It’s against the rules but… rather than use a “Day in the Life” format for this post, I’ve decided to focus on the work that I’ve done recently in my Algebra class.
A few weeks ago, our Supervisor of Secondary Instruction called a meeting of all high-school Algebra teachers in our district (there are five of us) to talk about the many unique issues involved with teaching this Keystone tested course at the high-school level. We had a productive conversation but I want to mention two things from our meeting that have really stuck with me. The first is that when we break students into small groups for instruction, it is not about separating three behavior issues into three different parts of the room. It has to be about moving students into homogeneous learning groups so that those who are ready to move forward can do that, while others take more time with the material. This is something I already knew but the reminder came at a good time for me and I reexamined my groupings as a result.
The other piece of the discussion that has stuck with me is a quick few sentences exchanged about the scope of the curriculum. I have often been torn between rushing through all of the concepts in the curriculum guide to expose students to as much as possible OR going slowly and thoroughly over the basic ideas of Algebra to ensure that students have a strong foundation. My fear is that the latter option leaves them with gaps in their prerequisite knowledge when they move forward. During our conversation last week, our Instructional Supervisor suggested that I might allow my lower achieving group to continue practicing the foundational skills while students who have demonstrated mastery of those skills move ahead to see more of the curriculum. Here’s how I immediately applied that idea…
We have moved on to our study of solving equations. This is what I consider to be the most important unit of study in Algebra 1. Students who aren’t able to solve equations this year will likely fail algebra. Students have seen this material in their pre-Algebra classes, but this is where the wide range of student achievement present in Algebra class really presents itself. We have students who look at “x + 5 = 12” and shut down immediately. We have others who have completely mastered this topic before they get to Algebra class, and most are somewhere in between.
After a few days of practice, I give the students a short (5 question/10 point) quiz to see where they are on the spectrum. I call this a “check-up”. In the past, I have used the quiz results to find out who is struggling with solving equations but have not felt that I could do much with that information aside from recommend that they seek help outside of class. After this quiz, we move onto some more challenging and concepts: solving literal equations and solving absolute value equations. Without an understanding of solving one-step, two-step and multi-step equations, students are unlikely to be successful with these last two lessons of the unit. This year, I separated the quizzes into two piles as I graded: students who have demonstrated that they understand the basic concepts involved with solving equations versus those who seem to be simply recalling or copying procedures without an understanding of why those steps are needed. I found a handful of students in each class who made alarming procedural errors on their assessments. I put together packets of one-step, two-step and multi-step equations for these students and had my coteachers pull them aside to work in a small group for the next four class days while the majority of students moved ahead to solving absolute value equations.
I split the remaining students in each class into two groups based on their quizzes.
GROUP A: Those students who had very few errors or no errors at all were assigned to watch a short video about solving absolute value equations and then try some problems on their own.
GROUP B: Students who demonstrated that they understood the main idea but still needed some guidance to avoid common mistakes worked with me to learn about solving absolute value equations. I was able to go slowly through the process and discuss important decision points with this group.
The next day, GROUP B was able to work on some independent practice while I worked with the students from GROUP A. I walked around with my small white-board in hand to watch each student solve one equation. I was able to quickly answer the few questions that arose and address misconceptions.
Yesterday, the whole class completed a practice activity similar to the one described in my last blog post where students moved around the room solving problems at various stations. The students who had been pulled out by my coteachers participated as well since I had mixed in some linear equations for review. Those students completed only the linear equation cards.
Today, while the rest of class began their study of literal equations, the students in each group who performed poorly on their equations quiz tried again. Each student showed improvement. The photos below of one student’s “before” and “after” quizzes shed light on how valuable this week was for him.