When I entered teacher training, even though I was far from possessing the necessary skill set to achieve it, I had a firm idea of what I wanted to do as a teacher, or more specifically what I did not want to do: I articulated this at the time as not “telling” mathematics to students. I would now rephrase this as not generally wanting to share that which could be discovered, but instead working in such a way where students had the potential to form and reach mathematical conclusions themselves.
In 2007 my PGCE tutors at the University of Birmingham were Steph Prestage, Pat Perks, and Dave Hewitt, three people who were very influential in different ways in both my development and my practice to this day. I had no idea when I started what I was going to be faced with and did not even contemplate it too much: before starting, my training was about gaining confidence in myself and leaving with a certificate that would allow me to teach in state schools. I knew my views of what I wanted in my future classroom were very different than I had experienced: perhaps I was just out of line with everyone else and indeed reality.
Thankfully that turned out to be far from the truth, as I was exposed to different thinking about mathematics and its education than I had previously encountered. Hewitt, in particular, approached the teaching of mathematics in a way that seemed to align with what I hoped to achieve, but to such an advanced level that I realised my grand philosophy was personal hubris and I had much work to do before I would be even remotely happy with my thinking and future teaching practice.
If I went back through my notes from the time, I am sure I would find many lightning-bolt moments in the course that influenced the professional and indeed man I have become. But I do not need to go to my notes to be reminded of writing I first met then and have revisited many times since, and what will become a focus of my writings here.
I cannot remember if Hewitt explicitly shared his educational writings or if I found them myself, as I wanted to learn more from this important figure in my life. I realised that within my idea of not “telling” there would be some elements of mathematics that would have to be shared; whilst much can be reasoned, I knew then that there were some parts of mathematics that were decisions made at some point in history or parts that were merely definitions. It turned out Hewitt had already divided mathematics along those lines, into what he termed the “arbitrary” and the “necessary”, in a three-part series published in the journal for the learning of mathematics. I immediately felt that I had a theory to latch my thinking onto and also to develop it; almost eighteen years later, this continues to be the case as it is my main philosophy for how I approach mathematics. This concept of arbitrary and necessary will be explored in many pieces to come, but ultimately will be behind everything I write.
Next: in the final autobiographical section of this introduction, further influences in training and beyond.
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