Things are going nowhere near perfect with me lately, but one thing that has gone mostly very well for me is the new, altered schedule. As of today, we have now spent about two solid weeks with the new schedule, and I can safely say that although there are issues, it is far and away better than what I (and the students) dealt with before. As I’m sure I have mentioned earlier, there three main differences in the schedule from what it was like up until now:
1. My period length has decreased from 110 minutes to 75 minutes
2. All 4 of my classes meet every day, as opposed to on alternating days
3. The classes were re-rostered to group the kids more homogeneously
Changes 1 and 2 combine to mean a nominal increase in math instructional time from 275 minutes per week to 375. I am seeing a huge difference in the amount of material I can cover. In addition, I notice much less fatigue from my students over the period duration. And when I have a bad class period, 75 minutes of hell is a lot easier to tolerate than 110.
In my top two classes, behavior is much easier to manage. That’s not to say that there aren’t problems, because there definitely are. But when I need to get the class back under control, it takes far less time.
Of my lower two classes, one, Group B, is split in half between me and another teacher. This also makes management much easier. The only major problem is my other lower class, Group D. They have the tendency to fly completely off the hook, like they were on Tuesday. But all in all, I feel like at the very least, Groups A, B, and C are being far more effectively serviced.
Planning for classes and keeping track of what happens from day to day is a much easier task, now that I don’t have to worry about which groups to lead my lessons with, whether a lesson is going to straddle a weekend, or whether a field trip is going to throw the whole thing off. Continuity for me is smoother and I can see that it working better for the students as well.
I have huge appreciation for the people who accepted changes so that this could occur, it makes my teaching task imminently more doable. It might even be possible to finish this curriculum before the HSA after all (in one form or another).
Today, I returned to school from a very much needed spring break. From my jolting return from winter break, I knew to expect things to be bumpy coming back, and the students did not disappoint. However, I think I was better prepared this time around.
I can’t say that we accomplished a whole lot of any of my classes today, besides (hopefully) getting the kids focused on doing work again. I hit them with a quiz that they probably weren’t well prepared for, which generally is not a very good idea. However, I think most students actually took it fairly seriously, and I hope it was a bit of a wake up call to them that I’m not wasting any time getting them back to work.
Twenty-two instructional days remain before the HSA, and things are not looking particularly pretty. During quarter 3, I think I tightened up my routines a lot, but I still wasn’t seeing much, if any, gain in results. This last quarter, I need to try to change up my approach.
Some things are going to have to wait until next year. Speaking of which, my fellow TFA first year algebra teachers and I have started talking about some things we want to iron out over the summer so that hopefully we can avoid the debacle that this year has been for all of us. One of the toughest questions is how to approach the teaching of algebra as a subject, given the students we have and the way they are assessed by the HSA.
The HSA is actually a very rigorous test of students’ abilities to apply the skills of algebra and data analysis to real-world problems. Nowhere on the test do you see problems simply demanding the students to “solve for x”. Most of the questions require the students to analyze a word problem carefully to find out what it’s asking for, then to synthesize skills from different parts of the curriculum to answer that question.
The problem in preparing students to do this is two-fold. First of all, my average student is shaky on basic arithmetic and not at all comfortable with the concepts and skills he/she should have mastered in pre-algebra. Secondly, the curriculum provided by the City teaches the concepts in isolation. Whereas the HSA questions usually require several skill to be applied at once, the assessment questions I’m provided in the curriculum are usually very one-dimensional. Even more problematic is the fact that the materials provided by the curriculum are even more simplistic.
So my dilemma is that in my limited time, with little appropriate material provided, I’m supposed to be teaching the students to the complex process of assembling skills to solve problems, when the students struggle to perform each skill itself.
Faced with this situation, the holy grail is to be able to teach the students the concepts, from which the skills will follow. If a student truly understands equations and the rules of algebra, they don’t need to know the step-by-step process of solving an equation, that follows naturally from their own understanding. Teaching concepts is extremely hard, especially when faced with an extremely diverse set of very frustrated students, who aren’t used to being made to think critically. And so the temptation is to teach the skills one-by-one, because most students can follow a step-by-step process. But the eventual issue is that the students will never truly understand the why behind what they’re doing, and there’s simply no way to teach an algorithm for every single type of problem the student might happen to see on the HSA.
