“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 Learners, educational 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.
“…if we believe that the most powerful learning that kids do can only be measured by their desire to learn more, then any innovation we introduce must focus on creating fundamentally different experiences for kids in our classrooms, with or without technology.” ~Will Richardson~
W.B. Cameron once remarked, “Not everything that counts can be counted and not everything that can be counted counts,” We live in a world where measurement, classification and comparisons have become part of our culture. We place a great deal of value on standardization, in the products we use, in the institutions we rely upon and systems we have created. Schools, because they support the priorities of our society, keenly reflect this reality. Ken Robinson expressed in this so eloquently in his noted TED Talk; it’s easy to see our schools as factories; where we process children in batches “based on their date of manufacture.”
I can understand why schools from the past were drawn to this type of thinking; they were tasked with preparing children for life and work in an industrial age. Learning was seen as a simple process- teachers transmitted knowledge to students, measured how much they had digested and then ranked and sorted them based on the results. In the industrial context, this type of thinking helped to ensure control and consistent quality- that is the essence of standardization. It’s easy for us to be drawn into this mode of thinking- we want our children to have the best, be the best and be able to compete in a global context. Will Richardson’s writings prompt us to challenge this mindset with good reason.
Our schools struggle with the tension between standardization and individuality. As parents we value the unique and varied characteristics of our children and face the challenge of fostering pro-social growth and development while honouring each child’s drive to be who they want to be and do what they wish. We are social beings; but people (and children are people too) rightly resist environments where conformity and standardization confine them or they are reduced to a number. Children are not test scores, numbers, marks or levels- there is no such thing as a ‘level 3 student’– these are constructs of our system and do not reflect that our children are so much more that that. It’s time for us to think about what we want for our children; is it standardization or the fostering of individual development and potential? Depending on one’s beliefs about this- our schools could look and feel very different.
“If you don’t underestimate me, I won’t underestimate you.” ~Bob Dylan
The wonder and beauty of human life is its diversity. The fact that we have different skills, appearances and dispositions is one of the reasons we have been able to evolve into the capable, adaptive and successful species we have become. Difference is good; and diversity is our greatest strength. With this in mind; it’s important to stress that not all of us learn the same way, at the same pace and with the same level of interest and engagement. The term that scientists now use to describe this is neurodiversity.
Over the past 20 years the information that neuroscientists and geneticists have made in understanding how the brain develops and operates has been staggering. So staggering that those of us who work in the related fields of education and mental health are only now beginning to understand the implications this knowledge can have on our practices. This needs to change. We now know that the assumptions that many of us have held about teaching and learning (as parents and as educators) no longer apply- particularly where it concerns students who learn and communicate using strategies or skills that don’t reflect the practices of traditional teaching methods.
We can no longer categorize students who learn or communicate differently as being disabled, or look at these differences as a defect or weakness- this diversity is our strength and the ways that all classroom teachers design teaching, learning and the assessment of learning needs to adapt to respond to these strengths. As a leader, I have a sense of urgency to create a climate where the staff I am leading can work together to learn, adapt and change how they teach so our school can respond the needs of all our learners.
It is time to change both our mindset and the tools we use; to use our creativity and our technology to adapt the ways that we design, assess and evaluate student learning. It’s time to change the ways we respond to student behaviour and alter the both the beliefs and the structures we use to provide remediation and meaningful instruction in a way that values the diversity of each child in each classroom in every school.
The eye only sees what the mind is prepared to comprehend. ~Robertson Davies~
We are products of a lifetime of experiences and the perceptions these experiences foster. Some may be familiar with the anecdote about the teacher who mistakenly mixed up the previous year’s class list test results and launched into the school year believing that the group with the high results was actually the one with low results – and vice versa. The subsequent confirmation bias, with a year of high performance from the low scoring class, may or may not be true (the web, after all, is a boundless source of these stories) but it sure makes a poignant tale.
The video above makes a great point about how we perceive the children and families we work with in our schools. Every one has a story-a set of experiences that they carry around in their hearts and minds. In schools we think a lot about the ‘stories’ our students carry and, when we are at our best we try to learn and understand these stories so we can better teach them.
Of course- we have our ‘stories’ as well.
I wonder if we are aware of the perceptual lenses we carry? Each of us has a lifetime of experiences that form the basis of our stories and these influence the opinions and decisions we make about our students and their families.
Something to think about…
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.
“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.
“Mathematicians do not study objects, but relations between objects.” Henri Poincare
I was chatting with a few of our staff this week about the ways we help our students develop their ability to work with numbers, specifically when they are adding and subtracting in the early years. An important point that I often stress when talking with parents and teachers about mathematics is that the area that many of us believe to be the critical focus of mathematics (the operations of adding, subtracting, multiplying and dividing) is actually of secondary importance.
Simply put- we spend way to much time trying to force children to memorize or learn the operations and not nearly enough time helping them understand the numbers they are using. Put another way- think of the numbers as nouns and the operations as verbs; in math, as in life, there are way more nouns than verbs and they are much more interesting!
This media clip on Using Open Number Lines from Dr. Alex Lawson does a great job explaining how using a model like a number line can support children to think about the quantity value and relationships that exist between numbers in a mathematical situation. It also shows how using models as a precursor to what we call the standard algorithm is important at all stages of mathematical development. For most of us, this type of instruction was just not used when we were learning math in school and it is too bad, because it would have save many of us from a life of math phobia.
A lot of students and adults think that using the algorithms is the math- it’s part of it, but not nearly the most important part. In fact, the algorithm can most simply be described as a way of showing (or modelling) what has been done with the numbers. A student who uses an algorithm to solve a problem without understanding the relationships between the numbers is no better off than a student that uses a calculator- they both don’t really know what they have done.That’s why we are using models like the open number line- they allow the student to see the connections and relationships between the numbers and build a model of how they can solve a problem.
There are only a few mathematical operations but the numbers are (literally) infinite- the numbers are much more interesting than the operations- tools like the open number line help our students discover and harness this idea.