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Teachers, Tinkerers & Learners
“When students step out of the door of the institution called school today, they step into a learning environment that is organized in ways radically different than how it once was.”
Richard Elmore
In spite of the some of the stormy events of the past few weeks; both in the atmosphere and the in political sphere, a lot of really cool things have been going on at our school. Primarily, we have had the chance to engage in some professional learning together in the key areas that are reflected in our School Improvement Plan and we’ve been working in our classrooms to tinker with and implement some of this new learning.
In earlier posts on this site I have referred to the ’3 I’s” of our school plan; Inclusion, Inquiry and Innovation and tried to connect these with our focus on effective mathematics instruction, supporting students with learning challenges and the use of communications technology to support 21st century learning. The video link above is a thought provoking piece on why these ideas are important for our students and our schools.
Over the past few months we have been working in small teams to develop and refine our own questions in these areas; forming teams of 4 to 8 staff members to research and inquire into the ways we can improve our mathematics instruction, understand the different ways that children learn and look at the ways we can use iPads as teaching and learning tools.
Today, a friend and colleague of mine, Dean Shareski, spent some time working with our staff, via a Skype video conference. Dean, who Skyped in from his home in Moose Jaw, Saskatchewan, helped us explore some of the media tools that are available through our partnership with Discovery Education Canada and offered up some practical tips on ways we can use social media tools like Twitter, blogs and Edmodo to support student learning and parent communication.
There was a time when a teacher could believe that they knew everything they needed to know to be successful upon their graduation; those days are no more. It turns out our license to teach is also a license to learn.
Mathematizing Mathematics
Students making sense of a real world problem in Ms McAlear’s grade 6 math class.
“As teachers do we see our role as initiating learners into mathematical communities, speaking and inquiring with young mathematicians at work? Or do we speak to them, trying to transmit a of skills and concepts…developed by previous mathematicians? Are we teaching the history of mathematics rather than mathematics? ~Cathy Fosnot~
It’s encouraging to see the enthusiasm with which our Park Ave. P.S. team has embraced our whole school focus on mathematics teaching and learning~not only because this is an area of personal and professional passion for me; but also because we are, as a staff, uncovering some powerful and important insights about the nature of mathematics and networked learning.
In stressing the importance of inclusion, inquiry and innovation my role has really been that of catalyst and coach; providing resources, structures and guidance for this learning. In our conversations so far, we have discovered that our students have a wider range of skills and, deeper understandings, than the tools that we were previously using; revealed. In our case, all our students, including those students who have been identified with learning disabilities, are revealing capacities and communicating ideas in ways that are both surprising and encouraging.
The problem shown in the photo above (The Sold Out Show) is a great example. In designing the task for her students, Ms M considered the models and strategies her students were using as they solved multi-step multiplication and problems. She created a problem that would push her students to better understand the relationship between these two operations as well as the important mathematical processes of reasoning and proving how they know their solution is accurate.
Rather than demonstrate and have her students memorize the steps toward an accurate solution, Ms M has crafted a problem that will help her students to build and communicate their understanding. The culmination of this task will see the students analyzing and questioning each other’s proofs with Ms M taking the time to highlight the mathematical relationships, ideas and terminology as they are doing so.
For many of us,this is a reversal of the model of instruction we experienced as students; one where the teacher demonstrated the singular procedure and skills that would be needed to complete a task, then assigned a similar task with the expectation that all the students would replicate what had been demonstrated. This model worked, for about half of us.
In our classrooms, we are asking students to show us what they know about mathematics and how they are able to apply this knowledge in context; then using these contexts to push them to a deeper understanding of how mathematics allows us to make sense of our world, communicate about our world and work to solve problems in our world~ a process that the Dutch mathematician Hans Freudenthal describes as ‘mathematizing’.
Creating classrooms where our students mathematize, rather than memorize, is our ultimate goal; as always, your comments and questions are welcome!
