Do fractions make you squirm? What’s ½ of 3/4?  Reducing the anxiety that fractions trigger in so many people is the goal of Trent University’s Vice-President of Research & Innovation, Dr. Cathy Bruce, and her research colleagues Tara Flynn and Shelley Yearley, in their new book, Rethinking Fractions: 8 Core Concepts to Support Assessment and Learning. 

“We've had ongoing challenges in North America where a large population of children, adolescents and adults experience anxiety and general dislike related to learning mathematics. It often ties to problems with our understanding of fractions and their use,” said Professor Bruce. “We've got to find ways to make mathematics joyful and meaningful. In this research program, we have worked with students and their teachers over many years to find that combination of joy and meaning.” 

An expert in math education and spatial reasoning, Prof. Bruce and her team spent six years working with over 2,000 students to learn what really works for elementary and secondary school children. Their book, which was an additional four years in the writing, is a professional resource for teachers that provides a critical foundation to understanding fractions and their use. One of these critical ideas is the importance of “unit fractions” (any fraction with 1 as the numerator, e.g., 1/5, 1/27, 1/10). They found that explicitly teaching students about units made a difference. For example, consider using the measurement of a metre as a unit. We can visualize a metre divided into fifths, or twentieths, or hundredths. And the unit of a metre is different than the unit of a centimetre, just as the unit of one-fifth is different than one-twentieth. 

 “This is partly an equity issue, in making sure that everybody has access to a really good mathematics understanding as a baseline which sets them up for success.” says Bruce. She goes on to explain how important fractions understanding is in life: “Consider the importance of correct dosages of medicine, for example. We definitely want to make sure we get the right treatment, without any dosage calculation errors!” A body of research also shows that a good understanding of fractions lays the foundation for success in algebra and other higher mathematics – which widens potential career pathways for students.  

Rethinking Fractions highlights 8 core concepts that Dr. Bruce’s research revealed as building blocks for understanding fractions. Dr. Bruce describes these 8 concepts as gears that connect and propel understanding of fractions when they work together, in combination. As Dr. Bruce explains, “It’s time to get those gears moving!” 

What’s next for Prof. Bruce? 

Prof. Bruce is connecting Rethinking Fractions to her ongoing research program called Math for Young Children. She has initiated a study to explore how young children naturally think about proportions and fractions. The goal being to give children rich spatial experiences that support later formal learning about fractions and their use. Spatial reasoning is predictive of later success in math, which is itself predictive of overall academic success, so it’s a great anchor for fractions thinking. 

“I am driven to improve mathematics teaching and learning,” said Prof. Bruce. “It's deep inside me. So I'm going to keep doing this work. I'm going to keep trying to find ways to make math really engaging and accessible for lots of people.”