Fractions gain traction with concrete models

Aug 27, 2013
Helena Osana, associate professor in Concordia's Department of Education, and Ph.D. candidate Nicole Pitsolantis are the two researchers who carried out the new study on how children learn fractions. Credit: Concordia University

If 3 is greater than 2, then ⅓ must be bigger than ½—right? Wrong. As thousands of students head back to school, 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 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 and the concept is not so clear. Show kids ¾ of a shoelace or talk about running ? of 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 , parents think they're not able to help. But 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 ? mark, then writing and pointing to the numbers '?,' 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 can successfully incorporate concrete models into other grades.

Explore further: Why are UK teenagers skipping school?

add to favorites email to friend print save as pdf

Related Stories

Time-poor parents go digital to communicate

Apr 16, 2013

Teachers are turning to twitter, blogging and Facebook as a way of keeping in touch with parents about their child's learning, and according to QUT education expert Associate Professor Margaret Lloyd it is ...

Recommended for you

Why are UK teenagers skipping school?

5 hours ago

Analysis of the results of a large-scale survey reveals the extent of truancy in English secondary schools and sheds light on the mental health of the country's teens.

Fewer lectures, more group work

6 hours ago

Professor Cees van der Vleuten from Maastricht University is a Visiting Professor at Wits University who believes that learning should be student centred.

How to teach all students to think critically

6 hours ago

All first year students at the University of Technology Sydney could soon be required to take a compulsory maths course in an attempt to give them some numerical thinking skills. ...

Consumer loyalty driven by aesthetics over functionality

23 hours ago

When designing a new car, manufacturers might try to attract consumers with more horsepower, increased fuel efficiency or a lower price point. But new research from San Francisco State University shows consumers' loyalty ...

User comments : 1

Adjust slider to filter visible comments by rank

Display comments: newest first

antialias_physorg
not rated yet Aug 28, 2013
I tutored a lot of children in math to pay may way through uni. Many of them had problems with fractions.
As soon as you applied fractions to money ("What's more: half a Euro or a third of a Euro?") then they had no problems at all.

Kids have experience with money. So the simple solution is: Use something they are familiar/comfortable with as a model.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.