New Territory: Mathematical Landscapes
“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~
Across Ontario schools are taking a deeper look into the the research and practice on mathematics teaching and learning so our recent work at Park Avenue P.S. in this area doesn’t make us unique. Like all schools in our district, we are part of a learning network; a family of 4 or 5 schools that have agreed to engage in joint work to support and improve our classroom practice. Our network will support our school focus on mathematics teaching and learning from K to grade 8.
As a first step, we have spent some time looking at what our student’s strengths and needs are in this area; using both our own assessments as well as our provincial assessment results from grade 3 and 6 (we will continue this work on our next PA day on Oct. 22nd). In addition, we have also started to read, think and talk about the most current research into effective math teaching; most adults have deeply ingrained experiences that often cloud their perceptions of what math actually is, leading to some confusion at school and home.
Rather than a set of pre-determined rules to be memorized, mathematics is actually a way of structuring and representing our physical world~ like a language. Since the best way to learn any language is to be immersed in it and use it-rather than be forced to memorize it- we are working as a whole staff to design problems and tasks that will help our students do this.
It is also important to note that all learning requires one to struggle and learning math is no different. The struggle we wish for our students is not, however, in the memorization of the mathematical concepts but instead in the development of these concepts. As I used to remind my students when I taught math,; trust what you know and understand, not what you remember.
There are three key areas we will embed into the work we do in our school and network and we are happy to share them:
- Inclusion: all students require support and instruction that draws upon their learning styles, experiences and starting points to construct their understanding of the mathematical strategies, ideas and concepts being taught.
- Innovation: real world applications, models, contexts and tools; designed will form the basis of our learning tasks~and this will look much different that what most of us recall as ‘math instruction’.
- Inquiry: just as most of the math problems we encounter in daily life require us to pose our own questions and often work with others to solve them, our students will be challenged to pose questions, hypothesize and struggle a little to find and prove their answers.
I’m grateful to our colleagues from the Mathematics in the City project, based in New York City, for sharing their research and practices and supporting our learning journey into this new territory and, as always, invite your responses.
Mathematics Makeover
“The essence of mathematics is not to make simple things complicated, but to make complicated things simple. ~ S. Gudder~
One of the areas we are going to be applying some focus, effort and time towards this year is mathematics teaching and learning. We know from our own classroom and school assessments that this is an area we need to look more closely at; and this sense is supported by the most recent results from the primary and junior provincial assessment in mathematics.
Most of us have a set of experiences in math that have helped to form our beliefs and feelings towards math, positive or otherwise. It is important to note that our understanding of how to teach math in a way that all students can understand and learn has changed a great deal in the last 20 years. And, as the ‘real’ world has also changed, the need for every student to be able to think critically, solve problems has become an essential part of learning, in math, and every other area of ‘school’.
The video clip at the top does a nice job of communicating our vision of what math class could, and should, look like. And this is the work we will be doing together as a team of professionals, teachers and support staff from JK to grade 8. We also have a responsibility to keep families informed about this learning, and how parents can provide support. This blog is one place parents can go to find posts, pictures and videos that will document, share and connect the learning that is going on at school with our families and school community.
We are all excited about the learning we will be engaging in; the Park Avenue Math Makeover is underway, please feel free to join us as we learn and grow together!
Tales of the Pink Table
Photo Credit: Peter Harrison
This Friday, the long and eventful career of a great educator and leader will come to an end. I’ve had the pleasure of knowing Diane Muckleston for 15 years, as a colleague, as a friend and, as a member of our district’s math curriculum team under Diane’s skilled and intentional leadership. We were originally introduced by the mathematics consultant of that time, Barry Scully, who thought that we’d make a good addition to the teacher-leaders team that he had helped assemble to support the roll out of the then new Ontario Mathematics Curriculum Document.
We worked together to pilot the use of problem-based math tasks in our classrooms, led after school workshops for teachers and worked on some district writing teams. Soon Diane assumed the consultant’s role that Barry had held and invited me to continue as a member of her math team. Being a new father, I often brought our son Peter, a toddler, to our after school planning meetings and he’d amuse himself with the multitude of colourful mathematics manipulatives. Intermingled with the math talk were conversations about the ups and downs of parenting, with Diane’s boys then approaching adolescence; I benefited greatly from her wisdom and insights.
