Archive for the ‘Mathematics’ Category

The Eternal Classroom…

May 14, 2016 4 comments

“Professional development that is most relevant for teachers is focused on teachers’ real work, provides teachers with opportunities to make choices about their own learning, happens over time, and contributes to building a professional culture of collaborative learning.”                ~Kathy A. Dunne~


Most of us envision schools as places where adults spend their time teaching children. Regardless of one’s pedagogical beliefs; constructivist, problem-based or old school transmission/bunch-o-facts, our concept of school is a place where only children learn. Though we recognize the need for  teachers to be trained, often this training (or professional development) is structured to occur out of school; at workshops, conferences or on training days.This structure does not serve either teachers or their students well.

I’ve been fortunate over my career to have had the chance to work with thousands of teachers in a wide range professional training contexts; from ballrooms filled with hundreds of teachers, to conference sessions and workshops, webinars and small group inquires. I’ve also had the chance to research all manner of professional learning structures and, in synthesizing these two sources of information, can summarize my belief about teacher professional training with the following theory of action:

If we use classrooms as places where both teachers and school leaders learn; then student learning will be richer, deeper and more impactful.

Over the past few weeks our staff have been engaged in some school-based professional learning focused on helping our teachers learn how they can use common assessment tools and practices to help them improve their math instruction.  We have put our teachers into small learning teams (3 or 4 members) and provided them with the time to express the challenges and questions they are wrestling with, explore common themes and patterns and connect them with the practices that may help us address these challenges.

It’s not a complex structure and it rests on the simple belief that teachers want to work together to improve their teaching.  In her article, Teachers as Learnerseducational researcher Kathy Dunne outlines 7 key aspects that all effective professional learning structures share:

  • Driven by a vision of the classroom
  • Helps teachers develop the knowledge and skills to create vision
  • Mirrors methods to be used by students
  • Builds a learning community
  • Develops teacher leadership
  • Links to the system
  • Is continuously assessed

Earlier in my career I served as a school-based Adjunct Professor for a teacher education program and upon completion of the program I would congratulate the teacher candidates with the following reminder; you don’t just have a license to teach, you also have a license to learn.  It’s folly to assume that all teachers enter the profession with all the knowledge and skills required to be successful. Teaching is a highly complex and specialized field that requires constant learning and that learning is best situated in the place where teachers ply their craft and, with colleagues who can best help them learn and grow.

John Hattie, in his work The Politics of Collaborative Expertise expresses the imperative that; rather than apply external pressures or mandates, school and system leaders focus instead on providing the structures and resources to support teachers to build their collaborative expertise; within and across schools. As a principal, I trust that the teachers I am leading wish to improve their classroom teaching and are eager to work with one another to do so; even if this learning is complex and demanding.

Teachers spend a large amount of their lives in classrooms; first as children and later as adults. It turns out that the best teachers continue to see the classroom as place where they can learn; we need all teachers to see the classroom this way.

This Year’s Model

April 9, 2016 10 comments

“The only way to learn mathematics is to do mathematics.”   ~Paul Halmos~


This week the Ontario Ministry of Education announced that they would be investing over $60 million in a province-wide teacher development strategy in mathematics. For those of us in the math community who have been fighting the good fight for years this was a “woo-hoo” moment (tempered,of course, with a sprinkling of “it’s about time”).

For those who like to reduce complex issues into simple media sound bites; it was another ripe opportunity to climb into the Edsel and bemoan the fact that we don’t teach the ‘facts’ anymore, lob a few rhetorical barbs using terms like ‘discovery math’ or  ‘back to the basics’ and engage in a little brand building for private tutoring programs and or advocacy groups designed to undermine the status and professionalism of our classroom teachers.

In the past, I’ve written about this issue in an effort to challenge these myths, share some of the research on effective mathematics teaching and provide those brave teachers who are actually working to improve their practice with the sense that this principal has their back. Writing about mathematics is an important part of my leadership and my learning.

