This blog is a repost of a four-part series I wrote for NCTM’s Blogarithm in 2016. Read the original post here.
we’ve talked about the importance of mathematical conversation and what it sounds like coming from our students. I know that as teachers, we already have a lot on our plates. Spiral review, standardized test prep, fluency practice, and now class discussion, too? Believe me, I had the same concerns at first. I didn’t appreciate the importance of student discussion until I started participating in workshops that focused on collaboration in problem solving that challenged my misconceptions. Placing myself in the role of a student allowed me to reconnect with what it felt like to engage a problem without being sure of the answer and to engage with my peers.
The good news is that there are ways to fit regular discussion in your classroom. Summer is winding down; now is when I like to look over my plans for the upcoming school year and ask myself a few questions:
Does this topic need to be taught directly, or can students do most of the work themselves?
It’s so easy as a math teacher to feel like I am keeper of the knowledge. It’s understandable; math has developed a bit of a reputation for being accessible to only the best and the brightest. However, many topics are within students’ reach simply by asking them to build on their prior knowledge. Many times, my students struggle with a topic simply because it sounds difficult. Luckily, this has an easy fix: I don’t tell them what we’re working on. By asking my students to engage with a problem without setting up their expectations, they have one less opportunity to opt out early.
One of my favorite topics for student-led learning is transformations in eighth-grade geometry. I assign different topics to students by readiness level and have them work together to understand their individual topic. Once they have mastered their assigned transformation, I then have students jigsaw to teach one another. Although students are doing the bulk of the teaching, I continue to circulate and make sure that they are questioning one another instead of simply accepting what their peers are saying. I spend the same amount of class time had I had taught each topic myself, and I’ve given my students the opportunity to be experts, which they can carry with them throughout the year.
Can I modify this activity to encourage discussion and collaboration?
I’ve been guilty of giving my students worksheets with page after page of practice problems. It is tempting to be lured by the idea that more practice is always best. However, education author Rick Wormeli says it best: “Students who can successfully complete five problems will be frustrated by having to complete fifty, and students who cannot successfully complete five will be frustrated by being asked to complete fifty.” Students can complete repetitive practice on their own time. I’d rather devote class time to activities that they cannot complete on their own.
That being said, standardized testing is the unfortunate reality for many of us. As a result, we are often required to include test prep as part of our classroom instruction, particularly toward the end of the year. Multiple-choice questions are often maligned for not providing meaningful information about student understanding. In my classroom, I like to turn this around by asking my students, “Without solving, can you eliminate some answer choices? How do you know?” This opens the floor for interesting conversations about reasonable answers.
How can I encourage students to participate?
As I mentioned in the last post, great conversations cannot take place in a classroom in which students feel like they are not safe or respected. As the teacher, it is my responsibility to set the tone for what is acceptable. It is important for me to establish a classroom culture early in the year where mistakes are not only okay but also encouraged as a critical part of the learning process. I post quotes in my classroom from important mathematicians and nonmathematicians who understand that mistakes are a necessary part of greatness. I also highlight my own students’ “lightbulb moments”—excellent questions, analytical observations, or aha! times. By calling special attention to a moment of great thinking, students are encouraged to reach outside of their comfort zones and have their opinions and concerns validated by their peers.
“That sounds great, but there’s no way my students could do that.”
Confession time: I have not been teaching this way for my entire career. I bought into the myth that because my students had behavior problems or came into my classroom with math deficiencies that I wouldn’t be able to use these techniques in my classroom. Finally, a mentor teacher asked me an important question that has become my new motto: “What’s the harm in trying?” By changing my mindset and trusting my students, I no longer rob them of opportunities based on my own fears or misconceptions. You’d be surprised what your students can accomplish!
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