Saturday, January 5, 2008

No Rest

With two days left in Christmas Non Denominational Winter Solstice Gift Giving Break, I have a ton of work left to do for school. It stems from two contradictory policies.

1) The end of the semester grading period is January 16. This is 8 weekdays after we get back from break, or if you look at it block schedule wise, 5 meetings. So we have a little over a week to levy exams

2) The dean of faculty has issued a hard line against work over break, unless you are in an AP. In the past, most teachers would just let it be due the day after we get back, so they could argue that the student doesn't necessarily have to work over break, they could start on the Monday after break. Well the dean said that this violates the spirit of the law, so it will not be permitted. Not even assigning something due the week after break is permitted. There should be absolutely no expectation that the students must work over break in any form whatsoever.

These two policies put the teachers in a very difficult position, because it makes the "assessment density" of the last week much much higher. For example, I had polled my seniors in early December about how many and what type of assessment they wanted. They wanted a lot of small quizzes, so we scheduled one take home quiz over break and one the day after they got back. But the dean put the kibosh on that, and now that take home is pushed back. So here is the list of things I need to do on my vacation.

1) Make a collaborative quiz for Calculus
2) Make a take home quiz for Calculus
3) Make a Review Sheet for Algebra 2H
4) Make an Answer Key for (3) and scan it
5) Make two Mid-Term Exams for Algebra 2H

And then towards the end of next week I will have to grade all of the above in addition to a History of Math Paper, and the following week I will have to write comments.


Wednesday, November 28, 2007

Implicit Differentiation

Yesterday I had a really rough Calc class. The subject was implicit differentiation, which is where you take a derivative of a function that is not strictly defined in terms of y. For example, xy + y = 2 is implicitly defined. Traditionally, it is a very difficult concept to teach, and I saw it coming so I prepared as well as I could.

I should probably interject here with a word on lesson plans. I rarely use them in the classical way they are defined by education theorists, because within five minutes of the class starting the best laid plans will be in ruin. A good teacher is not one who can determine the duration and sequence of every single problem to be done during a particular class, meticulously mapped out. A good teacher is someone who can effectively respond to student questions; he/she can take a seemingly tangential point, explore it, and then rope the investigation back into the larger discussion.

So in order to prepare, I mapped out the possible questions the students might have; I explored what they are weak on (chain rule in particular), and tried to think of innovative alternative explanations for when they inevitably will get stuck.

The class started, and they encountered some of the difficulty I had predicted, but a brave student said something I wasn't prepared for and that put me back on my heels:

"Mr. Brescher, I don't think [we learned/you taught] power rule right. This just doesn't make any sense"

I was just floored by the comment, because I am very personally invested in the amount of learning that goes on in my classroom. I paused for a second, and responded as best I could:

"Well, I know we only spent one or two days on it, but I have used it several times every class since then. If I was at all deficient in teaching it then, there have been ample opportunities over the last two weeks to ask questions and pick it up."

In my mind this was an unsatisfactory answer that just popped out to avoid an uncomfortable silence. I might just have to go back and reteach all of those rules.


Wednesday, October 3, 2007


I have two classes. Three sections of Advanced Algebra Honors, and two sections of Calculus. Over the past month I have noticed some trends with these classes and how I teach them. One positive trend is my ability to improve a lesson. I might have a lesson plan that I execute on my period two algebra class, and it goes nothing like I had hoped, so I modify it and run it on my period three algebra class. I can even make a third refinement for my period seven class. By that time I can anticipate almost any question the students might have or solve any problem that might arise with the calculator.

Case in point: Yesterday I delivered a strong but rushed performance on limits to my period one calc class, and I felt that it got the point across well, but I could have managed my flow a little better. So this morning I printed out the notes that I saved off the smart board from yesterday, and I am in the process of annotating them as a guide for my lecture today for period five. I know which examples work, which ones don't, and I can even remark where students reached epiphany ("oooooh, now I get it") and I can emphasize those points.

There are two disadvantages to this. The first is obvious: the students in period seven are obviously getting more than those in period two. I don't know of an easy way to remedy this without providing errata and "catch-up" lessons to the earlier classes on lessons learned from the later ones. And even this will cause the early classes to fall behind because we would be spending so much time visiting old material.

The other disadvantage is with my own memory. The classes fade together, and if I make an insightful comment to one, I am liable to forget I made it unless I write it down. Then when I go to make that same statement again, they have already heard it or worse, I assume I said it to a particular class and they never received the message. The key here is going to be in writing down notes on all of my lesson plans, and referring back to those on a regular basis. Even this seems really tedious and I don't think I could keep up with it.

Monday, September 10, 2007

First Days

Well, I am done now with two days of classes. I have a good group of kids, 57 in total. I have already started to form habits with the smart board and first class, our web portal/e-mail client.

I start off class with a window open on the smart board to a web program I developed that takes attendance. The students walk up and touch next to their names, and it registers them as present. It is one less administrative task I have to do, and they really enjoy getting up and playing with the technology. Next, for my Algebra 2 Honors students, I check to see that they have done their homework. I don't do this for the Calculus class, because I want them to start getting into a college mindset: if you don't do your homework, its your loss, and you need to be responsible for it. Next, I read out the answers to the homework, marking on the white board (occasionally referenced as the "dumb board") which problems they didn't get. Then I go over those problems on the smart board. When we are done with that, I save it locally, and then upload it to the First Class conference created for that class, and the students can then access the work we did in class at any time. Here is an example. We are still reviewing the summer work and last year's material, so I am not conducting actual lessons, but when that starts I am going to shift focus. The Smart Board will contain slides of key concepts that I will come back to several times during a lecture; a process, a diagram, an equation, something critical to the lesson. Then, on the white board to it's right, I am going to do examples using the key concepts on the left. This will serve to reinforce the lesson. I will give more details after I give it a go a few times, since at this point it is pretty theoretical.