When Diane assumed the role of District Mathematics Coordinator in our board, I applied to join the team as a consultant and was successful. In the fall of 2003 Diane led a team of 3 consultants (two elementary and one secondary). Over the course of that year we planned and facilitated in-school and after school learning sessions for over 1000 elementary and high school teachers. A year later three additional consultants were added to the team.
With Diane’s leadership our team pushed the boundaries of teacher professional learning; adapting a protocol for teacher joint work through lesson study, integrating technology and blended learning into our work, supporting and facilitating cross panel co-teaching and co-learning for networks of grade 7,8 and 9 teachers in the area of mathematics. The team met around an old rose-pink table that we had rescued from our board’s surplus furniture depot and around that pink table we established a culture of fierce, honest and respectful collaboration that was based upon the belief that every idea was improvable and every perspective was valuable. Everything I learned about the power of trusting, honest practice-based conversations for teachers I learned around that pink table.
The important thing about Diane has always been her skill and focus on developing people and building capacity; from that original team of 6 consultants; 5 are now school administrators and one is head of the math department at her school. As the first cohort began to move on, Diane continued to develop a further wave of leaders who continue to push the boundaries and engage in innovative and creative work with teachers; the consultant who replaced me has just accepted a faculty of education secondment, and so it continues. All this under Diane’s patient, determined and persistent leadership.
So, a couple of weeks ago; to celebrate her retirement, Diane invited all the past and present math team members to her home for dinner. There were over 20 of us, spanning the years of her district leadership, diverse in many ways, but singular in our love of mathematics, our passion for learning and our admiration for our leader. It was a delightful evening of conversation, laughter and catching up. In classic Diane fashion, every detail was considered, the preparation was flawless and the meal; perfection~well almost perfection~ no pink table.
A part of Diane will be embarrassed that I’m posting this to my blog, I know this, but I’m not sorry. I’m grateful for the friendship, the knowledge and the wisdom Diane has shared with me. I’m grateful for the friends and colleagues I have gained as a result of my time working as part of her team. And I’m grateful for the many contributions she has made to our school district.
Too many, perhaps, to count.
But…Why?
The lights go out and it’s just the three of us You, me and all the stuff we’re so scared of
~Bruce Springsteen~
We’ve had a busy few weeks at my school as we approach the March break in Ontario. Into year two of a new reporting timeframe, educators are adapting to the reality that with report cards going home in early February, the cycle and flow that we grew accustomed to has been altered (and change is scary).
Principally, the past practice was to use the last few weeks of February to assess, evaluate and report, which meant we could say things like “…this is important stuff, report cards go home soon!” to keep things in order and in response to the question “Why do we have to do this?”
Then we would all take a well-deserved break.
Now February and early March are filled with learning and teaching. With the next report card months away at the end of June, February now is the beginning of a learning cycle, not a culmination. Our thinking has had to shift and this is kind of scary for us. Fortunately, we have really brave and curious teachers at our school and they are eager to adapt and grow. So, I’ve been doing a lot of co-planning, co-teaching and professional inquiry, especially in our grade 7 and 8 classes, where the “why” question is not easily answered.
We’ve been exploring ways to build inquiry into our learning tasks; just in math for now and, soon in language and the other pursuits. We been thinking about ways to use the question “Why?” and adding the questions “How?” and “When?” and, “Why not?” as the launch pad for our learning.
Much of this was prompted by a spike in student actions that were not okay to us and required some responses (read disciplinary) and some reflection on our part as a team. We realized our older students were trying to tell us (and show us) that they needed something different and personal. We have decided to look upon this as their invitation for us to change; an invitation we decided to accept.
Early results from our students (and teachers) is this is good stuff. We are talking more with each other (and not at each other), we are using more complex and creating contexts for learning about number and taking the time to support our students to work in small teams to solve problems. We are all smiling more, and laughing more.
