“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…
“Go down deep enough into anything and you will find mathematics.” ~Dean Schlicter~
It’s common for people to refer to the changes schools are making to the methods we use for teaching math as “the new math’ as if there has been some recent, radical change to the discipline of mathematics. This is actually inaccurate as the ways that people have represented mathematical ideas (number symbols, drawings, models and charts) have not really changed much over the centuries. What has changed is our awareness of how mathematics can be taught and this is a function of both what we know about mathematics and how children learn.
It turns out that children learn best when they are engaged in tasks that are meaningful, authentic and provide just enough struggle to make it worth the effort. The short video from math teacher Dan Meyer (@ddmeyer) gives some helpful examples of how real, everyday situations and contexts can be turned into meaningful math learning opportunities for students.
The example above differs from the traditional math instruction that is familiar to most of us and I have had many opportunities over the years to help guide conversations in this area. When working with parents and colleagues I find it’s helpful for them to know about my past experiences in the area of mathematics. Along with having taught math in almost every grade as a K-8 classroom teacher; I also had the opportunity, for several years, to work at the system level developing and leading mathematics professional development sessions for teachers from all over our district.
The ironic part about this, as my own parents would attest, is that my experiences as a math student in elementary and high school could only be described as abysmal. I struggled greatly in my attempts to learn math- the times tables, the procedures, formulae and rules were all too confusing for me to keep track of or apply with any confidence. Upon graduation I refused to even consider taking any math courses when I moved on the university.
So when, as a novice teacher, I found myself in the awkward position of spending my first year having to learn the mathematics curriculum I would be teaching my grade 7 class-I’m happy to report that my second experience learning grade 7 math was much more successful. During that year (and in the years since) I realized that learning math requires the understanding that math is best learned through experiences, communication and the solving of real problems and not just through the memorization of the rules and facts found in textbooks.
I didn’t really learn to appreciate and understand math during my time as a student in school. In fact, everything I have learned about math; both in my teaching and how I use math in my everyday life, I have learned since I began my teaching career- again in the real world.