When I was young, there were two key ongoing experiences that would influence my thinking and philosophies when I entered the teaching profession.
The first was of myself as a learner of mathematics. Out of necessity and also teacher choice, in secondary school I largely learned mathematics by working at my own pace through text books, where I would follow along with examples given and then apply this mathematics to the questions in the exercises. Not only would I want to answer every question, I had a need to answer every question correctly. For a large portion of these questions I got the answers in the back on the first attempt, for the rest I would repeat until I did. My brain seemed to soak up this mathematical learning, apparently far more easily than those around me. I had no idea why. I was one of only three people in my year group who worked through the extra text books covering the mathematics required to obtain an A* at GCSE. Most of my peers did not seem to have a positive view of mathematics nor themselves as learners of the subject.
The second was regarding my mother and her reaction to mathematics. She was completely different to me; she would recoil in dread at the notion of being expected to perform anything she viewed as mathematics. Her story was hers to tell, but suffice to say that the root of her feelings lay in her formative years at school, where she had been made to feel inadequate and ‘stupid’ because she did not achieve highly in the subject: indeed, she had left school firmly believing she could not do mathematics. We thus approached mathematical problems with completely different mindsets.
I did not train to become a teacher immediately after my undergraduate studies. In the years betweenI helped several people with mathematics, most notably my mother. I saw bravery when she worked to overcome her anguish to want to improve. I found myself wanting her to understand how to answer a problem, which I realised was not the same as answering it. This was not how I recalled being taught, or at least not often. The development I witnessed was less rapid than the apparent success I had working with text in books but it was evident, especially and most importantly to my mother.
If my brain was different to my mother’s, I could not account for why. But I also realised that this was irrelevant to me; if everyone could achieve exam success in mathematics in the way I did, they would have done so already. So how else could mathematics be learnt and as a result taught, in a way to better ensure that all students access the underlying mathematics? And what is that underlying mathematics, and what does its learning look like?
These questions were at the forefront of my mind as I worked towards and entered teacher training in 2007. In 2025, they have and continue to shape my professional identity, practice and the ensuing writing with which you may choose to engage.
Next: teacher training, and beginning to formalise my thinking through meeting the work of Dave Hewitt and “Arbitrary and Necessary”.
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©2025 David M. Lawrence.
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