprepared.  The good side of this is that the number of unprepared kids dropped drastically this week, and it showed in the discussions.  Which means that, for the most part, the kids are back on the gas and finishing strong, just like I had hoped they would at the end of last week.

Next week will go quickly: Memorial Day Monday, test Tuesday, exam review and a couple end-of-the-year disruptions the rest of the week, and then final exams the following Monday and Tuesday.  Which means that technically I have completed the year without lecturing.  Never would have thought it possible...

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...

Flexibility

It's been a relatively abnormal week in terms of the schedule.  Monday I was out for religious reasons (any Orthodox Christian knows that this is "recovery week" from Pascha), and since I teach the honors-level pre-calculus, lots of my kids were out a day or two the rest of the week taking AP exams.  In fact, yesterday my first bell class was down to 12 students.  So, a few observations:

• The report from the sub on Monday was glowing.  The kids who were in class (the AP Chem test was Monday, so numbers were down) came in, got to work, kept track of the participation...all without needing a prompt from the sub.  Looks like they've taken ownership of the course and responsibility for their learning.
• Switching the groups every day as I do is an advantage during weeks such as this.  Since the kids are used to being with a different set of kids each day, they easily reorganized themselves into reasonably-sized groups when the number of absences made it necessary, and the conversations continued as usual.
• Along those lines, one of the students from my 3rd bell class was going to have to miss several days this week because of the AP tests.  Since she does not have a 5th bell class, she asked if she could join my 5th bell on the days she would miss 3rd bell.  Of course I said yes (seriously, a kid is asking to not miss class...what's not to love?).  Her experience, in her own words: 

"This is the beauty of this class. I was able to come into a completely different class than the one I'm normally in and have meaningful and interesting discussions. The format of the class encourages a kind of intimacy that doesn't usually exist in this school. I could sit down at a table with people and have a conversation, when I was probably avoiding eye contact in the hall three minutes prior. It's fantastic."

• Harkness for 12 is very different than Harkness for 30.  On the one hand, with only 12 students in the class we had one group instead of the usual three, which allowed me to be at that one table the entire class.  I saw and heard every comment, suggestion, and inquiry, and was able to keep the tally of the discussion points myself rather than relying on the students to double-check my count.  On the other hand, with me at the table with them the entire time, they were looking for my input more than normal.  So, 12 allows me to have more direct contact with all of the kids the entire class period, but 30 allows for (or more accurately, requires) more ownership on the part of the kids.
• The kids were great about making sure the kids who were absent were brought up to speed the next day, without me prompting them to do so.  They made sure that no one missed the opportunity to discuss any of the exercises.  Granted, the initial part of these discussion was much smoother than usual, since some of the kids had already discussed them once and could therefore more easily explain them to the students who were absent, but still, the team-oriented aspect of it was great to see.

Conclusion: Harkness is far more flexible than a standard class, and is able to handle schedule changes far more easily.  With this much disruption during the week, finding a way to make sure all of the kids got all of the information used to take some serious creativity.  Delivering a lecture more than once for the sake of the absent kids while figuring our what to do with the kids who didn't miss the lecture the first time made things interesting to say the least.  Having the kids who were in class the first time explain the new material to the kids show weren't there was one option, but for kids who aren't used to explaining the material on a regular basis this was difficult at best.  Meanwhile, the Harkness classroom just keeps rolling along without any major changes and, in all honesty, making more progress than the regular class does with the same disruptions.

So overall, a good week of learning both for the kids and for me...just the way it should be.

Listening

It's May, and even though we have five weeks left in the school year, there is always an atmosphere that arrives in May that makes it seems as though tomorrow is the last day of school when in reality it is five weeks away.  Prom is now over, AP tests begin next week, and so the struggle to stay focused continues.  On the good side, the overwhelming majority of the students are putting forth the effort, preparing for class, and responding positively to the requests I've made over the last couple weeks.  And the "poster class" is still doing pretty much everything right.  However, the other classes, while certainly better, are just not quite as on track as the poster class.  So, this week I tried to pinpoint exactly what it is that the poster class does better than the others, and I think I've figured it out: they listen.

By that, I don't just mean that they hear one another.  No, they really listen to one another.  They seriously consider the suggestions of each and every person in the class, trying to find the possibility of a solution in each proposal.  They respond to the questions and confusion others are experiencing, adjusting their explanations in the hopes that the new description of the solution will hit home.  They takes turns, rarely having more than one person in the group speaking at the same time.  They politely make corrections to the proposed solutions of others in the group.  There is a level of respect for the individual, in particular for the value of both their contributions and their needs.  And in all of this, the conversations do not feel forced or stilted...they are very natural, complete with a reasonable but unobtrusive dose of joking around.

The question, of course, is: what has gone right with this class that has not in the other three classes?  The answer to this still eludes me, because from my perspective I started each of the classes the same way at the beginning of the trimester, but have needed to give reminders to the other classes throughout the term that the poster class simply hasn't needed...if it ain't broke, don't fix it is coming to mind.  I really need to continue sifting through things to try to figure this out.

Finally, there is a very real test of Harkness coming on Monday: I won't be at school.  Pascha is this Sunday, so in addition to those church services we will be back at church on Monday morning.  The test will be this: the plans I left for the sub state, quite simply, that the class is run through student-centered, student-run discussions, that the kids know what to do, and that they will take care of the class for the day, including keeping track of the participation points.  I told the kids this at the end of class on Friday, so they know the expectations for Monday.  We'll find out in Tuesday how much progress they were able to make and how much they have taken responsibility for their own education.  In other words, we'll see how much Harkness has become part of the way they approach learning.  I'll let you know the results next week...