Fractions Learning Pathways

Please Note: The purpose of this interactive planning tool for teaching fractions is to provide educators with a research informed framework. It includes a range of field-tested tasks (grades 3-10) that have proven to be effective in Ontario schools.

Created by Dr. Cathy Bruce, Tara Flynn and Shelley Yearley.
Fractions Learning Pathways are inspired by Dr. Jere Confrey’s work, based on international and Ontario classroom research, and informed by feedback from classroom teachers and student thinking.

– Mixed, improper and proper fractions should be interspersed throughout fractions teaching and learning so that the
students build flexibility with these early.
– “Models” include linear, area, volume, and set representations.

Yearley, S. & Bruce, C. (2014). A Canadian Effort to Address Fractions Teaching and Learning Challenges. Australian Primary Mathematics Classroom Journal, 19(4).

Bruce, C., Flynn, T. & Bennett, S. (2014). Fractions Report for 2013-2014. Submitted to the Ontario Ministry of Education, Toronto, Ontario.

Bruce, C., Flynn, T. & Bennett, S. (2014). Fractions Operations Literature Review. Submitted to the Ontario Ministry of Education, Toronto, Ontario.

Bruce, C., Chang, D, Flynn, T & Yearley, S. (2013). Foundations to Learning and Teaching Addition and Subtraction of Fractions. Comprehensive literature review submitted to the Ontario Ministry of Education. Toronto, Ontario Canada. Posted at and

Bruce, C. & Flynn, T. (2011). Which is greater: One half or two fourths? An examination of how two Grade 1 students negotiate meaning. Canadian Journal for Studies in Science, Mathematics and Technology Education, 11(4), 309–327
>View Journal

Bruce, C. & Ross, J.A. (2009). Conditions for Effective Use of Interactive On-line Learning Objects: The case of a fractions computer-based learning sequence. Journal of Education.
>View Journal /Show Abstract

Conditions for Effective Use of Interactive On-line Learning Objects: The case of a fractions computer-based learning sequence Students are challenged when learning fractions and problems often persist into adulthood. Teachers may find it difficult to remediate student misconceptions in the busy classroom, particularly when the concept is as challenging as fractions has proven to be. We theorized that a technology-based learning resource could provide the sequencing and scaffolding teachers might have difficulty providing. A development team of teachers, researchers and educational software programmers designed five sets of fractions activities in the form of learning objects, called CLIPS. As part of a larger mixed-methods study, 36 observations as well as interviews were conducted in four classrooms, grades 7-10. Four students were selected by their teachers for CLIPS use from each of these four classrooms because the students were experiencing difficulty with fractions concepts. CLIPS use contributed to student achievement, provided the conditions enabled an effective learning environment and students experienced the full sequence of tasks in the CLIPS. In this article we describe the conditions that enabled student success. Three interacting contexts affected successful use of CLIPS: technological contexts (such as access to computers with audio), teaching contexts (such as introductory activities that prepared students for the CLIPS activities) and student contexts (such as the level of student confidence and opportunities to communicate to a peer). The study illustrates how a research-based set of learning objects can be effective and provides guidelines to consider when using learning objects to enhance mathematics programs.

Ross, J.A., Ford, J., Bruce, C. (2009). Student Achievement Effects of Technology-Supported Remediation of Understanding of Fractions.
>Download Article

Bruce, C. Ross, J.A. & Scoffin, S. (2007). Tools to support low achievers: A mixed methods study of students learning fractions. Interim Report of Ontario Ministry of Education & Training Research Grant, Peterborough, ON: Trent U/OISE of UT