Norm day

Tomorrow is “norm day” for our district. That’s the day when classes are supposed to be balanced and administrators get a final count of students, which is to determine the number of teachers that should be employed at a school. Some of my colleagues wondered aloud whether our administration will change enrollment figures around to make them look “good” or to demonstrate needs to the district and then change them around some more to meet the realities of students’ needs and our resources. I’m trying not to be cynical or get (too) frustrated, but I am expecting more enrollment changes this week.

Algebra tiles, graph theory disaster

I’ve seen Algebra Tiles used, but never used them myself until today.

2009-10-05 algtiles3(This arrangement of tiles has area 4x^2+4x+1.)

Again, I was surprised by how much trouble students have with the concepts of area and perimeter. Going to try to address that tomorrow and then try the algebra tiles again. I’m using the algebra tiles to help students understand addition and subtraction of polynomials.

My fifth period Math Lab was a complete disaster today. Based on their performance on the graph theory activities last Friday, I overestimated the students’ readiness for today’s activity. Today’s activity was way too vague and open-ended; I didn’t provide enough scaffolding for the task and instead got a lot of blank stares and goofing off. Even the students that seem quite diligent were twiddling their thumbs, bored and confused. It was a huge disaster. One student blamed me publicly for giving confusing instructions–and he’s right. I’m not as concerned about them not completing the task as I am them feeling like this class is a joke. What’s more, there was a new student today who didn’t speak much English and no one in the class spoke Armenian. I didn’t know how to communicate with this student and felt bad about that.

What now? I think I will need to swallow my pride and put off the rest of the activity rather than keep forging ahead. Even if I could figure out the right scaffolding to give, I think I killed any budding interest in the topic. Also, I have a feeling that my enrollment on this class is going to change quite a bit again this week.

Adaptation #3: Paper management skills

With so many more kids turning in more pieces of paper so much more frequently, my paper management skills are stretched to the breaking point. This includes paper that I give to students and paper that students give to me. I’m trying not to collect homework on separate pieces of paper, but instead students finish their homework in composition books. That has been a boon so far. The problem is that classwork has generally been done on loose sheets of paper and I want to collect them and give feedback on them so students take the work seriously. My organizational problems are compounded by the fact that I am shuttling between two rooms since I don’t have a room of my own, so I have to lug the papers around and it’s easy to get things mixed up.

Coordinate plane activity

Coordinate plane on floor

Last Thursday, my third period Algebra 1 seemed to need some more help with locating points on the coordinate plane so we used an activity suggested to me by a veteran math teacher. I used blue painters’ tape to mark off x- and y-axes, and took advantage of the tile floor in the school hallway. Each student was given one coordinate and the students were asked to stand at their coordinate.

The activity revealed who understood how to locate a point on the coordinate plane using coordinates, and who did not. Some who did not know asked their friends, others stood on the side lines and I helped them find their spot. Next time, I need to be more careful not to “out” students who don’t understand a task.

Adaptation #2: More active, less passive learning

In my college classes, I am able to use the interactive lecture style most of the time. It’s an extremely efficient way to convey information to students and I can see that students are learning based on their performance on short tasks that I assign during class. This teaching strategy works at my college because our students are highly motivated, know how to learn and behave in a lecture style class, and have excellent prior experience with mathematics.

In my RCHS classes, I have to limit my lecturing to a few minutes at most. Students don’t seem to be able to endure listening to me for more than a few minutes at least at this point, even if my lecturing is peppered with student questions and responses. (Perhaps I can slowly train them to do this?) So, to make the use of every moment in class, I am mostly asking students to do mathematics in class. My class time is usually spent like this: start class with a warm up activity, make announcements, give students instructions on a task, then let students work on the task while I walk around and help individual students. I haven’t gotten good enough to plan for closure at the end of class, but I am working on that.

I’m not sure it would be obvious to someone visiting my class that learning is happening, but I think it is. The trick is in designing the right kind of mathematical tasks that get students to learn without me telling them much. And wow, doing this well takes so much time and effort.

Complex Instruction rocks!!!

Another noteworthy thing happened today. Today was the first day that I began weaving ideas from complex instruction into my class. I’m thrilled at how well it went.

Up to now, I’ve had students sitting in groups of 4 and I’ve told them to “work together” but I never gave explicit instruction on how to do this. Today, I began telling them why working in teams is important and how to do it. The task for each group was to solve a word problem using the guess and check method, record their guesses in a table, then present their answer to the entire class.

