Teaching Algebra I

This is the first year I have been completely uninvolved with “first year” algebra. I use quotes because in high school, almost all–say, 80%–have taken the class at least once, and a good 20-30% have taken it twice. A fraction have taken it three times.

I wake up each day grateful that I’m not teaching algebra I, despite the fact that I’ve spent more time thinking about how to teach algebra than any other subject. But I rejoice nonetheless. No class is designed more perfectly to slap you in the face with the insane inadequacies of our educational policy. See Tom Loveless’s study,The Misplaced Math Student, for great research on the idiocies of putting unprepared students in eighth grade algebra.

Challenges

Schools with majority URM (under-represented minorities, aka black and Hispanic) can simply pretend to teach algebra. I’m speaking here of charter schools and urban comprehensive schools with no high-achieving population to worry about. Pretending to teach algebra doesn’t do much for test scores, but it’s a lot easier for classroom management if you can give struggling students something they know how to do.

But many Title I schools are in the suburbs, which aren’t as economically homogeneous as they used to be and these schools have it much tougher. First, they can’t track, because their majority minority population sued back in the 90s. So all their classes are “heterogeneous”, progressive-speak for “put functionally illiterate/innumerate kids, struggling but not completely unskilled kids, ready-to-learn kids and highly skilled kids all in the same classroom and yammer about differentiation”. Second, because they have kids who are ready to learn algebra, they have to actually teach algebra. So they have to figure out a pace that doesn’t lose the middle and doesn’t bore the top. The bottom is largely left out of the equation. Unless you differentiate, and differentiation is a lot of work.

Last year, I taught all Algebra I: three regular courses and one Intervention, a double period course. Because the best thing to do with kids who are terrible at math is give them twice as much time to feel inadequate.

Differentiation

I slowly moved to a differentiation model. First, I started giving the top kids separate lessons, which was partially successful. It gave them more challenges and they did very well, but they felt neglected because I didn’t always get back to close up with them. By the end of the first semester, I’d seen a second group, skilled but slightly less motivated, start to break away from the pack. At the same time, I had about 20 students who simply had not demonstrated understanding of the first semester basics–and I’m very flexible in demonstrating understanding. These students, I decided, would go “on contract”. I would give them a D- if they demonstrated they could graph a line, factor a quadratic, solve a complicated multi-step equation, and make a reasonable stab at solving a system.

So I had four groups, which I called Purple, Black, Gold, and Blue. They had different objectives, different assessments, but not different standards. A Gold student could get, at best, a B-. If any gold student started doing better than that it was time to move them up. It worked beautifully, if “beautifully” can be used to describe teaching kids who still struggled with math. By setting up the groups, I was able to formalize the process of working with them–“Okay, golds, you’re clear on what you’re doing? Good, I have to check in with the Purples”. I could give myself time to close up with the top kids, who all agreed they were not neglected in the second half. I designed lessons in three day chunks and staggered them so that I could introduce a lesson to Gold while Purple, Black, and Blue (heh) were on day 2 or 3 of their lesson. The contract kids in particular did very well; I still lost nearly half of them to chronic absence and/or refusal to work, but three of them moved out of Contract entirely and the rest of that half passed with a D-. I had a low failure rate.

Most people who saw my class in action said it looked like an enormous amount of work, and it was. But you pick your stress levels. I found it far more stressful to teach one lesson to 30 kids with a four year range in ability levels than I did to design four lessons for smaller groups.

Results

Did the kids learn algebra? I was able to compare the scores of 200 students who took algebra two years in a row. I had by far the most students of any algebra teacher. My students incoming test scores were 15 points below two of the teachers, and 30 points below one of them. In other words, I got most of the low-scoring kids, and I had no students with Advanced or Proficient scores on their previous year’s test, unlike the other teachers. When I broke down the comparison by incoming ability level, I did roughly as well as all the other teachers. Specifically, my students improved at a slightly lower rate than the other three teachers, which makes sense when you consider I had more low ability kids, but my standard deviation was, along with one other teacher, much lower.

For example: Teacher A, who had a class average 30 points higher than mine, had spectacular results with a couple of the 10 Far Below Basic students she had, but the others didn’t do as well. So the standard deviation of her new average was huge, whereas mine was pretty tight. Translation: I improved more students by smaller amounts, but had few huge wins. My improvements, like to like, were on par with the best teacher in the department, an algebra specialist who I very much admire, although our teaching methods couldn’t be more different. In my opinion, my differentiation allowed me to be a better teacher. But I don’t think it works for everyone.

I had no kids with Advanced scores; I attribute this in part to my failure to really challenge my top students. On the other hand, my top students all came in with Basic scores the year before, and almost all of them moved to Proficient (a few moved to high Basic). A number of the contract kids had Below Basic rather than Far Below Basic scores, which was a good sign.

