Sharing Good Practice
“WHAT’S THE STORY?” USING CONTEXT TO DEVELOP
REASONING AND COMPUTATIONAL FLUENCY
BY CORY A. BENNETT, PH.D.
P
art
of
the
beauty
of
mathematics lies in the
solutions; we can know if we are
correct or incorrect. However,
the solution is not the most important
part of doing mathematics. In fact, it is
actually the last thing that matters and
is really only the tip of the proverbial
iceberg when doing mathematics.
What this means is that the majority of
doing mathematics comes well before
we get a solution. Doing mathematics
includes such things as understanding
the nature of the problem; identifying
key
variables,
quantities,
and
operations
involved;
considering
possible solution pathways; and
reasoning about this information.
One way to help students attend
to these skills is by grounding the
mathematics in a context. By creating
a story for the calculations, students
also create meaning around the
operations. This helps them to use
mathematics to find a resolution to
the story rather than operating on
numbers for computational reasons
only. For many students, performing
calculations is just about “answer
getting” as they do not see, or have not
considered, what these calculations
mean.
In one third grade class, that was just
learning about multi-digit subtraction
within 1000, the teacher used the
expression 145 – 29. This expression
was rigorous enough for the students
as it involved operating on numbers
that have a digit in the hundreds place,
which was new to them, and required
regrouping, a skill they had learned
previously. However, the teacher set
the stage by telling a story in this way:
Teacher: The other day I was making
cupcakes for all the students attending
the end of year school party. I knew
there were 145 students all together
but the two fourth grade teachers
told me their classes would not be
attending because they would be on
a field trip. The fourth grade teachers
also told me there were 29 students
altogether in their two grades. I was
left wondering how many cupcakes
I should make for the rest of the
students. I would like you to help me
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think about how I should go about
figuring this out.
The students were then asked to talk at
their tables about how they might help
the teacher figure out what to do. After
a few moments, the teacher brought
the students back together and a
rich conversation pursued that was
lead almost entirely by the students.
They talked about estimating, “145 is
almost 150 and 29 is almost 30 so that
you should probably make about 120
cupcakes”; identifying the appropriate
operation, “well, you are going to
have to take the 29 away from the
145 because you don’t need those
[29] anymore”; and regrouping, “I see
that we are going to have to do some
exchanging because it is not easy to
minus the ones.”
Class Time
In time, the teacher had the students
develop their own stories around
expressions. Students were given an
expression and were told to create a
story that would match the expression.
Next, they were to exchange their
story with a classmate and the
classmate provided feedback on why
they believed the story did, or did not,
match the expression. The students’
efforts became about reasoning and
using mathematics appropriately to
make sense of the calculations.
Context matters. It helps students
learn to make sense of and reason
about, calculations and operations.
So when you are looking at helping
students make meaning out of
calculations, ask them “What’s the
story?” And listen to how they create
meaning from context.
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.