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.
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.
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 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.
The problem with the stigma around mental health is really about the stories that we tell ourselves as a society. What is normal? That’s just a story that we tell ourselves. ~Matthew Quick~
This week schools and workplaces in communities across Canada will continue the conversation about mental health as part of the Let’s Talk campaign on January 28th. The initiative, sponsored in part by Bell Canada, has been instrumental in raising awareness of the issues and statistics related to mental health; for both children and adults. As a school board, and school community, we are working to better understand the needs of the members of our communities who face mental health challenges so we may meet these needs in a way that is respectful, collaborative and supportive.
In the context of our school we have grown in our understanding that mental health impacts not only our students, but also the parents of our students and our staff. A broad term, we see mental health manifest itself in many ways; usually through behaviors like withdrawal, volatile and impulsive actions or extreme mood swings. These can be the result of anxiety, attention difficulties or communication disorders; such as Autism Spectrum Disorder. Whether they are the result of environmental conditions, the stresses of daily life or neurologically based; these difficulties are real for those who endure them and deserve to be treated as such- behavior, after all, is communication.
Our goal his year has been to reduce the stigma associated with mental health, while we learn about, and add to our tool kit of strategies and resources in this area. The leadership of our school HUB Team (Helping Understand Behavior) has been key in moving us toward this goal; during instructional and non-instructional time, in our classrooms, hallways and playgrounds. Just as the student who has physical challenges is entitled to a wheelchair or pair of glasses, or a student with a learning disability benefits from the use of a laptop; students with mental health challenges have the right to learn in an environment where they are safe and supported. In our classrooms, we make use of a wide range of tools and approaches; from yoga balls (instead of chairs) to noise reducing headphones and sensory bins as well as activity breaks and yoga.
Each of these is designed to help the student develop the skills to self-regulate so they may socialize and learn as part of our school community and understand that differences are not weaknesses. This is new territory for schools, as our past practice has been to punish children for behaviors that were often the result of underlying mental health issues and, in doing so, we not only added to the stigma, but failed to recognize the behavior as a call for help.
Moving beyond January 28th, we look for more opportunities to continue this important conversation.
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.
“Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost.” ~ W.S. Anglin ~
Our supply of those rolls of brown craft paper are depleting rapidly here at Park Avenue PS and with good reason. Over the past year we have looked deeply into the structures and design of our classroom learning environments to ensure they reflect the best practices of universal design for learning and have a degree coherence and consistency across the grades. As a result, one might notice now that our K-8 classroom environments share some common characteristics such as desks or tables arranged in groups to support students working in teams and more open floor space, learning tools and materials stored in a more accessible manner and an intentional use of the walls as visual supports for learning.
Traditionally, classroom walls have been used to display completed student work, more often than not student art work, or written pieces completed by all the students, While the intention to acknowledge and celebrate tasks that have been completed is noble, the question that begs to be asked is how does displaying learning that has already happened help a student who is struggling with what is being learned now? Rather than being a static archive of what has been learned, the walls of the effective classroom need to be an evolving, active documentation of what is being learned.
Education researchers refer to the use of charts and images showing the learning goals, components of a successful task and anchor charts showing the meaning of the strategies and terminology; as essential components of an effective classroom- or ‘high yield’ teaching approaches. And this, is where the rolls of craft paper have become so helpful.
One of our highly experienced Special Education Teachers, Anita Simpson, is creating, along with her students, a Math Wall (it literally fills a wall) that represents the key Big Ideas, Models and Strategies from the Mathematics Landscape of Learning she and her students are exploring. As you can see in the photo above, the wall shows a record of the strategies that students have learned and will need to use along with the models and ideas that connect with these strategies. In Anita’s class, students can be seen glancing at the wall to check the meaning of terms, remind them of strategies or to explore the relationships between the ideas, models and strategies. The wall serves as an anchor chart and road map that is visible for all.
With exception of the ideas, strategies and models labels, the wall was blank in September. Together with her students, Anita has carefully documented the learning on the wall-it’s an impressive sight. So impressive that similar walls are popping up in classrooms all over the school.
Over my 2 plus years as principal at Park Avenue I have stressed the importance for us to develop a set of coherent, common practices in mathematics teaching to support student learning. Mathematics is at it’s core a language; and tools like Anita’s math wall allow our students to immerse themselves in this language while they are engaged in meaningful problem solving- which is the core of a comprehensive math program.
More craft paper, anyone?
“Every accomplishment starts with the decision to try.” anonymous
My colleague and mentor (from afar) Cathy Fosnot describes traditional math instruction as’ “teaching math as if it were a dead language.” rather than the living, dynamic and fluid field of study that it actually is when it is taught effectively. As a teacher, consultant and now, principal, I’ve spent most of the past 20 plus years trying to help students understand mathematics this way while trying to defend this practice to parents and other skeptics (including, quite often, my own colleagues).
It was with appreciation and a sense of relief that I viewed the short video (above) that our York Region District Mathematics Curriculum Team created last spring. The video was posted to YouTube with the intention of defining what effective math instruction should look like, sound like and feel like for all of the students in our district, from kindergarten to grade 12, and help communicate the components of an effective, comprehensive mathematics program to our community and stakeholders.
Unlike the math instruction many of us recall (insert unpleasant memories here) a comprehensive math program (CMP) is a synthesis of meaningful problems (drawn from real contexts), teacher-led mini-lessons (based upon the struggles students are encountering) and games and puzzles (to support student curiosity and make connections to real life). These three components form the basis of the math instruction we provide at Park Avenue PS and I am really proud of the manner in which all of our teachers have embraced this framework.
