First day, Fall 2009

Today was my first day back to teaching. As I mentioned previously, I am intending to start using a problem-based approach to my Geometry Honors class, so I am intending to do some blogging about how well that is working.

Today, however, was all about delivering information and getting our feet wet. Although I handed out the book of problems to my Calculus BC class, I’m still in the process of typing up the Geometry questions, so they will be getting them a bit at a time, starting Thursday.

In my Geometry Honors class I began by having some directions on the board and a problem. As students tend to clump together when they come in the room, I break them up a little at first by having them arrange themselves by birthdate around the room. I use trapezoidal tables which I have arranged in a sort-of circular configuration – as close to a Harkness Table as I can come. For more on the Harkness philosophy, click here.

Two interesting things occurred in my second Geo Honors class. First, there were 12 girls and 3 boys! I have never had such a lopsided arrangement – and definitely not in favor of the girls. I’m really excited to see what this does to the class dynamic. The second thing is that same class has two sets of twins – and three students with the same birthday! (Well, two of the three were a pair of twins, so maybe that doesn’t count.)

Once arrange, the problem was one I have seen around the internet before – it may have even come from the Google test. Given the following numbers, determine the pattern:

1

11

21

1211

…

The first class worked on it for about 12 minutes. There was some great discussion, although I definitely had to give them some hints to keep working. Granted, it was first period in the day. The second class worked on it for about the same amount of time, but a group of 4 that were working together were coming very close, and sealed the deal when I gave them the next line:

111221

They were able to continue the pattern and explain it clearly to the rest of the class.

We did a quick name game, the reason being they need to know each other to be able to work together solving problems. It gave them a chance to get out of their seats and engage in a fun little activity. The rest of the period I began explaining the ‘plan’ for the year. I figure it will take a week or two for it all to sink in, but we will start with the problems after the next class (Thursday).

In my calculus class we did my traditional first day problem:

If A=(0,-10) and B=(2,0) find the point(s) C on the parabola which minimizes the area of triangle ABC. Maximizes?

What I like about this problem is that students immediately run to an integral, which they then try to differentiate. The solution is mostly geometric with only a little bit of differentiation.

I taught a number of my BC students in Geometry Honors a number of years ago, and it is really fun to see them 4 years older. It’s going to be a good year!

Gone for a bit…

Now that I have started posting again 2-3 times a week, I feel obligated to let everyone know that I will be attending our schools 11th grade Wellness Retreat from tomorrow (Tuesday) morning until Friday afternoon so, while I have posts I am working on, there will be no new ones before this weekend.

Have a great 4 days! I look forward to sharing my thoughts on the experience, as well as how the first few days of school go next week.

Ciao.

Winding Up For the New Year

This year finds some things the same and some different in my schedule. I am continuing, for my 7^th year, to teach AP Calculus BC. This will be the third year that I am using the problem solving curriculum I have modified from Phillips Exeter Academy’s program. This summer’s edits have been less substantial than last year, mostly fixing typos, changing some wording and deleting a few redundant and/or unnecessary problems, and redrawing a few graphs. Although I had been concerned that the program would not work as well for last year’s group, the AP results have convinced me otherwise.

What I plan on working more steadily on with regard to Calculus is making assessments that better reflect what I am asking them to do, staying on top of reading their weekly abstracts, and writing/LaTeXing my solutions and comments to the problems so that, hopefully, by the end of the year I will have an official ‘Teacher’s Guide’ to go along with the problem set. This is especially important to me because I am hoping that in two or three years I can pass this class to another person – who will continue what I have started – and work on the AB course next.