Teaching concepts directly is simply not realistic. I really believe that only the brightest math student have the abstract thinking capabilities to work that way. I think I’m a reasonably sharp mathematician, and even I struggled in high school math when it got too abstract, and I had fantastic math teacher my entire life.
What I’m looking to do is find a happy medium. I’m envisioning a curriculum that focuses on teaching students the “tools” of algebra. By tools, I mean the things we write on paper to solve algebraic problems–the expressions, the graphs, the patterns tables, and so on–and the rules for using them. Instead of focusing on the abstract theory of negative numbers or on specific methods of subtracting them, I want to show the students what a number line is and how to use it to see the difference between two numbers. I want to show them how two number lines form a graph, and how they can use that graph to see the relationships between two numbers. I’m hoping that by knowing the tools inside and out, the concepts will follow as the student sees how the different tools–function tables, graphs, and equations, for example–relate to each other and show the same underlying concept in different ways. And with that understanding of the tools, I’m hoping the students will have an easier time attacking these complex HSA problems and be much better prepared for higher math. We’ll see I guess, but pretty much anything’s better than what I’ve had going this year.
I’m up late trying to get my 3rd quarter grades in order, since they are due tomorrow. I can’t really whine about that, because I put myself in this boat. But part of the reason I’m up so late is because I’m so backlogged on test grading. Besides fatigue and procrastination, part of the reason for this is that grading tests is about as enjoyable as having my teeth drilled (or so I would imagine).
Grading tests is so discouraging. Test and quiz scores in my classes generally average about 30-40%. And this is considering the fact that I let them use all of their notes on the quizzes, and the tests are designed to look exactly like what they did on their homework and classwork papers. On most of my tests, almost all of the answers can be found by looking elsewhere on the test. On some portions, I provide a guided walkthrough of the steps to solve a problem. The students are provided calculators. I work with kids after school. We grade and discuss quizzes in class. We review all the unit concepts the day before the test. I pass all my tests along to the special educator for suggestions on how to modify them so that my IEP students get their required accommodations, and so she can administer the test to her students. She teaches the students who are pulled out for math, and sometimes adds additional work for her IEP students on top of my test.
I just don’t know what my students are learning if they’re stumped by the most basic problems on the test. I’ve received bright students who have transferred in from other schools, and watched their performance decline while they are in my class. My NWEA scores in the winter were lower than my scores for the summer. It is awfully hard to find the motivation to keep planning detailed lessons and synthesize my own lesson materials when my lessons clearly just aren’t reaching my students. I had one of my better students in one of my classes get frustrated when I wouldn’t come over to help her right away and tell me, “That’s okay, I don’t need your help anyway. Everything I learned in Algebra, I learned from my teacher last year.” I get lots of comments like that all the time, 99% of which I pay no mind. But in cases like that, I feel like there’s some truth to it.
I know I’ve figured a lot of things out of the course of the year, and I know plenty of very specific things I still need to improve. I’m working on them, but I just don’t feel like it’s coming together in time for the kids I have now. And I know it’s probably not all just my instruction. I think A-day/B-day was awful for the students. I also think the vastly differing math levels of students in my class made reaching everybody all the time pretty much impossible, when I only have a tiny handful of students who can truly work indpendently. We switched to the new schedule today, and I’m hoping I’ll notice a major difference.
I’m just really worried that despite all the blood, sweat and tears I’m putting in, and despite all the sacrifices everyone on the team is making, we might still have less than 10 students pass this test. I’m still banking on the fact that it’s going to come out better than that, but I don’t have a whole lot of evidence to lead me to think so.
It’s a lot harder to believe people when they tell me I’m doing even a halfway decent job when the data right in front of me says that even my some of my very best students are totally missing the mark. I guess all I can really do at this point is keep fighting, and pray that things start clicking for the students big time before the HSA.
Tomorrow is going to be rough. If I’m lucky, I might be able to catch 3 hours of sleep tonight.