The component where we are applying the most focus at this time is the mini-lesson- a 5-8 minute lesson designed to build student understanding of our number system along with the mathematical models and strategies that students can use when they are solving meaningful problems. In the photos below one can see two examples mini-lessons
The photo on the left shows one of our grade 4 teachers showing the whole class some of the different models, or tools, students can use to solve and prove the answer to a 3 digit from 3 digit subtraction problem and stressing with the students the importance of using a model and strategy that they understand. In the photo on the right, Our grade 1/2 teacher is guiding a small group students to use diagrams to keep track of the quantities of numbers they are using in a 1 digit from 1 digit subtraction problem. Notable is the use of an erasable whiteboard (sorry, no work sheets here) and the use of talk; teacher to student as well as student to student, as the anchors of the mini-lesson.
In most cases, the biggest problems are not solved with grand, sweeping efforts but through the steady application of effort over time. We are seeing the impact of mini-lessons as it is changing the way our students think, reason and prove in mathematics and, more importantly, the way they feel about mathematics. By breaking the complexities of mathematics into accessible mini-lessons we are giving our students the both tools and the confidence to try- I applaud the work of our teachers and students for making this decision and appreciate our district math team from providing the structure of the comprehensive math program to guide this work.
There is an old saying from that wise old author Anonymous that goes something like this; we are all experts on education because we have all had experience with education. Of course, for all of us, to varying degrees, this is true. Every generation of schools has to understand, and wrestle with, change. In schools we see changes in student demographics, changes in pedagogy as a result of research and emerging technologies and changes in the demands and expectations that parents and society have of our schools.
Too often, we think of the changes and challenges we are seeing in our modern schools as being about technology or the moving away from teaching the basics. Not true. The real change and challenge is related to who actually ‘owns’ the learning and how this learning can occur. The schools we went to were based on the premise that the teacher owned the knowledge and gave it to the students- who in turn, demonstrated success by regurgitating this knowledge back to the teacher. The questions we asked as students; “will this be on the test?” are not the questions our students today are asking; “why is this important?” or “why should I do this?”
All the nostalgic whinging in the world will not change the fact that the children that this generation of parents have raised (and are raising) have been conditioned to ask these why questions. What we have learned about the brain and how people learn, along with the powerful, connected information tools we now have, is that learning is an instinctual process that is driven by the curiosity and creativity of the learner. The most recent research indicates that people who are curious and act upon their curiosity lead more productive, complete and satisfying lives.
It turns out that “Why do we have to learn this?” is actually the question all students should be asking. For us as educators and parents, this is a great challenge- the schools that we knew are not the schools we now need. The emphasis on recall and memory still plays a role but they are nested within the curiosity, critical thinking and creativity of the student.
At our school; we have noticed that this type of thinking and problem solving is an area of struggle for many of our students and, as a result, we have invested a great deal of time and energy in learning how we, as educators, can guide our students to use questions to launch, sustain and consolidate their learning.
Interested in reading more about this? Try Amanda Lang’s recent book The Power of Why.
As we engage in re-imagining public education in the coming years, I believe that we must re-think the use of space, the use of time, the structure of the school day and year, the sorting of students by grade, the use of schools within communities and, probably the most significant, the structure and content of curriculum. Not everything will need to change but it is important to ask the question: “is it right for today or are we doing it this way because we always have?” ~Ken Thurston~
This past week the Director of our district school board, Ken Thurston, announced that he will be retiring at the end of July. (For my American cousins, in Ontario the title Director is akin to Superintendent). I’ve had the chance to work with Ken in a variety of roles over the 14 years I have known him. He was one of my school superintendents when I was in the classroom, I had the chance to work with him when I was local union steward and committee member and, for the past 4 years I have been proud to serve as a vice principal and principal under Ken’s leadership. It was Ken who sat across the table and led the conversation that resulted in my appointment to the position of principal.
One of key traits I have observed consistently in the years I have known Ken is the importance he places upon relationships. Whether he is thinking about students, staff, parents, unions, community members, trustees, or policy makers, relationships matter most. The other trait I have observed is the willingness Ken has to question the status quo, imagine alternatives and grant agency to those who wish to do likewise.
At Park Avenue PS our students, staff and parents often tell me that I think “differently’ on many issues, sometimes in little ways, sometimes in more radical ways. I do so because we have had a Director not only granting permission, but actually challenging us to do so- Ken’s question, quoted in bold text above, guides my daily work.
During our short time together working as the principal of our school community we have asked ourselves this question and given ourselves permission to re-think our use of tools, time and curriculum. Over the course of our intensive math professional learning this week I challenged each of our grade teams to rethink our concept of how we teach our math curriculum- both in structure and content- and look more closely at how we can use the Landscape of Learning to provide developmental instruction that challenges and meets the needs of all our students.
As we learn how to do this in math, and gain confidence, I’m sure we will find lots of ways to apply this in other areas of our school community and better inform our parents in this area so they can both support and better trust the work we are doing in our classrooms. Re-imagining our school, and re-shaping it to meet the challenges of the world we live in now, is the work that each of us; staff, parents and students, must do together.
Back at our first staff meeting together I remember saying to our staff that I didn’t want to change everything, just the things that weren’t working, and we would make these changes together. I’m encouraged that, even as he prepares to depart, our Director is giving principals and teachers permission to re-think, re-imagine and re-create our classrooms and schools.
Of course, it’s more than likely I would have continued on this path regardless; but sometimes it is better to have permission rather than have to beg forgiveness.