It does get a little tiring when I hear good teachers and robust research dismissed as a ‘fad’ or categorized as some new age ‘yoga-like’ phenomenon- btw, why would anyone have a problem with yoga?  It especially grates me when retired teachers jump into the fray to undermine the efforts that our current teachers are engaged in to learn and grow their practice (so much for solidarity sisters & brothers).  It bothers me because it lacks logic and here’s why:

Extensive research has been done into the area of teacher knowledge, experience and classroom practice in mathematics and it has consistently revealed a common theme; most elementary teachers have a limited background in mathematics and express a lack of confidence in their teaching of this subject.  Of course, the obvious point to be made here is that these very same teachers are almost all  products of the very same teaching practices that are held up by the Edsel squad as the solution to this crisis in mathematics education (oops).  The other obvious point to be made here is that the solution to any lack of knowledge or confidence (with teachers or anyone else) is always the same- learning and training designed to close the gaps in practice and build the skill set of the workforce.

What I have learned from my own research and from over 20 years of working with students and teachers in the area of mathematics is that mathematics is a powerful tool for communication and understanding that requires a deep understanding of our number system and how numbers relate to, and operate with one another.  It is because most of us were taught just to memorize procedures without understanding that so many of us struggle with mathematics in our everyday lives. I also know that we rarely solve today’s problems (let alone those we we encounter in the future) with yesterday’s ideas.

In the video above, Dr. Cathy Fosnot (@ctfosnot) articulates how important it is for teachers to know how to help children model their mathematical thinking in order to push them towards an understanding of how our common procedures and algorithms actually function so they can use them appropriately- watch the video and you will be struck at the complexity of this task. Teachers can learn how to do this, I’ve seen it and done it myself. It’s not easy and requires (wait for it) professional learning- $60 million spread out over tens of thousands of teachers is a start.

Ultimately, mathematics is about asking questions while justifying and providing proof of one’s thinking; anyone who tries to convince you that they have a simple, magic bullet solution to teaching mathematics in a way that meets the diversity of learning needs and challenges of a typical classroom ought to be held to this expectation (as all classroom teachers are).

Next time the media wants to do a story on the teaching of mathematics I hope they seek out some of the skilled, innovative and effective teachers we have doing the job now; I’d be more than happy to pass along a few names…


Real Math

February 4, 2016 Leave a comment

“Go down deep enough into anything and you will find mathematics.”   ~Dean Schlicter~

It’s common for people to refer to the changes schools are making to the methods we use for teaching math as “the new math’ as if there has been some recent, radical change to the discipline of mathematics. This is actually inaccurate as the ways that people have represented mathematical ideas  (number symbols, drawings, models and charts) have not really changed much over the centuries. What has changed is our awareness of how mathematics can be taught and this is a function of both what we know about mathematics and how children learn.

It turns out that children learn best when they are engaged in tasks that are meaningful, authentic and provide just enough struggle to make it worth the effort. The short video from math teacher Dan Meyer (@ddmeyer) gives some helpful examples of how real, everyday situations and contexts can be turned into meaningful math learning opportunities for students.

The example above differs from the traditional math instruction that is familiar to most of us and I have had many opportunities over the years to help guide conversations in this area. When working with parents and colleagues I find it’s helpful for them to know about my past experiences in the area of mathematics. Along with having taught math in almost every grade as a K-8 classroom teacher; I also had the opportunity, for several years, to work at the system level developing and leading mathematics professional development sessions for teachers from all over our district.

The ironic part about this, as my own parents would attest, is that my experiences as a math student in elementary and high school could only be described as abysmal.  I struggled greatly in my attempts to learn math- the times tables, the procedures, formulae and rules were all too confusing for me to keep track of or apply with any confidence. Upon graduation I refused to even consider taking any math courses when I moved on the university.

So when, as a novice teacher, I found myself in the awkward position of spending my first year having to learn the mathematics curriculum I would be teaching my grade 7 class-I’m happy to  report that my second experience learning grade 7 math was much more successful.  During that year (and in the years since) I realized that learning math requires the understanding that math is best learned through experiences, communication and the solving of real problems and not just through the memorization of the rules and facts found in textbooks. 

I didn’t really learn to appreciate and understand math during my time as a student in school. In fact, everything I have learned about math; both in my teaching and how I use math in my everyday life, I have learned since I began my teaching career- again in the real world.

Success: More or Less?

