A Middle School Teacher's Journey from Direct to Discourse-Based Math Instruction

By: | 06/03/2021
Category: Instruction

I’d like to say that I transitioned from a traditional direct instruction style of teaching to a student-centered, discourse-based style of teaching out of well-informed personal conviction. Or that I read some incredible thought leadership and recognized that my students needed more than I was giving them. Or that I simply realized that I needed to hear more of my students’ thinking in class.

I’d like to say those things, but if I did, it wouldn’t be true.

My first few years in the classroom were a blur. I was a capable teacher, but I practically sprinted from task to task. Lesson planning, grading, classroom management, professional development—every aspect of my work got exactly as much attention as it needed to get done well and no more. I was so busy being a teacher that I didn’t have time to think about teaching.

When my curriculum director announced that we’d be completely changing how we taught math in our school, I gave it as much thought and time as I could spare: none. Teachers, like entertainers, know the show must go on. My fellow math teachers and I accepted this news like the professionals we were and carried on.


"Teachers, like entertainers, know the show must go on."


A big curriculum change shouldn’t have been a surprise. Even before the “Big Change,” my colleagues and I spent a lot of time digging into data, looking at students’ work on recent assignments, and talking about trends we saw in our classes. Although we had impressive growth numbers, our students’ performance on open-response questions were behind where they should be. Also, high school teachers would report back to us that our former students struggled more than they expected, given the students’ test scores and grades. Our successful-looking students weren’t as successful as we thought they were.

The common thread we identified was a lack of problem-solving flexibility. Students were proficient at solving problems they’d seen before, but when faced with something new (e.g., a different problem type, a surprising application of their mathematical skills, or an open-ended or exploratory problem), they were lost. To be truly fluent in math, our students needed to be able to flexibly apply their knowledge to whatever problems the world put in front of them.

The Old Plan

Before we adopted the new plan, most of the other teachers and I used a fairly basic direct instruction routine for our lessons. Here’s how a typical class would go:

Time

Section

0:00–0:02

Greet students, read the day’s learning objective, and have students write down homework for the night.

0:02–0:07

Students work on an opening activity that reviews or activates pertinent skills while I collect and track homework and/or pass back graded work.

0:07–0:12

We go over the opening activity together, with me asking questions related to my intent in picking the problems.

0:12–0:17

Students take notes in a classwork packet while I explain the day’s new concept.

0:17–0:20

We work on a problem or two as a class.

0:20–0:40

Students work on the day’s problems, with me circulating to help, check progress, and differentiate as needed. I occasionally bring the class together to answer common questions or address misconceptions.

0:40–0:46

Students work on a silent, independent Exit Ticket.

0:46–0:50

Students pass up their Exit Tickets, we restate the topic of the day, and I give any closing comments or questions.

0:50

Students are dismissed.

 

It wasn’t a bad plan for a rookie teacher. It was simple, easy to understand, lent itself to routine, and made it so I had a prayer of “getting the job done” each class. Unfortunately, it trained students to expect knowledge to be given to them directly rather than having to (dare I say, “getting to”?) discover it for themselves.


"There was no yeast in the bread—no room for exploration or growth. My routine was safe, but it was not good."


The plan’s biggest flaw was that it only achieved its explicit goals: students only learned what I wanted them to learn. There was no yeast in the bread—no room for exploration or growth. My routine was safe, but it was not good. Since many teachers used a similar routine, it made sense that we were seeing similar issues.

The New Plan

What my curriculum director proposed was to dramatically shift the in-class, intellectual heavy lifting from teachers to students. To do this, we would need to repurpose this part:

0:02–0:07

Students work on an opening activity that reviews or activates pertinent skills while I collect and track homework and/or pass back graded work.


And get rid of this part entirely:

0:12–0:17

Students take notes on a classwork packet while I explain the day’s new concept.


Students would still start class with an opening activity, but instead of it being an opportunity for review, intervention, or data collection, it would be a chance for students to work with a problem that introduced the next skill or concept students needed to learn. The opening activity would be achievable, but it would require students to take a step beyond their knowledge. Teachers would still circulate as students worked, but instead of focusing on collecting homework and filling out trackers, we would be looking at students’ work to decide whose work to share with the class and in what order to do so.