This is a much nicer way to lead up to a break, I think:)
Counting on Oral Language
“In a community of discourse participants speak to one another. They ask questions of one another and comment on one another’s ideas. They defend their ideas to the community, not just the teacher.” Fosnot & Dolk 2001
Language is the definitive and most enduring human technology and words are the tools of thought. It is language that translates impulses and needs into the rational thoughts. It is language that conveys these thoughts, first inside our own minds and then to the minds of others. It is language that spurs action, prompts reactions and carries all that we pass on from generation to generation, culture, science, ideas and knowledge. And, all language development must follow the simple path that has been tread upon for eons; from listening and speaking to reading and writing.
My colleague @CarmelCrevola has worked with focus and purpose to move our shared understanding of the importance of oral language to a position of prominence as a context for teacher professional learning. Drawing upon current research as well as the lessons learned from collaborations with schools and school districts around the world, Carmel compels us to examine the type and quality of oral language instruction that all students receive, with a particular focus on early learners. What I appreciate about Carmel’s work is the fact that it is practice-based, informed by classroom work and is transferable to all teaching contexts and content.
Context and content are key for me as I see some powerful connections between this work and the shift that we are working to achieve in the design of effective mathematics learning experiences for students. The components of effective, accountable talk can be broadly categorized as: expressing thoughts and opinions, justifying a point of view, questioning and clarifying as well as listening and responding. Each of these components can be more discretely broken down into specific prompts that can become a focus for ongoing classroom instruction.
For me, talk is the the foundation of all effective mathematics learning communities. Author and mathematics educator Catherine Fosnot challenges us to engage students in meaningful mathematics learning contexts and to create classrooms where the interplay of ideas, models and proofs is the norm. When I reflect upon the oral language components I see many rich opportunities to integrate oral language instruction and the learning of important mathematics. The essential tools of the mathematician are not only numbers, models and symbols, they are thoughts, opinions, conjectures, proofs and, most importantly, questions. Each of these tools can be the focus for explicit oral language instruction, leading to more focused writing and reading instruction within the content area of mathematics.
As we lead and learn, in our classrooms, schools and networks, we face a great challenge of building knowledge of effective practice on the fly. My goal as a school leader is to ensure that student and teacher learning is focused, important, efficient and deep. Looking at the connections between oral language and mathematics as a focus for our learning and teaching allows me to achieve these goals. By ensuring that our mathematics learning ‘floats on a sea of talk (Britton, 1983) we push our students to do the very things that mathematicians and other thinkers have done throughout the ages and provide language learning that counts, literally.
Tales from Camppp, V.2 or Mathematicus Mortis
“Most of us teach mathematics as if it were a dead language.” Catherine Twomey Fosnot
What is ‘important mathematics’ for you? Is this question easy for you to answer, or is the asking of it so anxiety-prompting that you need to take deep breaths and sit down, or run to the wine rack? Are you one of those educators who are certain that you know all you need to know about the teaching of mathematics, or are you one of the many who slink down in your chair, hoping you won’t be called upon?
It should not be a surprise that research has provided a fairly robust and clear vision of the most effective approaches for teaching mathematics in elementary and secondary school for teachers to draw upon. After all, mathematics as a discipline has been with us for thousands of years, it’s not like it is ‘new’. It is impossible to think, view, act or speak without using mathematics. And, unlike language, it is based upon a consistent, concrete set of principles that hold true everywhere in the know universe. How’s that for an unlimited, juicy context for learning?
Why is then that most school math instruction is so…limited? Why is it that we focus so much on the memorization of tricks and short cuts to apply the algorithms for computation? Why is it that most of our mathematics instruction is focused on drill or simple, contrived ‘ number situations? Why is it that we look at school mathematics as a series of subjects, or strands, to be covered, rather than as a way of discerning and describing patterns and relationships in the world around us?
For most of us, the answer is simple, we teach math the way we were taught. And we were taught by teachers who did the same…and so on. Leaving aside the issue that no pedagogy should stand unchallenged for even one generation, let alone several, let’s consider the world that demanded the mathematical understandings that underpinned this instruction. A world where calculations were carried out by clerks, not computers, where measures and financial matters generally involved face to face interactions and where opinions where formed based upon conversations and community cultural norms and values. An analog world formed the basis of this mathematics.