We had a very good year last year, and our year was widely considered successful because of Algebra results. I taught more algebra students than anyone else, so in addition to specific results, it’s fairly evident I did a decent job. Nonetheless, I was moved to Geometry and Algebra II this year. As I said, I give thanks daily.

Classroom Management

So if my kids learned well, why am I so thankful to be out of algebra? Because classroom management difficulty correlates directly with the percent of the class with no skin in the game, and in my classes that was 10-20%. I would regularly check my students’ grades in all their classes; all my disruptive students were failing all their classes. For the most part, they are just waiting out the clock until they can go to alternative schools of some sort. They don’t mind going to school; it’s fun. It’s social. It’s their life. Learning, behaving, and engaging–not so much.

I say this to all new teachers: getting this population under control is imperative. Start by moving kids away from each other. I have often pulled a desk (or two) way up front and made a talking kid (or kids) move to that seat. The disruptor will usually then go to sleep. Fine by me. Many teachers are philosophically opposed to sending disruptive kids out of the classroom. Get over it. If moving seats didn’t work, or multiple warnings didn’t work, give them the boot. Ignore the pressure your management will put on you to stop sending them out of the classroom (although you will, inevitably, think 8 times before doing it). It’s incredibly hard to be patient and controlled enough to send kids out of the classroom until and you won’t always win the battle, but you must fight. Sing me no sad songs about these kids and their problems. They are making it impossible to teach the others, and you owe the others every bit as much.

What is essential, though, is to always hold to the rule no harm, no foul. I kick a kid out one day, he wants to come in the next day and works, I give him my full attention. And behavior never affects the grade. I had more than one student who showed functional understanding of algebra despite being a monumental pain who was often sent out. Those kids passed.

And it’s also essential to reach out in every way you can. I told every one of these students that I wanted to pass them, that I understood this was a course they didn’t like and didn’t want. I also turned to differentiation because I hoped that it would give the unmotivated strugglers a sense of possibility–and it did work, for a lot of them. You never want to take their behavior personally. But you also don’t want to tolerate it.

So don’t bleat ineffectually at your students, and don’t teach to a room that isn’t quiet.

Curriculum Paths and Classroom Management

Survey math teachers and you will find that Algebra I classes have the most severe classroom management challenges, quite apart from being difficult to teach content-wise. We put kids in classes they don’t understand and make them take that same class two or even three times. By the time they are sophomores, these kids know they can’t graduate. They are failing all their other classes, too, but in math, a lot of the high achievers get winnowed out into geometry, many before they even get to high school. The proportion of nohopers is insanely high.

By Geometry and Algebra II, most of your kids have skin in the game. Even if they don’t like math, they have something to lose. Classroom management moves from being a nightmare to a manageable challenge.

I’ve been working with a colleague on a math sequence that will find a path for the no-hopers. Remember, from a purely pragmatic standpoint, that the more kids who fail algebra, the more kids who will leave your school for a credit-generating factory–and take their attendance dollars with them.

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4 responses to “Teaching Algebra I

  • What I Learned: Year 2 « educationrealist

    [...] 2 was all algebra, all the time. Few things are as draining—or as revealing of the utter emptiness of our educational [...]

  • Algebra Terrors « educationrealist

    [...] retrospect, my second year of teaching was my most brutal, thanks to my schedule of all algebra I, all the time. I learned a lot. I never want to go back. [...]

  • Who I Am as a Teacher | educationrealist

    […] Here’s how I taught it, and here’s how they did. I only failed 10 kids out of the final 90, or 11%. (Elijah had left. Eduardo got his permit, and DeWayne made it back onto the football team.) That’s the highest failure rate I’ve ever had, but then it’s the last time I taught algebra I. It’s easier to work with kids in geometry and algebra II—they’ve got skin in the game, and graduation becomes a real objective as opposed to the remote possibility it presents to a sophomore taking algebra I for the third time. […]

  • micdef

    This post might be my silver lining. I am teaching first year algebra to 8th graders with a wide range of ability. It should be know surprise to me that I have some classroom management issues because some students can not interact with the material. What their doing in an algebra setting is beyond me and I’m sure their is something on this is another post. Suffice it to say that I do not mind creating more work for myself if it will help students focus their attention on their objectives for the day. Some questions:

    1. Could you expand on this… “I designed lessons in three day chunks and staggered them so that I could introduce a lesson to Gold while Purple, Black, and Blue (heh) were on day 2 or 3 of their lesson.”

    2. Say a student from a low level group got everything correct and the grade on the paper was only a C+. Would that student find it odd and ask for clarity?

    3. Do you have any post talking about block scheduling? It seems like an impossible task to keep students of low ability on task for this length of time (80 minutes). If you expect to kill some of this time with the “release” you talk about, well that only seems to create more problems. By giving them something to work on individually it as if I am saying to them “Here, now is the time to talk about basketball…”

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