“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…
“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.