Barbara Shreve and her colleague Phil Tucher discuss what the course "Algebra Success" is.
Algebra 1 is a major gatekeeper for students. Schools and math departments are faced with the challenge of preparing more and more students to be successful in Algebra. This lesson illustrates a coaching relationship centered on addressing and supporting the needs of students who have struggled in Algebra. Intervention classes are becoming more common in schools. This lesson and coaching episode focus on an algebra intervention class and the way to raise the level of mathematical thinking student are engaged in.
BARBARA SHREVE: The students in Algebra Success are in the second half of an Algebra 1 course and so they do have a regular 90-minute algebra class each day. And at the transition point between the two halves of algebra, their teachers help to identify some students who would really – who were making good progress in algebra, but were either working incredibly hard or had some small gaps and places where they had huge strengths. And we determined that some additional support and opportunities to revisit where they had gaps, or have additional ways to look at things along the way would actually benefit them and their success in the second half of algebra where things become even more abstract in the way that we structure the curriculum here. And so we wanted those students to have the support to continue on. So these are not students who, um, they're students who may have been successful to a degree in their Algebra A class, they're not all students who were not successful. Although some of them were not successful as their grade measures it, but their teachers saw potential in them. And then by a series of assessment measures, we determined, like, on some key foundational concepts that they were emerging in their understanding, or kind of shaky and had some misconceptions that we wanted them to be able to continue to address along the way. And get that additional opportunity to ask questions and maybe see new concepts introduced in an alternate way.
Algebra A and B at San Lorenzo High School together comprise Algebra 1. It's slightly more time than you would have in a traditional Algebra 1 class because we're on a block schedule so that students take 90-minute classes every day, but together they form a full algebra sequence. So some students have had part of that in middle school and will enter into the sequence in Algebra B, other students will take the full year here. Um, students in Algebra Success, that class partners and mirrors only the second half of the course, and so they have that additional support at that time.
The curriculum of Algebra Success is an evolving piece. We've had the course at the school for three years and it has morphed a bit over time. Right now it's set up so that students have an opportunity to preview some of the pieces and concepts that will lead into what they're learning in Algebra B. So we worked a lot on multiplying binomials and distribution in preparation for them starting to factor in their regular algebra class. We have also worked over time on spiraling some of the key pieces of solving equations and some of the mechanics that tend to slip when they're not always in front of students and what they're working on at that moment. So at the same time when new concepts towards the middle and end of a unit in their regular class, when they're starting to come to places where they're solidifying those ideas, this class provides an extra place to ask questions. So I'm trying to put materials in front of students that raises those questions, or gives them a context to figure out where they're getting stuck on their own as they're working through problems and identify those places, and get the support they need to work through them. So the curriculum comes from me in conversation with the algebra teachers and seeing where they are in their pacing and trying to match and anticipate what's coming next and what they're reporting, "This is a place where my students continue to struggle," so that I can offer the students in Algebra Success a chance to work on those struggles, and then be the people in their Algebra B classes who are resources for their peers.
In these classes I have two groups of students that I see every other day. I have a total of, right now it's 52 students enrolled. It was as high as 60 earlier in the year and we've had some changes in shifts and placement. Um, on our algebra team we have 6 or 7 different algebra teachers that I'm communicating with. To a degree their students are clustered in one section or the other but it's not exclusively that way. It's more a matter of where it then fits in students' schedules. And – but as a whole, most of that group has agreed to be somewhat on the same page. So they will be within a day or two of each other curricularly in terms of what they're introducing. And when that's the case, and when they are that close together, that has been a huge benefit to the Success class. Not only for my trying to target appropriately, but also for students to be able to truly be resources to each other and not feel ahead or behind or held up. Just not because they are but because of where their teachers are in introducing things.
So, um, I communicate with these folks and um, when we've had a coach, I've been able to help communicate a little bit through the coach who's able to see those students in other classes. And when that's not been the case our team tries to meet every Thursday afternoon for about an hour and a half, and get together to check in about where they are with curriculum and how that's going. They have also been pretty good about communicating with email. So if a student has an amazing day, they'll send me an email and let me know. And if a student has a big question or if in general they do, they'll send me an email and I’ll try to follow up as well. I'll send questions to update where are we curricularly because not everybody is able to make those afternoon meetings. But in general those afternoon meetings are a key place for the team to stay on pace and I then I can do some quick check-ins. They also observe each other during their preps to be able to stay on the same page.
The students had been working in the regular Algebra 1 classes on quadratic equations. In that work students had learned algebraic procedures such as factoring quadratic expressions, finding the roots of a quadratic equation (x-intercepts), using the quadratic formula, and graphing parabolas. Often students learn each procedure in isolation of others and seldom connect the ideas and methods together. The teacher, Barbara Shreve, created a lesson to help students reflect on these different procedures and learn to make connection with how they are related and when to use one procedure over another. She uses a powerful lesson technique, re-engagement, where she poses methods used by different characters. The students must analyze each character’s work to make sense of whether the solution is right and then justify their claim. She also included an activity that asks students to match the test question prompts with the first step they might take the solve the problem. This lesson could be considered a re-engagement lesson because it takes ideas students have been taught and re-visits them by posing the mathematical ideas in student work. The class is required to analyze the student work and make sense of what is right or what is wrong and why. This engages students in high cognitive work.