I was a bit concerned at first because I rearranged students into new groups. They had previously been sitting with their friends so they were now separated and did not know their teammates. Also, I wasn’t sure how well they would take to the long set of instructions that I had to give them.

I explained that to get a job and be a productive member of society one has to learn how to work well with others. I explained that each group of three students would work together to solve a problem. They would have to do that while playing one of three roles: recorder, reporter or resource manager. The recorder was responsible for making a written record of the work (the table with the guess and check numbers), the reporter was responsible for telling the rest of the class how the group came up with an answer, and the resource manager was responsible for getting supplies (calculators and textbooks) for the group.

I finished my instructions, then students self-selected their roles. (I’ll experiment next time with randomly assigning roles, but since one of the roles involved talking in class, I didn’t want to force students to do it.) When I gave the signal to start on the task, the students jumped into action. It was amazing. Every group was able to complete the task and came up with a beautiful solution to their problem.

Of course, there were some behavioral and status problems. Two students in a clique of three who were now separated did not want to participate. One boy told me he didn’t want to work. He put his head on the table. The other told me he didn’t want to work and was more defiant. I explained that their participation was crucial to the success of their team and that they had to participate or go to the office. I told them that I would come back in a few minutes and by then I wanted to see that they had selected one of the roles in their group.

Both boys were clearly causing problems for their group. One girl told the defiant boy something like “You don’t want to be on this group and if you don’t help us we don’t want you on the group either.” It was so hard for me to not get angry, but I did my best. Somehow, after more coaxing both boys participated somewhat. One boy reported that he contributed the correct answer for his group, and I congratulated him on that.

At the end of class, I made sure to give strong positive feedback for their display of excellent groupwork skills. I am definitely going to use more complex instruction in my classes and hone my complex instruction skills.

Two final quick notes: (1) For some reason there were only 15 students in class today. I know teachers are always wanting to reduce class size, so I won’t say this too loudly:  That was almost too few students for the complex instruction style class. There might have been even more lively discussions at the tables if there were more voices. Question is, how will this work in my class of 36?

(2) The two boys who didn’t want to participate were part of a clique of three boys who have been very rowdy so far. After rearranging the students, the third boy was on the other side of the room and he was totally engaged. It was the highlight of my day to see him so successful. He was the one I mentioned at the end of my other blog post from today. I’ll be very curious to see how the three boys interact with each other again. The two were definitely making fun of the third for being so engaged in the math, but I’m not sure he heard them from where he was sitting.

Motivating students

Some small successes to report today!

Another immensely helpful thing I learned from the book Adding It Up is that intrinsic motivation is a largely a function of two things: how much a student values the task at hand, and whether they believe they will be successful at that task. Thankfully, both of these are squarely within the control of the instructor.

Today, I told my Math Lab students that I would be showing them some mathematics rarely seen by high school students because it’s an advanced upper division math topic in college: graph theory. We started a multi-day activity on graph theory today and by and large, it was pretty successful. Most of the students were engaged in the tasks I gave them. This was an improvement from the first day that this class met on Wednesday; about half of the students were on task. I hope that this was both because I gave them interesting tasks that were grounded in real applications (so it had higher value to them), and while the tasks were challenging they were pitched at the right level (so students felt like they could be successful).

A similar thing happened in my 6th period Algebra 1 class today. I gave students a selection of word problems from the CPM Algebra 1 textbook and gave very explicit instruction on how to read problem statements and how to use guess and check to solve the problems. One student who was very reluctant to do work so far came alive–he came up to me at the end of class to ask me whether he was getting one of the problems right. He was a different student than I had seen so far. Maybe what I’ve stumbled upon is this: a teacher’s goal is to get students hooked on learning by helping them feel successful when they do it.

Today’s challenge: getting textbooks

Today’s goal was to get books for my students. I was unsuccessful because the textbook office could not locate my classes in their computer system. But even if they could, it seems they’re out of textbooks.

It’s very difficult to teach without a textbook. I can’t assign homework, I can’t ask students to open their book to look at something in class–I have to generate or copy everything that I want them to look at or to do for homework.

Today’s progress: I WAS ABLE TO GET ROSTERS FOR MY CLASSES!! Hooray! I still can’t access the information myself but I got help from our office manager, who figured out that all of my classes are listed in the system under the name “Unfilled Position 5.” I’m quite fond of my new name.

Armed with these rosters, I hope to have more success with textbooks tomorrow.

By the way, in case you were wondering if school is still chaotic, it is. One teacher told me today that his conference period suddenly disappeared when he was informed he had just picked up another class of students. And it’s already the fourth week of school…