Working with the Smart Board isn't without it's quirks. There are two modes that write on the board: One draws over all of the applications, but as soon as you click anywhere else, you lose what you just wrote. The other is the notebook program that I use to record the problems. It gets confused sometimes, and the result is that we lose the last half of a problem. I am still working on how to fix this. The other problem is that occasionally the Mac Mini that I host the programs on runs slow or hiccups, and it doesn't register my input, so I have to wait for a second before I can continue. It is very disruptive at first, but I have found ways of just rolling with it and it is not nearly as bad as when I started .

Overall, my classes are very well behaved, and they seem to be involved thanks in part to the technology. I hope that this lasts.

Thursday, September 6, 2007

Pre-First Day Notes

Well, class begins tomorrow, and I have to say the room has really come together. They dented the smart board to the point that it wasn't working, so we got another one. They gave me a twelve foot whiteboard when I needed six, so I scrounged around and got a four by three foot board. The desks were delivered. My teacher desk was a hand-me-down from another teacher, so it is larger than it should be, and I don't have the keys to the locking drawers, but I have a desk. I have a room that has been successfully pieced together from all of these different places. Is it what we asked for? Not really. Is it a classroom? Certifiably yes.

In the end, all of this doesn't *really* matter much, what matters is the content and the interaction with the students. So long as they have somewhere to sit and I have something to write on I can teach. It has given me a nice cynical attitude for dealing with the administration, but I was going to get that one way or another.

Now for decorations. I have plans to buy three portraits to put over what used to be a fireplace. The three I am thinking about are, from left to right, Euler, Liebniz, and Gauss. They are not very pretty men, in fact I dare anyone to find a picture of Liebniz where he is smiling, but they represent the cultural heritage of modern math, and I think they would add a little class to the room. On another wall, I plan on putting a family tree for all of the major mathematicians, using small portraits and a bit of text describing each person. That is going to take some time, and I have yet to scan the picture of a nice portrait frame to make it look nice.

I will post pictures of my classroom as soon as I can.

Wednesday, August 22, 2007

So I am currently sitting in the middle of a less than stellar education workshop. I will bite my tongue a little, simply because I don't know yet exactly who is going to be reading this. My school sends all of its new teachers to this four day workshop hosted by the New Jersey Association of Independent Schools. The hope is that they will learn what it is to be an independent school teacher; what it is that makes our experience different than other teaching experiences. Instead, we have a topics course that covers a lot of basic elements of teaching blended heartily with impractical educational theory.

I swear to God, this is a direct quote: "I think its funny that we say we cover material, shouldn't we be revealing it?"

In the end I have gleaned some useful tidbits that will help in lesson planning and classroom management, but they amount to maybe an hour's worth of learning, and I have, thus far, sat through close to fifteen hours of boring lecture. There are far better uses of my time.

I talked to Jodie last night about an array of topics, most importantly how critical my attendance is. On Thursday volunteers are going to do small mini-lessons based on what they have learned, and Jodie said that she will turn a blind eye if I were to "disappear" for that day of lecture. The administration isn't keeping tabs on us anyway, and I have much more constructive things I can do.

Jodie has said that we can meet with John Mascaro (Dean of Faculty) to tell him what we think of the workshop. Its not that I am opposed to workshops, its just that there are plenty of other topics that I would love to learn about: technology in the classroom, classroom management, or something in that vein.

I just hate being taken out of a paying job so that I can sit and listen to some guy lecture about getting in touch with student's feelings.


Wednesday, August 15, 2007

When I was substituting here at Morristown-Beard in the spring, Jodie Miller, the head of the department, came to me and asked me if I could manage teaching in the computer lab, once it was converted to a classroom. This is the general layout.

A few things to note: Those black dots are immovable structural pillars that create a dead space that cannot be taught across. If I put the kids on one side, I must teach on that side as well. Jodie also is moving from one classroom to another and needs a department-head office, so we agreed she could carve up a piece of the room for herself, and we decided upon this plan.

This hinged upon the removal of the tech closet, and the seating arrangement would be cramped for 14 students, but we absolutely had to have 14. Construction comes, headed by the groundskeeper Bob Rivello, and they do very little we asked for.

I suspect that instead of ruffling the feathers of the tech department, he made the decision to leave the tech closet as is. That meant that the door to my room now has to be the door to Jodies room, and he needs to put a door to my room somewhere else. That somewhere else is where the blackboard was supposed to go. When I made this image I had no idea what we were going to do, but Jodie and I have since moved some desks in to see how we could make it work, and we came up with a workable solution: The blackboard is going to go opposite where it was planned, on the East wall. My desk and bookcase will go behind the pillars, and the desks will be in clusters of two on each side of a wide central aisle.

This is all assuming that Bob and the fire inspector don't nix it before school starts. I am also very frustrated with how slow furnishing the room is going. We are now two and a half weeks out from the beginning of school, and there are no desks, not blackboards, no teacher's desk, nothing. Just a new carpet. They haven't even installed a new light switch (the old one is now in Jodie's office).