Sharing Good Practice
HELP STUDENTS TO DEVELOP
THEIR MATHEMATICAL IDENTITIES
BY CORY A. BENNETT
Resources: www.corestandards.org/Math/
Practice/
Mathematical and Learning
Norms
There are various acceptable ways to
establish classroom learning norms
but one that helps with productive
struggle centers on the importance
of quality work over completed work.
This learning norm also strengthens
an important mathematical norm
that values the process of doing
mathematics over the answer or the
completed product. There is no doubt
that answers matter in mathematics
but they are the last thing that matters.
The way students think about,
conceptualize, and engage with the
content matters far more as the answer
will not mean anything if their thinking
is not sound.
H
elping students to learn to
do mathematics, rather than
just calculate and determine
solutions, requires students
to adopt the identity of a student
mathematician. This includes adopting
the academic behaviours, habits of
mind, and ways of interacting with the
content in order to conceptually learn
and apply the mathematics even when
faced with unfamiliar or new situations.
Essentially, learning how to struggle in
productive ways—ways that leverage
a growth mindset, value persistence,
and view mistakes as opportunities—
requires students to have particular
learning conditions met prior to being
able to engage in productive struggle.
Common approaches often focus
on the nature of questions asked to
students, asking students to “think
more” on the problem, or “try a
different way.” While such suggestions
and actions can be helpful, they are
only helpful if other conditions are
in place. Three of these conditions
include:
Students’
mathematical
identity, mathematical and learning
norms, and beliefs about doing
mathematics. To avoid your own
struggles in helping students learn
how to be a mathematical problem
solver who can and does struggle in
productive ways, attending to these
conditions can help tremendously.
10 |
Jan - Feb 2019
|
|
Mathematical Identity
A student’s mathematical identity is
paramount to their overall success
in mathematics. Recently I asked a
group of elementary and middle
school students to draw a picture of
a mathematician. In not one drawing
did they draw a student. All of the
drawings were male (except for the
drawing of a robot) and nearly all were
older wearing eye glasses and lab
coats with scraggly hair (anyone come
to mind?). Unless students understand
that they can be a mathematician, they
will struggle to relate to the content.
A few tips to help strengthen students’
mathematical identity include referring
to them as mathematicians and the work
they do as work of mathematicians.
Also, point out and commend them
when they use mathematical behaviors
(like those found in the Standards of
Mathematical Practices link below) and
demonstrate persistence. Also, remind
them that mistakes are expected;
anything worth learning will fight
back, paraphrasing one of my favorite
quotes from the Danish mathematician
Piet Hein.
Class Time
A few tips to help build strong
mathematical and learning norms
begins with altering some grading/
assessment practices. Instead of
assigning a grade or score to an early
learning attempt, provide focused
feedback with the expectation that
revisions are expected. Even then,
make the classroom discussion on the
process, and what they learn from the
process, rather than on just the answer.
The norms we set for mathematics
should reflect the kinds of behaviors
and habits of mind we expect to see
from students. A good resources and
list of mathematical norms you might
want to use with your students can be
found at YouCubed link below.
Resource: www.youcubed.org/resources/
classroom-norms-poster/
Students’ mathematical identity, the
mathematical and learning norms in
the classroom, as well as students’
and teachers’ beliefs about doing
mathematics are all prerequisite
conditions to supporting productive
struggle and developing students’
Mathematics identity.
Dr. Bennett is a passionate educator who strives for equity in learning for all
students. As a global consultant and an Associate Professor of Education
specializing in curriculum and instruction, he has worked with educators
throughout the United States and across the Middle East, Europe, Australia,
and Asia.