“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.
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.