November 28, 2015 Leave a comment

“The traditional school often functions as a collection of independent contractors united by a common parking lot.”   ~Robert Eaker~

After a move to a new school in September and, what could only be described as an interesting fall, I’m starting to feel a little more settled with my (not so) new surroundings. Over the past few months I’ve had the chance to focus on getting to know the school community, the students, families and staff and see, more or less, how the school ‘works’.

It is often noted that there is greater consistency in practice across schools than within a given school. During 24 years in public education, working at 10 schools in various capacities; teacher, mentor and administrator I’ve had the opportunity to observe this phenomenon first hand.

The key challenge many schools and school systems face is one of both complexity and diversity. With so many variables and influences to factor; people, context and resources, trying to enact a change initiative is akin to the iconic cat herding commercial from a few years back.  Often, we are feel we need to respond to complex problems with complex solutions; but the more I think, read and reflect upon this, the more it occurs to me that these problems actually demand simple solutions and that require a focus on relationships and doing less, more effectively.

David Kirp, an American public policy researcher and author, wrote about this recently in his book Improbable Scholars.  One of Kirp’s main assertions is that successful schools and districts avoid trendy, fancy or complex improvement strategies and instead focus on these three key areas:

  • rich early learning opportunities for all children;
  • a strong focus on language-rich instruction across the grades, and;
  • professional learning for teachers using school-based collaborative structures.

Success, it turns out, is a matter investing more in the collaborative capacities of classroom teachers and less on the external factors and tools that we have come to rely upon in many of our schools.

For me the word that best describes a truly effective school is coherent. A coherent school is one where teachers direct their resources and focus towards the development of logical, well-organized, consistent and effective teaching practices across the school.  As a school leader my task is to engage the professionals I’m working with to create this coherence.  As an example, collaborative assessment of student learning is one area where digital tools can help immensely as we can use media tools to gather and analyse a wide range of authentic student work samples as our teachers make use of tools like Google Classroom and Dreambox to support both their classroom teaching and professional learning.

Though we may use new tools, technologies and strategies to accomplish this, it is not the intention to add ‘more’ to the work we do in schools but rather to reduce the use of ineffective or inefficient practices and establish the structures necessary for teachers to work together to create coherence and communicate in a meaningful manner with their students and families.







Moving on…

June 3, 2015 2 comments

“Farewell has a sweet sound of reluctance.”    John Steinbeck

Photo: The Old Glory   Ujbanyiv’s Fotothing

Our district announces the appointments and transfers for principals and vice-principals for the next school year in early June and last night, my name was on the list. After 3 fun-filled years as the principal at Park Avenue Public School I will be moving on to serve as the principal at Clearmeadow Public School this coming September.

Changing schools is not a big deal for most school administrators; we get the chance to work in multiple schools as vice principals and, as a result, are well versed in managing transitions. We also are aware that we have committed to a school system, and not just a school. In a district like ours, with over 150 schools, principal movement is a reality. Additionally, a big part of what drives those of us who choose this role is an willingness to embrace change and experience the challenges and opportunities that different schools offer. This was certainly one of the aspects that drew me to school leadership.

That’s not to say that I am doing cartwheels about leaving the school I have served for the past 3 years. I’ve had the chance to get to know a wonderful group of students and their families and work alongside an amazing group of dedicated professionals. But I always knew my time at Park Avenue would end and it has.

There’s an old saying the goes ‘it’s better that people think fondly of you of wherever you go, instead of whenever you go’; I certainly hope that’s the case for me (although one never really knows). I know that together we have made many changes in our little school during my time here. Some of them were my idea but, honestly, most of the changes were ideas that our staff, students and community came up with- I was just the guy who said, “sure, let’s try it…” and, sometimes, “how much does it cost?”  Either way, I am proud of the changes we have made and the things we have accomplished.

As a staff we launched a school-wide modern learning professional inquiry on how to use technology to enhance teaching and learning, together, with our parent community, we explored effective mathematics instruction and have taken a much closer look at how we can respond to the mental health and anxiety-based needs of our students. All good stuff- and it will continue.

All this good stuff; the ideas and the initiatives, came from the staff and students at our school- and almost of of them will be staying around. I’m not-but they are; and the work we began will continue with our new principal Bruce Baynham. Bruce will bring a fresh perspective and add his ideas to the mix-this is the way of public schools.