Next, rather than the teacher explaining the day’s lesson and students taking notes, we’d put students’ work on the opening activity under the document camera and ask other students to explain it. Students had to examine each other’s work, make sense of it, and talk about what they saw and understood. Teachers would lead by asking questions, guiding students toward the day’s big idea without doing the thinking for them. The discussion would end when we agreed on the big takeaway from the problem.

Here’s what our classes looked like under the new plan:

Time

Section

0:00­–0:02

Greet students, read the day’s learning objective, and have students write down the next homework assignment and turn in last night’s homework.

0:02–0:11

Students work independently on a problem that incorporates a new, never-before-seen idea or skill. I circulate to look at students’ work and decide which work I want to share and in what order.

0:11–0:20

I show students’ work on the document camera and lead a class discussion about the problem. Students explain one another’s work and come to an agreement about what the big idea for the day is. We all record the big idea for the day.

0:20–0:30

We apply the big idea to a few more examples. Students still do all the intellectual lifting.

0:30–0:45

Students practice the new idea independently, with a partner, or students’ choice, depending on the lesson, class, day, vibe, etc.

0:45–0:50

Students complete an Exit Ticket. We repeat the big idea for the day.

0:50

Students are dismissed.


It seemed like a good plan. Our administration would provide us with the resources that we would use for every lesson. Students would practice solving new problems with unfamiliar skills every day—exactly what they struggled to do on major assessments and in high school. They’d also get to see each other’s work, exposing more strategies and perspectives. I anticipated another benefit: if students knew their work could go up on the board, maybe they’d write more neatly.

Making the Changes

One difference I noticed immediately was that I didn’t need to print anywhere near as much as I used to. A few application and practice problems were plenty for each class period—no more big packets. Less printing also meant less time at the copy machine, meaning more time for me to do literally anything else.

Planning was easier, too. I needed to read the prep documents, know what the big idea for the lesson was, and solve the problem using the big idea. I tried to anticipate a few different strategies students might use to solve the problem, but it was okay if I didn’t predict them all.

I realized that the best way to ensure students were doing the intellectual work was to use as few declarative statements as possible during instruction. I tried to limit myself to three per class. This meant I was leading the discussion by asking questions. While some teachers prepared their lines of questioning in advance, I didn’t find preparation helpful. Instead, I tried to focus on responding authentically to students in the moment.

The Impact of the Changes

Students loved the new routine! They seemed to enjoy class more and were more engaged. Because the emphasis was on meaning making and how people solved, rather than on the answer, there were more opportunities for their work to feel significant and helpful. Students who struggled with math were presented with frequent, low-stakes ways to participate, and because they saw several different perspectives on the same problem, they had a better chance at understanding the day’s big idea.

I loved the new routine, too! Teaching was more interesting. Running class discussions was an immersive, satisfying experience. Preparing this routine helped me understand the standards and my students better, making me a more perceptive and insightful teacher. Limiting myself to asking questions meant I talked less, which was particularly helpful as I frequently suffered from laryngitis. Not only did class time fly by (in a good way), but because students focused on fewer higher-quality problems, I had less to grade. To top it off, at the end of the year, our state test results confirmed what we were seeing in our classrooms: students were improving.

That said, if I could have changed one thing about how my colleagues and I executed the new plan, I’d have added something like the Family Letters in i-Ready Classroom Mathematics. Without textbooks or explicit, traditional notes, parents couldn’t easily follow along with what their children were learning in our class discussions. Mathematical models like tape and bar diagrams, double number lines, and area models aren’t always intuitive or familiar to adults—even adults fluent in algorithmic computation—and that meant parents couldn’t help their children with their homework with confidence.

Now, with the luxuries of perspective and time, I’ve been able to do all the contemplative academic work I couldn’t squeeze into my day when I was teaching. My intuition told me that the changes we made to our teaching were positive, and now my pedagogical knowledge has caught up with it and agrees. I’m glad I had the trust in my team to run with these changes. They’re better in hindsight than I ever could have hoped.

Teacher and students sitting on the floor.

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