I recently wrote an email to a high school colleague about the process I have used for myself to transition from a teacher-directed, lecture-driven classroom to one that generally uses small-group instruction. In this blog post, I will share what I wrote to her as a way of “taking off the top of my head,” like I do when teaching my 7th graders, to see if sharing my thought process as it happens in the moment will be helpful.
Topic: reviewing a Skill Assessment (quiz) on translating between forms of linear equations (i.e., write an equation in slope-intercept form in standard form, etc.). This is a struggle for our students, although it’s better this year because we did a few days on literal/explicit equations at the start of the module.
Preparing for Class
Background: The students took a quiz with four problems on Thursday. We had a field trip on Friday. I took the quizzes and sorted them out, as follows, for groups on Monday:
- One student got a 100%. I returned her quiz to her at the start of class (after I reviewed the agenda and checked HW).
- One student got a 91% by making two mechanics errors. I returned his quiz to him and asked him to revise his errors on his own and to bring his work to me when done to check.
- Two students were absent; they needed reteaching, but they were both out.
For the remaining students, I started with the second question on the first page (on rewriting an linear equation in standard form). I pulled all the quizzes with errors on this problem and sorted them into three groups, as follows: I had about 12 students who did the algebra correctly but left a fractional coefficient, which they can’t do in standard format. I had another three or four who made some larger error, such as leaving the fractional coefficient and putting “C” rather than a value. I pulled six students from the first group and we talked about their error (“What went wrong? How can you fix it?”). When they were done, I checked their quizzes. If that was their only error, they took their quizzes and returned to their seats. If there was another error, I kept their quizzes and called them back for a different group later in class.
Then, I repeated this process with the other six students with the same error. Finally, I repeated the process again with students who had compound errors.
Regrouping–Moving on to the Next Problem
At that point, about one-third of the class was all done meeting with me, a handful of students were working independently on revising their own errors, and about one-third of the students needed to work with me on the two questions on the back of the quiz.
I called all of those students, about eight of them, to work on the back of the quiz in a single group. Because there were eight of them and because the errors were varied (i.e., not dividing every term by seven or not putting it into the right form or writing it as a single fraction at the end, etc.), I simply told the students we were going to do the problem all together. I used a white board with the group, seated at a lab table to the side of the room, and I wrote out one step at a time while the students made suggestions. Once we had finished the problem (correctly), the students worked to correct the final problem independently while they sat at the table, asking me questions as needed.
Wrapping it up
I sent most of the students away and worked with three others who had a smattering of totally random errors. Two students remained at the table to finish up their work and to check it with me.
At that point, it was 2:12 (we were done class at 2:25). I reminded the class that we had a quiz the next day on solving systems with graphing, so they should consider if they needed to see me. In response, a group of three boys came over and we talked about their work, including the limitations of solving via graphing, a reminder about graphing from slope-intercept form, and how to check work with substitution/elimination, which they had already discovered on their own. Two of them finished by the bell; one stayed a minute after class to talk about how to use substitution to check his work with graphing.
My high school colleague inspired this email by saying to me that she felt like she was “cheating” if she didn’t engage in full-class instruction and I think she is not alone in feeling that way. I have a hard time feeling like it’s “cheating” when I worked directly with students for literally the entire period. (You can see the data in the checklist copied in below.) Every student got direct intervention in groups no larger than eight…how often do we get to do that? Every student got targeted support (and, in all cases, they got none when the needed none, rather than having to sit through instruction they didn’t need at that moment). Groups were fluid and responsive, rather than scripted. When I talk about it that way, this approach of using small groups doesn’t look like cheating to me!