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This Year’s Model

“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…


  1. Karen
    April 9, 2016 at 12:59 pm

    Well said, Brian.

  2. April 16, 2016 at 1:03 pm

    You may be referring to me in your blog.
    Can you locate a large-scale study, that has included control groups, to prove the efficacy of constructivism,.I would be interested in reading such a study. I try my best, and do fail at times, to stick the topic of math and to not make personal comments.

    • April 17, 2016 at 1:41 pm

      Hi Theresa

      Thanks for the response- if you are the teacher that was quoted in this CBC post http://www.cbc.ca/news/canada/hamilton/news/retired-teacher-calls-for-review-of-ontario-math-curriculum-1.2499356 then I guess you could be one of the folks I was referencing. If you scroll down through the comments you will see a few other retirees (and others) who offer perspectives that (as I opined in my post) are easy to express; represent catchy sound bites and don’t really add any substance to the conversation about math teaching and learning. I only ask that the media go beyond these voices and include the perspectives of those teachers who are actually implementing the teaching approaches successfully.
      I use my blog as a space to connect and engage and do refer to the research links that have informed the work I have done in this area. I don’t advocate for pure constructivism or support the use of terms like ‘discovery’ or ‘inquiry-based math”. Through my experience and research I have learned that direct instruction is an essential aspect of math teaching and the knowledge of the teacher is integral in making this happen (I won’t re-hash my previous posts).
      Over the years I have worked with hundreds of elementary teachers and pre-service teachers in various capacities and roles. In each instance I can say that the majority, when given the chance to express their own disposition towards teaching math have expressed a lack of confidence ( I made no mention of the word ‘fear’) in their knowledge of teaching math. Having said that, one can be ‘certain’ and wrong about something at the same time- history is filled with examples of this. I ask the teachers I work with do be reflective about the work they do and examine the practices they use- certainty can stagnate into a set of static practices that don’t account for new ideas and perspectives; my understanding of mathematics requires that we all be open to new ideas and perspectives.
      As an mathematics educator I respect your perspective and appreciate your willingness to engage in the discussion about mathematics teaching and learning!

  3. April 16, 2016 at 1:13 pm

    There are elem. teachers who are afraid of math ; there are many who are not. Accuracy is important. Whether I am retired or not is not important and I support teachers first and foremost. 32 years of experience in the classroom has taught me what is important and what works. I have zero fear of math and quite frankly, I can’t think of a single teacher at my last school, who was afraid/lacked confidence with math. Cliched writing about massive teacher math fear could, I think, be refined.

  4. April 17, 2016 at 3:55 pm

    Interesting. Yes I was in CBC.
    I can change the word fear to lack confidence.
    I will look at your blog more closely;sound-bites are sound bites and do speak ti the gen’l. public to some degree. Certainly, there is a huge amount of anger in gen’l. public and there are many discouraged teachers. The approach of the Ont. government certainly has been social constructivist, with somewhat of a shift recently. I sat through much of that PD I understand that boards and schools can vary in their approach or emphasis.I still maintain that there are many teacher, who do not lack confidence in math. I will go through your blog more closely. Thank you for your comments.Teresa

  5. April 18, 2016 at 9:26 am

    The opinions of retired teachers certainly do add substance and are not smply sound bites and should not be summarily dismissed as such. Granted, they are only write short comments in a newspaper. These retired teachers frequently represent the views of teachers who are still working , but are afraid to speak. And afraid is apropos here. To dismiss the experience of these teachers is foolhardy. Perhaps you should listen to them.

    • April 19, 2016 at 6:54 am

      Hi Theresa

      The perspectives of all teachers add to the discussion- those are who are currently in the classroom as well as those who have left active teaching. We are in the midst of a era where past practices and beliefs are being challenged by many practicing teachers with good reason; the needs of our our students require us to do so. Along with the perspective of those who are critical of change I only ask that that the media offer examples of those who are not:


  6. Jonathan
    April 23, 2016 at 8:51 am

    Hi Brian and Teresa,

    Brian great post.


    You may want to look at the work of Alex Lawson (http://www.pearsoncanadaschool.com/index.cfm?locator=PS28F9). Though her book is K-3 at the moment she did follow students from K-8 and studied their mathematics.

    You can also look at Cathy Bruce’s work: http://www.mathforyoungchildren.ca/about.html. Her study in spatial sense is amazing. Her work proves that yes traditional teaching is good and better than just letting students wander and explore (which by the way no teacher does) but the best is the combination of both.

    I also think that many parents have no idea what is in the curriculum. Multiplication facts, long division, and borrowing and carrying are in the curriculum. However, they can conceptionally be confusing for kids. Take a look at long division (360/6). We would first start with how many times does 6 go into 3 and say that cannot be done. Big mathematical problem: 1) that is not 3 but 300, which 6 does go into (50); 2) 6 can go into 3 it just becomes a fraction. Yes, the long division method is a tested procedure that students if they follow a prescribe method, will get the answer but it is flawed.

    Personally, I teach a sense of numbers and understanding of what division actually means. I will also follow up with if our traditional ways of math worked so well why is it that as adults many of us cannot do math? Why is it that we struggle with basic grade six computations?

    I have grade twos learning about the distributive and communitive properties of multiplication, they can compensate and use the constant difference strategy for addition and subtraction. They are mentally adding two digits by two-digit numbers in their head. I have grade 6’s talking and conjecturing about first differences in linear functions. They are solving complex algebra questions while coding variables for robots and computer science. Oh yeah, they are all 100% ELL. Math is about making students understand the value of numbers. It is making them see how numbers work and why they work.

    You may also want to look at the types of questions our students are falling behind in and not just the test scores. The questions indicate that it is not the fact questions or the procedural ones but the application of those questions. Students struggle to know how to use their knowledge. For me, that is because they never learned how. There needs to be a balance.

    Thank you again, Brian, for a great post and I apologize for the small rant.

  7. May 14, 2016 at 12:40 pm

    Hi Jonathan- so sorry I’ve taken so long to respond; my life (work and otherwise) has been way too busy the past few weeks. I appreciate your adding your perspective to the conversation. Though I’m quite happy to have responses that offer dissent to the points I am raising it is helpful when teachers who are adapting and learning about their math teaching practice weigh in – we need to hear voices like yours in order to help make the required change happen for all teachers and kids.


  1. April 22, 2016 at 5:00 am

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