Ad Infinitum – From Bright Spots to Bright Landscapes

PRIMEd Principal
October 2015


This YouTube  video describes the essential shifts in mathematics instruction and serves as a useful tools for leaders working with families and community members.


Mathematics is as much an aspect of culture as it is a collection of algorithms.

~Carl Boyer~

In order for meaningful change to occur, change that will impact the mathematics outcomes for every student in every classroom, we must have school leaders who are willing to initiate, foster and enhance collaborative mathematics learning structures that impact every teacher. The National Council of Supervisors of Mathematics (NCSM), through the PRIME leadership framework and its companion resource, It’s Time, has equipped us with two powerful tools to guide this effort. As a principal engaged in the work of building this capacity, I draw upon these resources to structure my actions, guide my reflections, and sustain my courage.

As expressed in It’s Time, it is imperative that principals lead in a way that helps teachers envision, believe, understand, practice, receive feedback, and work collaboratively while holding themselves accountable to each other and to their students. The staff at Park Avenue P.S., the school I most recently worked with, is well on its way to achieving a school-wide transformation of math teaching and learning. Over the past few years, mathematics teachers have worked hard to move from a few ‘pockets of exemplary practice’ in some classrooms to a ‘landscape of exemplary practice’ evident in all classrooms.

Strategies for Implementation

Parents are seeing their children using mathematical models and alternative strategies that initially seem strange or unusual to them. At first, we were getting questions, lots of questions. Most of the concerns were based upon the lack of understanding of how mathematics teaching has changed over the past 20 years and how these changes have been received by parents and the general population. A big part of my job as principal is to try to help people understand both our practice and our pedagogy. There are three key messages I try to convey through my advocacy:

  • Addressing Concerns with ‘The New Math’ – There is no such thing as ‘new math’. Math is the language we use to understand and describe the patterns, relationships and characteristics of our universe. This language is expressed using numbers and symbols that have remained constant for thousands of years and will remain so as long as the fundamental physics of our universe remain the same. We can use a lot of terms to describe math, but new is not one them. The emphasis in mathematics has always been on understanding number patterns and relationships to improve thinking and reasoning; this is far from a new
  • So What is New? – Over the past 30 years a few things have changed where it concerns education; in math, and all other disciplines. Across the globe, we now expect that schools will ensure that every student will meet a high standard of literacy and mathematical understanding. Every nation expresses something similar to the Conference Board of Canada’s Employability Skills Index. In addition, research into the neurological, psychological, and sociological factors around learning have had a profound impact on the pedagogy and teaching practices of teachers as they respond to this research in their classrooms.
  • The ‘Real Basics’ – Whether referencing the Common Core State Standards (CCSS), the Ontario, or Alberta Curriculum Standards, parents are struggling to understand why we aren’t just teaching the basics. The diversity of models and strategies that our teachers are introducing are vastly different from the tools they used to get by in their own studies. By ‘basics’, parents usually mean things like the standard algorithms for addition, subtraction, multiplication and division. Anyone who has tried to actually explain the algorithm for long division without using tricks or vampire analogies (just what is a goezinta anyway?), knows that an algorithm is anything but ‘basic’. The algorithm often works against the desire for students ‘understanding’. The real ‘basics’ are the numbers. Our emphasis on helping students understand our number system, using meaningful models and thoughtful strategies, equips them to leverage mathematics in its truest form; a powerful, logical language for solving problems and communicating. These are far more useful life skill when compared to the traditional set of clever tricks and shortcuts. If a child doesn’t understand the relationships among the numbers they are working with, then they don’t know the math. Oh, and it is also important to note that since algorithms are culturally based, there are actually many algorithms. In fact, there are far more than we, in the western culture, have experienced or could even fathom.


Across North America, principals and teachers are working together using collaborative structures to better understand how to teach mathematics in a way that will enable each student to become confident and capable communicators in mathematics. Not an easy task, but ultimately a worthy one. At its core, mathematics is a language that is expressed using numbers – the beauty of which is the infinite nature of these numbers, not unlike the infinite capacity of our teachers and students.

Guest Blogger

Brian Harrison is an NCSM member and K-8 principal with the York Region District School Board. During his 24 years in public education he has taught at all levels in the elementary school system, served as a school Math Coach and worked as a District Mathematics Consultant. He feeds his appetite for collaborative learning at Clearmeadow P.S. in Newmarket, Ontario, Canada and online through his blog, The Open Office and on Twitter as @bharrisonp.

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