Fractions Gain Traction With Real- Life Models

Aug. 27, 2013 — If 3 is greater than 2, then ⅓
must be bigger than ½ -- right? Wrong. As
thousands of students head back to school
next week, many will use exactly that kind of
thinking when faced with fractions for the first
time. New research from Concordia University
shows that for children to understand math,
teachers must constantly make the connection
between abstract numbers and real world
examples.

Helena Osana, associate professor in
Concordia's Department of Education, and PhD
candidate Nicole Pitsolantis put this theory to
the test in a classroom of fifth and sixth
graders. Their findings -- published in the
professional journal Teaching Children
Mathematics, as well as in the British Journal
of Educational Psychology -- show students
understand math much more clearly when
teachers use pictures and concrete models to
demonstrate what fractions actually mean.
Those connections are even stronger when the
model is personally meaningful to the
students. Write out '¾' on the blackboard and
the concept is not so clear. Show kids ¾ of a
shoelace or talk about running ⅓of the way to
school and suddenly they get it.
Although teachers already use models when
talking about fractions -- for instance, to show
a picture of a pie with slices eaten -- they
often put them away too quickly. To prove that
the constant use of models made a bigger
impact, Osana and Pitsolantis tried teaching
with models for only part of the lesson and
then the entire lesson.
They found that students showed much greater
understanding when the models were
continually present. "Our study shows teachers
should not only include pictures and models
while teaching fractions, but also have them
side by side throughout the class while
continually making clear connections between
the concepts and the models," says Osana.

The lessons produced by this research have the
potential to go beyond the classroom. "This is
something not only useful for teachers but
also for parents," says Osana. "Because
children are studying fractions, parents think
they're not able to help. But parents can have
positive effect on learning too. Something as
simple as writing '¾' out on a piece of paper,
then demonstrating what it means to use ¾ of
a cup of sugar, or filling up the gas tank until
it reaches the ⅔ mark, then writing and
pointing to the numbers '⅔ ,' can really go a
long way towards demystifying math," she
says.
Pitsolantis, who also teaches fourth and fifth
grade math at Lower Canada College in
Montreal, says that the depth of
misunderstanding that happens when models
are abandoned surprised her. She and Osana
are now testing out how teachers can
successfully incorporate concrete models into
other grades.

Story Source:

The above story is based on materials provided
by Concordia University .

And ( sciencedaily magazine ).