All Research

Three literature reviews were completed during the course of the research project. A number of brief research summaries were developed from these literature reviews to allow educators to identify key instructional decisions known to improve student learning. They include suggestions for precise classroom instruction.

Literature Reviews

Foundations to Learning and Teaching Fractions: Addition and Subtraction [pdf] [html]
Fractions Operations: Multiplication and Division [pdf] [html]
Rational Number Teaching and Learning [pdf] [html]

Math Teaching for Learning Research Summaries

Ways We Use Fractions [pdf] [html]
Developing Fraction Number Sense [pdf] [html]
Purposeful Representations [pdf] [html]
Rectangles, Number Lines and Circles, Oh My! [pdf] [html]
Developing Proficiency with Partitioning, Iterating, and Disembedding  [pdf] [html]
Building Understanding of Unit Fractions [pdf] [html]
Building Understanding of Equivalence [pdf] [html]
Building to Addition and Subtraction of Fractions [pdf] [html]

A major component of the research project was knowledge mobilization of the key findings of fractions teaching and learning. A number of resources are available in order to allow all educators access to a range of professional learning supports.

Paying Attention to Fractions

Paying Attention to Fractions [pdf] [html]
  • Actions to Develop Fractions Understanding [pdf] [html]
  • Intentional Tasks to Develop Fractions Thinking [pdf] [html]
  • Fractions across Strands and Grades: Sample Tasks [pdf] [html]
  • Being Responsive to Student Thinking [pdf] [html]
Paying Attention to Fractions Overview [Adobe Presenter]

Videos

Fractions Research Top Ten Lessons [video] [transcript]
Teaching Fractions: What's the Big Deal [webcast]
Teaching Fractions: Focusing on Unit Fractions [webcast]

Virtual Learning Sessions

Unit Fractions

Based on Paying Attention to Fractions and related research, this Adobe Connect session will explore the role that unit fractions play in developing a solid fraction number sense across K-12 learning. In this session you will have opportunities to:

  • understand what a unit fraction is and how this changes the way we think about fractions;
  • examine how unit fractions can support learning across number systems and algebraic contexts;
  • develop deeper understanding of fraction as a number by engaging in the actions of partitioning, iterating and disembedding.
Click here to get started.
Comparing Fractions

Through a variety of classroom ready activities participants will gain a deeper understanding of purposeful selection of representations, foundations of equivalency and comparing fractions. Using both participant and student thinking, discussion will highlight mathematical thinking and anticipated responses.

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Addition and Subtraction with Fractions

Through a variety of classroom ready activities participants will gain a deeper understanding of purposeful selection of representations, as well as foundations of addition and subtraction of fractions. Using both participant and student thinking, discussion will highlight mathematical thinking and anticipated responses. As well, the role of fraction number sense and connections to prior learning of operations will be explored.

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Multiplication and Division with Fractions

Multiplication and division of fractions is frequently taught solely based upon the algorithms. This strategy obscures the mathematics, particularly in the case of division where multiplication is used. Research in Ontario classrooms have uncovered the importance of purposeful representations for fractions instruction, especially in the learning of multiplication and division of fractions. This session will explore these learnings through classroom ready tasks.

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Professional Learning about Fractions: A Collaborative Action Research Project

Over six years of research a range of qualitative and quantitative data was collected about fractions learning and teaching and professional learning. This data is shared in a variety of documents and videos. The two videos included detail the history of the development of the Fractions Learning Pathways and the reserach findings.

Ontario Fractions Research Videos

Fractions Research Overview [video] [transcript]
Fractions Research Findings [video] [transcript]

Ontario Fractions Research Summaries

Planning for Effective Professional Learning in Mathematics [pdf] [pdf bw] [html]
Fraction Research Summary 2017 [pdf] [html]
Fractions Research Summary 2015 [pdf] [html]
Fractions Research Summary 2012 [pdf] [html]