PLANNING FOR EFFECTIVE
PROFESSIONAL LEARNING
IN MATHEMATICS:

INTRODUCTION

Dr. Cathy Bruce and her research team from Trent University, in partnership with the Ministry of Education, have been conducting research on fractions teaching and learning in Ontario since the fall of 2011. The goal of this research has been to investigate effective instructional strategies in the difficult-to-teach and difficult-to-learn area of fractions. We wanted to better understand how to support students in the development of their understanding of fractions concepts and procedures. Throughout this process, we have gathered classroom-based evidence by working with teachers and students in a highly collaborative process that has involved nine school boards, 238 educators, and with targeted data collection involving 3235 students, spanning Grades 3-12. This work has led to the development of many resources for teachers and math leaders, including the Fractions Learning Pathways resource. (See p. 8 for more information on these resources and where to find them.)

With the project entering its final phases, the team looks back at the lessons learned through seven years of engaging in teacher professional learning and research at school boards in Ontario. In this document, we share strategies for maximizing the success of teacher professional learning in fractions. This document may be of interest to you if you are: a system or school leader, a mathematics consultant or anyone who is responsible for professional learning in mathematics.

WHY FOCUS ON FRACTIONS?

Fractions are central to mathematics understanding. They are an essential aspect of number sense, of course, but fractions also cross into many other aspects of mathematics such as measurement. Fractions knowledge is a predictor of success in algebra, is essential to understanding probability, and involves high levels of spatial and proportional reasoning. It is perhaps because of the complexity of the relationship between fractions and this web of connected mathematical ideas and processes that they are notoriously difficult to learn and teach. These difficulties have been researched and documented starting in the early primary years, and are shown to persist through middle, secondary and post-secondary education and into adulthood in North America (Orpwood, Schollen, Leek, Marinelli-Henriques, & Assiri, 2011). The stakes are high for students; a shaky grounding in fractions can prevent individuals from pursuing advanced mathematics and shut students off from a significant number of career opportunities in later life. For example, the STEM domains (science, technology, engineering and mathematics), as well as fields as broad-ranging as medicine, construction, art and design all demand considerable fractions knowledge. Researchers have noted that there is “a great deal of agreement that learning rational number concepts remains a serious obstacle in the mathematical development of children” (Behr, Harel, Post, & Lesh, 1992, p. 296). Fractions are a worthwhile area of focus for both teachers and students, as a foundational concept in mathematics with many connections to other important areas of mathematics.

CHARACTERISTICS OF EFFECTIVE
PROFESSIONAL LEARNING

A recently conducted study, The State of Educators’ Professional Learning in Canada (Campbell, Osmond-Johnson, Faubert, Zeichner & Hobbs-Johnson, 2016), comprehensively investigated professional learning in Canada across all 10 provinces and 3 territories. The researchers examined “promising practices” as well as challenges in the Canadian context.

Following an extensive review of the literature, the researchers found that effective professional learning:
- is focused on quality content, that:

• is evidence-informed;
• is subject-specific;
• is focused on pedagogical content knowledge and student outcomes; and
• balances teacher voice and system coherence (goals are aligned).

- possesses a design for learning and implementation to include:

• active and variable learning;
• collaborative learning experiences; and
• job-embedded learning.

- considers issues of support and sustainability, strengthened by:

• sustained duration;
• the availability of resources; and
• supportive and engaged leadership.

Their study on the Canadian education context further found that effective professional learning:

• balances evidence, inquiry and professional judgment;
• focuses on diverse student needs;
• maintains an asset-orientation towards both students and teachers;
• provides opportunities for collaboration that are job/classroom-embedded; and
• benefits from the support of system and school leaders.

These findings are consistent with earlier studies such as Hill’s 2004 study which highlighted that effective professional learning must be: inquiry-based, focused on student thinking, collaborative, job-embedded, content- and pedagogy-focused, teacher-driven and sustained over time.

In the Ontario fractions research, the professional learning that has taken place was developed with these characteristics of effective professional learning in place.

APPLYING THE FEATURES OF EFFECTIVE
PROFESSIONAL LEARNING: LESSONS FROM
THE ONTARIO FRACTIONS PROJECT

Professional learning for teachers is central to supporting the learning and teaching of fractions, given the complexity of the mathematical content and the need for classroom and teacher supports. The fractions research team, along with participating educators, have identified a number of features of the project as central to the success of professional learning in fractions in the Ontario context. The research team recommends that these guidelines be at the heart of professional learning designs and initiatives:

• allow considerable time for learning about the mathematics, including trying out tasks for later classroom use.
• provide opportunities to interpret student thinking (e.g., by analyzing and discussing student responses).
• identify areas where students are struggling and co-develop precise strategies to support students in these areas.
• include a knowledgeable other whenever possible, who can support specific content knowledge in teachable moments.
• refer to research-based resources, such as research articles and summaries, as well as lessons and tasks developed through research processes.
• engage teams of educators in collaborative processes, including classroom teachers as well as administrators, coaches, special education teachers and educational assistants, to draw on a range of insights and expertise on student learning and to ensure common understandings.
• build in structures for accountability by asking educators to return with evidence of student thinking from individual students, small groups or classroom activities and discussions.
• consider a range of learners across ability and grade levels.
• maintain a focus for the professional learning over a long period of time, such as one year or even longer, for deep learning.

FRACTIONS
LEARNING
PATHWAYS

The Fractions Learning Pathways is an
interactive planning tool intended to
provide educators with a research
informed framework.

» Available on edugains.ca

SCHOOL-LEADER FACILITATED PROFESSIONAL LEARNING

School administrators can implement content-based activities into staff learning opportunities, such as staff meetings or lunch-and-learns. Classroom visits are an additional structure in this model that brings the learning back to the classroom, and provides the impetus for school leaders to get directly involved with the teachers in their work. The information gathered during shared classroom observations can form the basis for subsequent staff meeting topics that keep the professional learning focused on the mathematics learning at the school.

A Model of Mathematics Leadership

Figure 4. A school leader sustained a focus on fractions by basing staff meeting content learning on the activities explored in a Family of Schools collaborative action research.

GREATER PRECISION THROUGH TEACHER INQUIRY

In the six years of active classroom research in the Ontario fractions project, teams focused very closely on student thinking and precision of task design and teacher moves. The observations of the teams led to important findings about powerful instructional strategies that support deep understanding in fractions (e.g., precise use of language, visual representations, active learning strategies). Below are some transformative learnings from the teams:

CORE SUPPORT DOCUMENTS FOR
MATHEMATICS LEADERS

In 2003 and 2004, three expert panel reports were released to inform mathematics learning and teaching in Ontario classrooms.

Early Math Strategy

The Report of the Expert Panel on Early Math in Ontario

Teaching and Learning

Mathematics The Report of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario

Leading Math Success

The Report of the Expert Panel on Student Success in Ontario