By Shelby Strong, posted August 1, 2016
So far in this series, 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:
topic need to be taught directly, or can students do most of the work
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.
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.
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!
In the final part of this
series, I’ll share some of my favorite resources for encouraging conversation
Strong is a middle level math educator in Jefferson
Parish, Louisiana. She is passionate about mathematics and currently serves as
a Louisiana Teacher Leader. She is an active member of Twitter Professional
Learning Communities and has given presentations at the district and state
level on improving mathematical instruction.