So, soon I will bid farewell. I will miss this place but I am excited about the the next steps I will take in my professional journey. In the meantime, I plan on enjoying every last second of my time as principal at Park Avenue Public School.

Numbers, Numbers Everywhere

February 2, 2015 Leave a comment

The essential fact is that all the pictures that science now draws of nature, and which alone seem capable of according with observational facts, are mathematical pictures.         ~Sir James Jeans~

Over the course of this school year our teachers have been digging deeper into their understanding of our mathematics curriculum; specifically looking at the ways that number sense and numeracy are evident across this curriculum. Our math content is divided up into 5 areas, or strands; Number Sense, Measurement, Geometry, Patterning & Algebra and Data Management. This is done more so for organizational purposes, and to ensure that students understand the many real world contexts in which math can be used. A big part of this process for us this year has been to lead each grade-based learning team through professional learning sessions where they have analyzed, discussed and organized our mathematics curriculum into a Year at a Glance planning framework.

math plan

The Year at a Glance Plan for Grade 3/4

The Year at a Glance plans have allowed our teachers to see these connections that exist between the strands, map a pathway of critical learning and big ideas from grade 1 to grade 8 and design tasks that reflect, and connect, these relationships between the strands. Of course in the real world, these strands are inter-connected and, thus are not designed to be learned as separate, discrete topics. For example, a simple task like measuring will require students to draw upon what they know about numbers, geometry, algebra and, in recording their results, ways to represent their measurements as data.


A measurement task that connects multiple strands.

Understanding our number system with a degree of fluency is essential for students to engage in this type of thinking. Just as those students with a wide vocabulary are able to speak, write and read in a wide range of settings more effectively; students who understand our number system are better equipped to see the connections and relationships that exist when they are measuring and working with shapes, data or patterns. A deep and flexible understanding of numbers is developed when we use models and strategies to connect number with quantity, movement and space. It’s more than just writing the numbers down, it’s about understanding what the numbers mean, what the numbers can do and, why our number system works- everywhere.

The many ways we can 'show & know' numbers.

The many ways we can ‘show & know’ numbers.

The tasks we are designing for students, and the way we are teaching them reflect this shift in the understanding our teachers have about our curriculum and how mathematics is used in the real world.

ad infinitum

November 14, 2014 3 comments

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

One of the things I admire about the teaching staff I work with and lead is their willingness to take risks and adapt. I think it’s really important that kids spend their time with adults who care about them and have a high expectations; and these two concepts are not mutually exclusive. We are well under way on our journey of school-wide transformation in math teaching and learning and are at the point where those ‘pockets of practice’ that were evident in some classes are now evident in all our classes. Parents are seeing their children using models and strategies that seem strange and unusual to them and we are getting questions, lots of questions.

Most of the questions or concerns we hear are 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. Part of my job as principal is to help people understand our practice and our pedagogy so let me try to address a few of these concerns:

  • ‘The New Math’  There is no ‘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 folks. The emphasis in mathematics has always been on understanding number patterns and relationships to think and reason, this is far from a new phenomenon.
  • So What is New? Over the past 30 years a few things have changed where it concerns education; in math and all other disciplines. We now expect that schools will ensure that all students meet a high standard of literacy and mathematical understanding (see 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. In other words, we know we are capable of, even though we may not all be capable of it yet.
  • The ‘Real Basics’ Often, parents struggle to understand the diversity of models and strategies that our teachers are introducing and question why we aren’t teaching the basics. By basics they usually mean things like the standard procedures for addition, subtraction, multiplication and division- also called algorithms. 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 real basics are the numbers, and our emphasis on helping students understand our number system using models and strategies that make sense to them allow them to use mathematics in its truest form; a powerful, logical language for solving problems and communicating rather than a set of clever tricks and short cuts. If a child doesn’t understand the numbers they are working with, they don’t know the math. It is also important to note that since they are culturally based, there are actually many algorithms, more than those of us who experienced a western education can even fathom.

Across our school, we are working together as a team of educators to better understand and teach our curriculum in a way that will enable all our students to become mathematically capable. 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 students.

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