I was capable at what I was asked to do at school. And I certainly remember speed and accuracy being rewarded there. University was more of the same and looking back I learnt how to do well, without any deep understanding. I did get frustrated at the assessment and got a sense that exams were a speed contest, not an opportunity to show deep understanding.

Unfortunately for me I feel as though my honours and postgraduate years were so overly scaffolded that even then I didn’t really learn what it is to do mathematics. No disrespect at all to my supervisor who is one Australia’s finest applied mathematicians – I know he thought he was doing his best by me. At the time, I thought his approach to my “research” internship was entirely appropriate, because it was like my undergraduate years. Looking back I wish he wasn’t so attentive and had me work out things for myself.

I finished my PhD in three years and three weeks and the following day took up my lecturing job in north QLD. This was 1993. I had moved to a department in decline and there was no broad culture of research or doing of mathematics. The most authentic doers of mathematics were actually the physicists on the floor below, but it took me a while to work this out. It was very much a place where we did direct teaching in the way I had experienced as a student.

By 2007 I was in a multi-disciplinary school and my responsibilities extended outside of mathematics into physics and assisting with off-shore delivery of IT. Somehow my efforts in teaching were recognised and I got approached to take a leadership role in the science faculty. It was a role where I had no power. I was supposed to use my “influence” to raise the profile of teaching. This did give me an opportunity to reflect – not on mathematics, but on what we were doing in our BSc – and I decided to focus on numeracy, because I knew this was an issue frequently discussed by the cohort of academics. I got to mix with other learning and teaching people across Australia and be involved in some great projects.

In 2010 I decided I needed some help from somebody with a knowledge of education, because I wanted to formalise some of the work I had been doing. I ended up meeting the mathematics educator, Jo Balatti. I did not ask for her. This was the person the Head of Education got me to meet.

It did not take long before Jo started telling me about her struggles with the maths pedagogy subject. She very quickly got me to realise that I as a mathematician had a responsibility to focus on the cohort of preservice maths teachers. There was a lot of distrust between education and the sciences and maths within the university, so there was not a history of cooperation. But Jo pointed out to me that her students were doing at least four subjects of maths in my discipline before she begins to teach them maths pedagogy in education – and that her experience was these students were very weak when it came to explaining mathematics concepts and procedures.

My interactions with Jo lead to a lot of reflection by me about mathematics and the way it needs to be taught. This is not to say that I had not contemplated this before. Despite my own lack of profile in research mathematics I knew enough from the conference circuit that mathematics is a very powerful bunch of knowledge and pursuits in mathematics are not procedural in nature. However it was not until I thought about Jo’s words that I really began to understand how our approaches in maths teaching were unhelpful.

Jo & I co-wrote a subject for preservice maths teachers – and this subject has given me an opportunity to revisit so much of mathematics – in a way that we hope helps aspiring maths teachers to do a good job. And I agree with the message in the word clouds of Tracy Zager – that there is so much to the body of knowledge we call mathematics that we ought to get across. This includes the messiness of problem solving and the absolute thrill of the light-bulb moments where connections are made and the beauty of the structures within mathematics are revealed.

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