Philokalia

Philokalia (Gk. φιλοκαλία): love of the beautiful, the good

There is a certain, I would say unfortunate, trend that has occurred in both mathematics and music education during my teaching career that has really begun to bother me recently.  While on the surface is appears as thought they are very different trends, I would say that at their root they are, in fact, the same.  Before I get started, though, full disclosure: I am also certified to teach high school music, and spent the first 10+ years of my career teaching both math and music, as well as directing theatre.  

In music education, the trend has been to make almost everything a competition.  On one side, I understand the need to win competitions, because that makes it easier to justify the existence of the music program at the school.  To be clear, I think that the need to justify the role of the performing arts in education is absurd, but right or not the need is there.  What this can lead  to is a band or choir working on much less music for a much longer time with the goal being to make the performance perfect, since perfection is essentially what it takes to  win competitions.  What can be lost along the way, however, is the inherent aesthetic beauty of the music itself.  The focus changes from moving the audience to impressing the judges.  And in my opinion that is not a good thing.  In many instances there is a need for greater balance between being competition ready and just playing the music.

In mathematics education, there has been a push toward making sure the mathematics being taught is useful.  If the content is not immediately and obviously applicable to the everyday life of the student, then it is not important, or at the very least not as important as that which is applicable.  What gets lost along the way is the inherent beauty of the subject and the joy of just solving the puzzle.  My graduate degrees are in pure mathematics, so I find it fun to take the pieces, discover the patterns, and "play the game".  Don't get me wrong: I understand the need to show the kids that math is useful, and that this usefulness can be a great motivator.  But one of the things we tried to put into the exercises we created as we built the course was a balance between the basic mechanics, the applications, and the "math for the sake of the math".  And what's amazing is how the kids actually appreciate and enjoy the math for the sake of the math.  

In both math and music, we have, in many ways, abandoned the beautiful for the useful.  And while I understand the need for the useful, I firmly believe that we need to rediscover a love of the beautiful.  

Taking Notes

We have reached the end of the first trimester, with final being given last Wednesday and Thursday. At the end of each trimester, as the kids take their exam, I collect their binders and grade them for completeness. The binder is to contain everything: handouts, notes, tests...everything. One thing I have noticed in making the transition to Harkness is that the kids don't really know how to take notes. Before making the change, the kids were ok at taking notes, meaning they were ok at scribbling down what I wrote on the board, but even then they missed a lot of the important information because they normally didn't write anything down unless it was written on the board. And in a Harkness classroom, with so much of the information being delivered in the course of the discussions, the kids have a difficult time discerning what they should be writing down. It's not surprising to me that the kids who do well in the course tend to be the ones who have organized binders and a fairly complete set of notes. I really focused this trimester on what the successful kids were doing as far as their notes were concerned, and will be "imposing" the following on the kids next term:

(1) The homework must be done on a separate sheet of looseleaf paper. Some of ths kids try to do the initial work on the actual worksheets. None of the successful kids do this.

(2) Corrections are to be made on the homework sheet without erasing the original mistake. The successful kids understand that they need to learn from their mistakes, and they tend to make corrections in pen next to the original work so they can remind themselves of what their instinct told them to do originally, and so they can have the self-awareness to avoid making the same mistakes in the future,

(3) A clean set of notes must be made on looseleaf paper during the discussion, especially at the end of the discussion of each exercise. The reason for the looseleaf paper is to allow the kids to see their original work as they write the clean set of notes, but still be able to keep them separate from each other.

(4) A glossary and a formula sheet must be created as we make our way through the trimester and kept at the end of the "clean notes" section of the binder.

For my part, I will need to check the binders with a certain amount of regularity, the hope being that not only will this improve things for the kids in my class, but also in their other classes. Granted it will be up to them to transfer the skills, but my hope is the success I'm anticipating will be contagious. I'm certain I'll write more about this later...

Being Human

It is amusing for me to watch the student office aides when they walk into my classroom with a note for one of the kids in my class, simply because most of the time it's difficult for them to find me.  It's clear from the look on their faces that they don't expect to me to be seated around the table with my students.  Most often they look toward the board first, then toward my desk, and finally toward the lectern, at which point I raise my hand, waving it back and forth to get their attention and inform them of my location.  The same thing happens when another teacher unfamiliar with Harkness comes to my room.  The administrators, however, are not only used to the fact that they won't be able to immediately locate me in my classroom, but they will sit down at one of the tables with the kids when they come in to my classroom for one of their monthly walk-through observations.  

While I never would have expected to be saying this a couple years ago, there's no place I'd rather be in the classroom than seaeted with the students.  When I used to lecture, I tried as much as possible to be a real person. When we went through the homework, I didn't rely on prepared notes or the work I had done in going through the exercises ahead of time.  Instead, I worked through the problem, talking through my thought process, and, yes, occasionally making mistakes.  I didn't try to hide the fact that I make the same sorts of mistakes the kids do...mistakes along the lines of 1x1=2 (which, for the record, is a mistake I made on one of my Ph.D. preliminary exams).  In short, I didn't hide the fact that I am human.  There are some teachers who feel threatened by even the possibility that they might make a mistake in front of their students, and even when they do they try to cover it up rather than simply admitting it and moving on.  They don't make a move at the board without first consulting their notes or the textbook.  They promote an air of invincibility and absolute control that, quite honestly, I have never understood.  In my opinion, this is one of the reasons some teachers are hesitant to implement, or are even hostile to the idea of trying, a discussion-based method of instruction in their classroom.  They cannot bear the thought of not being the infallible master of the domain that is their classroom.  They cannot bear the thought that their students just might figure out that they are human.  

For me, building a solid rapport with my students has always involved making sure the students understand it's not me against them, but rather us working together to help them learn the material.  And one of the things I love most about Harkness is that I get to sit at the table with the students and just by the physical arrangement of the room emphasize that we are in this together.  I love the fact that I get to hang out with the kids a learn some math.  And yes, I've learned plenty of math from the kids over the years, most especially during the last year and a half.  I love the fact that they know I'm not perfect, and that one of the things they learn in my classroom is that it's ok to make mistakes so long as you admit them, learn from them, and try to avoid them in the future.  In the course of the discussions, I find out more about the kids than just their math ability.  I find out about their other classes and the parts of their lives outside the classroom they are willing to share.  I get to hear about marching band rehearsal, soccer practice, youth  group, Catcher in the Rye, and family holiday traditions.  In turn, they get to find out that I'm very sarcastic, that I root for the Buckeyes, that some of the novels they have to read for English class I like but others I don't, that church is important to me, and so on.  In other words, without crossing any inappropriate lines, we get to be real with one another.  We get to be human.  And against the backdrop of being human, we learn some math for 70 minutes a day.  I honestly can't imagine my classroom being any other way.