Some things I’ve come to appreciate…

A weekend of enlightening conversation with John Mason, Anne Watson, Danny Brown and Tom Carson has drawn me to attend to these ideas which, to some extent have been on my mind for the past 6-12 months. 

My understanding of pedagogy and mathematics is always evolving

Disagreeing with some things I believed in the past is ok.  My disagreeing with myself about disagreeing with those things is also ok…  
Entrenched positions on pedagogy are unhelpful  

Direct Instruction, problem based learning, inquiry, discovery… etc  I believe that a good mathematics classroom involves a range of teaching approaches and strategies.  Opportunities to practice skills are essential but so too are opportunities to apply that learning, to approach ideas from different perspectives as well as opportunities to reason and debate.  I conjecture that without creating opportunities to think mathematically, then many of our students will not learn to think mathematically.

It is possible to accept the quote below while often using direct instruction

“The power to learn rests with the learner. Teaching has a subordinate role. The teacher has a duty to seek out ways to engage the power of the learner.”

ATM, Guiding Principles

Collaboration in learning about learning is fundamental

The most significant catalysts in my professional learning have been other people.  Without the wisdom and insight of others I would be little further forward than 5 years ago. 
Actively listening and ask questions

Listening to others is enlightening.  No matter their experience in relation to my own.  It may impact on how I run my department or support colleagues.  It may change the way I see my entire pedagogical approach.  Always ask more questions – to learn more about what they think or to make them think.  Offer my own opinion, only, to hear their opinions.  

Being mathematical in front of my learners and with my learners is fundamental

This is who I am as a teacher.  I didn’t realise this was the essence of it, until I had this pointed out over a pint of lager on Friday night. 

Stop being so hard on myself

 “Good enough” has to have meaning.  What is good enough for today?  Tomorrow?  A months time?  In a year?  5 years?  The relentless pursuit of excellence at the expense of my own physical, mental and emotional health is unsustainable.  Step back sometimes. 
No such thing as a rich task, only rich pedagogy

I can write as many lovely little tasks as I like, but unless the task is used richly then it is just another worksheet. 

Teaching between the desks

I should try to never be tempted by the computer and my comfortable chair while children are in my classroom.  No matter how well they are doing, and no matter how much other work there is to do, the teaching and learning is why I am there.  These opportunities to support, challenge and extend learners – these opportunities to make each what each child is thinking feel valued occur most when I teach between the desks. 

The power of learner generated examples

If one truly understand the parameters of a question one can not only create a similar problem, but begin to consider the range of permitted variance.  Students are capable of this.  

What is important is not the doing, but the awarenesses that have arisen from the doing.

This is mathematics.  This is teaching.  This is life.  

For now, these are some thoughts.  

I hope to look back in a year and be shocked at the naivety.     

It means I’m still learning.  


  1. Hi Chris, I found this very powerful. You write with real clarity and expression. It seems to me that you are in the process to assimilating and integrating seemingly (but not really) dichotomous approaches… You get to the heart of the matter: subordinating teaching to learning. I don't think it's a coincidence that that phrase holds little meaning until you experience the power of it for yourself!Thanks again, Danny


  2. This is indeed a lovely, thoughtful and important piece of writing; reflective and humble. Gattegno’s phrase: “Subordinating teaching to learning”might be seen as abrogating one’s responsibility as a teacher; I don’t. This is partly because I put much thought in preparing for teaching; into lesson planning. My planning involves thinking about how I can cause students to become actively involved in lessons; my responsibility is to seek to spark their interest and how I can do this with minimal input. At issue is how the phrase fuels my pedagogy and causes me to think carefully about what it means “to teach” in ways which places the power of the learners at the core of my thinking.


  3. Thank you both for taking the time to comment. It is appreciated. I think the issue is that with all of this talk of “evidence” and the move to a HOD post 3 years ago, I’d lost a little bit of who I was as a classroom teacher. What doesn’t change, though, are the values: social justice etc. I’m reading through quite a few of your ATM articles just now Mike. I really hope to have the opportunity to chat about your approach in person at a future branch meeting!


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