The digital world we live in now demands that we focus our mathematics teaching to develop each student’s understanding of important mathematics ideas so they may learn to solve authentic meaningful problems, in context, and, with purpose and creativity. This is the mathematics that has been with humans for thousands of years, long before the shop clerks of the 19th century co-opted it. This is the mathematics we spent the week talking about at MathCamppp.
Sounds great…how do we do this? Deborah Loewenburg Ball’s research suggests that we need both mathematics content knowledge as well as pedagogical content knowledge to pull this off. In other words we need to know that math our students need to know, as well as how to develop lessons that push students to develop this knowledge. Processes such as Lesson Study (an action research model developed in Japan), when grounded in research-based resources, can develop both of these areas when used by teachers. As does co-teaching with a knowledgeable coach. These are the processes we are implementing this year at our school to support our teachers as learners. Among the key insights I gained from my time at MathCamppp was the understanding that we have lots of people willing and qualified to support this process.
The question I have is what is stopping us? To paraphrase Simon Sinek, perhaps it is not what, but why? We focus so much on the what of mathematics; the rules, the labels, the stuff, that we forget the importance is in the why. We have only four operations in math (+,-,x,/) yet we have an infinite quantity of numbers, the why, my friends, is in the numbers, the patterns and the relationships. Why do we need to teach so that students may learn ‘important mathematics’ to solve real problems, in context and with creativity and purpose? Because they will need to be able to do this to make a life, because mathematics shouldn’t be the sole property of the elite, because a digital world means a mathematical world, because mathematics is not a dead language.
Tales from Camp, v.1
I just spent a week at camp! Specifically, a summer learning camp funded by the Ontario Ministry of Education and the Council of Ontario Directors of Education (CODE) through the GAINS initiative. I was at Math Camppp – not a typo, the three ‘p’s represent the precision, personalization and professional learning referenced in the book Breakthrough by Fullan, Crevola and Hill. Our camp was located on the sunny shores of Lake Simcoe at the Kempenfelt Conference Centre in Barrie, Ontario. A Literacy Camppp was hosted a few hours away, in Parry Sound, Ontario.
Over the next few entries I’ll post some of my reflections and insights related to some narrow themes (like the current state of mathematics education in Ontario), and some broader ones (like the role of technology and social networks, what constitutes juicy professional learning and the zero sum game of over valuing LITERACY over literacies.)
Across the Water, Over the Land and Through the Air
Math Camppp (#mathcamppp) was a face to face and online gathering of over 200 K-12 classroom teachers, district personnel and school administrators from across Ontario. Our focus was on exploring the concept of proportional reasoning through an emphasis on developing conceptual understanding of important math through problem solving. As we gathered together on the first night a few of us were delighted to see some of our tweeps f2f for the first time. We were quite sight, clustered around the buffet, handhelds out, the Geek Brigade assembled. Over the course of the week, the diverse dots of my PLN were connected, often with the facilitation support of tweeps from around the province (and beyond) thanks to @TechieAng and @r_o_y_a_n.
By the third day, we were connecting with our tweeps from the other camppp in Parry Sound through some common followers. By Friday morning, we were tweeting highlights from Alec Couros (@courosa) and Marian Small’s (@MarianSmall) between the sites, sharing common messages and making connections around the key messages and big ideas. This, of course, is not novel or unique. There are any number of mediated professional learning experiences that occur on a regular basis within and across social networks.
And that is my point: it is evident that we are in the midst of a wonderful shift in education and we have social networks to thank (or blame). No longer are passionate, innovative educators just left to the often harsh whims of the learning culture within the four walls of their school, they (we) have the choice to access a support network of professionals from around the world. They challenge us, they fill our buckets and they expand our horizons.
A true learning community is build upon trust, common purpose and the belief that every idea is improvable. We also know that, as Richard Elmore says, “Isolation is the enemy of improvement.” Are we seeing, through social network, the breakthrough that we though we would never see in school-based professional networks? Will these networks grow and sustain change? Will they impact learning in school-based networks positively or create even more tension? Thoughts, anyone?
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