Meanwhile, I will be teaching Geometry Honors for the third time (and I have taught regular Geometry four different years), and I will be introducing the problem based method in this class as well this year. I plan on keeping the overall goals of the course the same – my five essential questions – but focus on the problem solving more heavily. Similarities to the Calculus class will be the format of the problems, the overall format of the class, and the emphasis on learning by doing. The differences will focus on more structure as these are 8^th and 9^th grade students, more skill practice periodically, and tests which will still focus on skills as well as problem-solving. Instead of starting from scratch with the Exeter materials (which are integrated except for Math 4, which is mostly calculus) I am relying on the Geometry problems from Emma Willard School in Troy, NY. The teacher there previously had taught at Exeter and went to EW to try and use the Exeter program there. What resulted is the Geometry curriculum I will be using. I will make some modifications to it – notably changing the Geometry Sketchpad investigations to GeoGebra ones – and otherwise some minor cosmetic changes. My goal is to blog the results throughout the year here.

Additionally I will be co-chair of the Math Department again this year, although with a new co-chair. Our school is trying to capitalize on the fact that we are a K-12 school and my co-chair is actually the former 6^th grade math teacher who is now part-time co-chair and part-time math coach for the elementary teachers. I am really looking forward to working with her this year, and I am looking forward to collaborating with her.

Finally, a goal of mine at our school – and something I will be blogging about soon – is to clarify our placements for students, parents, and teachers. We are not an open enrollment school in the math program, a lot of the reason being that the inevitable switching of courses that often happens when someone has signed up for a more difficult class and realizes they will get a C or a D is not sustainable in a school with few students where a handful of students can decide whether or not we are able to have an extra section of a course. As a result we try very hard to place students in a class that is both challenging and successful (i.e., A or B) for them. The placement guidelines are rather stringent, but they tend to focus on maintaining membership in a particular track as well as what would cause movement to a lower track. Although we tell the parents we are open to moving students, when appropriate, from a Regular to an Honors class, in reality there is little in our placement guidelines that suggest how this is done. It is often left up to the teacher, and in some cases the teacher won’t make the recommendation because they don’t feel they were able to do anything with the students in the regular class that would allow them to assess their fitness for honors. So one goal of mine this year is to clarify this process to make it more transparent, possible, and flexible. We’ll see.

‘Coming Out’

No, I’m not gay – not that there is anything wrong with that!

I decided that I do not want to entirely hide my blog. I am interested in promoting it, particularly as  I want to focus more on the teaching I am doing, but to do so will open up the possibility that it will get back to the school I work at. As a result I have password protected several entries that I feel were a little too personal about where I work. I also decided not to delete my non-education related entries – they are part of who I am and what I believe – and I probably won’t entirely avoid making them in the future, but the focus will be teaching and education.

It is always possible that I have left some things in here, so I will read through the entries again and it is possible others will be hidden.

I am looking forward to possibly gaining more readers, and I am committing myself to at least 2-3 blog entries a week, although hopefully I will do more. One thing I want to blog about is my new Geometry Honors curriculum, which will follow in style what I have been doing in Calculus BC the last couple years.

See you later!

It Has Been Awhile

I know it has been awhile since I last posted. This last year I took on the role as co-chair of our math department and for a number of reasons this consumed my life over the past six months. Now that it is summer, and I have returned from my summer conference, I am now teaching a summer calculus class to two students who want to skip our Calc AB class right to BC next year. It has been a lot of work – more than I had planned – and as a result I have not gotten to the planning I wanted to yet this summer.

I will begin the third year of the current iteration of my Calc BC class this fall. This will be my 7^th year teaching BC, but the 3^rd since I started the problem-solving approach. It has been going well, and I am now contemplating introducing the same method for the Geometry Honors class that I will be teaching this coming year. My AP exam results for the last two years of this method have been good. Out of 13 total students (yes… that’s all in 2 years), 11 earned 5s and 2 earned 4s. Of the two that earned 4s, one had missed nearly a month of school for various reasons in the month and a half before the AP exam.

This all brings me the question I am thinking about. To what extent should students be doing math versus learning about math. Just to clarify what I mean. I consider the typical presentation, followed by examples, followed by practice to learning about math. Repeating what the teacher shows you is not doing math in my opinion. That is technical training, not doing mathematics which, to me, is a much more creative process. I already try to balance this, although I admittedly tend – at least in my Calc BC class – on the ‘doing math’ side.