We are all evolving beings, and if we are not currently satisfied with our performance or knowledge as a teacher it is important to realise that what we will be tomorrow can be greater than that we are today should we sufficiently work upon our selves, and who we were yesterday informs who we are today. A combination of ideas I possessed before I started my training to be a teacher, my experiences since, and the wisdom of my influences have led me to develop an ever-firming sense of what I believe as an educator. Working with the Association of Teachers of Mathematics (ATM) led me to greatly appreciate the existence of its aims and guiding principles, which it was said were the basis for all of its work as an entity. Similarly, in the background of everything I do and the work I produce here are a similar set of principles. The extent to which my work meets these has and does vary, but I measure myself on what it is I am working towards:
Only awareness is educable (Caleb Gattegno, The Science of Education Part 1: Theoretical Considerations)
Mathematics is a way in which we make sense of the world, and our human nature has us as natural mathematicians; our teaching should look to reach and develop this (following ATM)
A questioning rather than accepting nature is fundamental to the development of both one’s self and one’s teaching, and this should be embraced. The same nature should be encouraged and developed rather than subdued within students
In the most powerful classroom, teaching should be subordinated to learning and thus a fundamental operation of the practitioner is to assess and respond (following Gattegno)
The mathematics classroom should always be about its learners, not its teacher
Self-belief in learners should be encouraged and promoted; the notion that one “cannot do mathematics” should never be accepted, and intelligence-judging language or values should be contradicted
Mathematics teaching should focus upon the “necessary” and seek ways to engage with and develop this (following Dave Hewitt)
Teaching mathematics is not the same as teaching pupils to learn mathematics, and both must be attended to within a classroom (following many, particularly The Psychology of Learning Mathematics by Richard R. Skemp)
Teaching takes place in time, learning takes place over time (Pete Griffin, Mathematics Teaching 126, following John Mason)
Learning is often messy rather than neat and linear; planning and preparation must take this into account and the practitioner must battle the notion that their role is the delivery of packets of information irrespective of and formulated away from the needs of the learners in front of them
Teachers should aspire to be the best versions of themselves by removing judgment and instead adopt a continuing developmental view of their own practice in response to their students’ learning, by engaging with themselves and with others
The developing teacher never loses sight of themselves as a lifelong student, of their subject and its learning, and of their learners as human beings
Collaboration is powerful for both learners and teachers: we always can learn from one another
Whilst knowledge of current research and evidence is powerful and desirable, falling prey to solely that which is currently en vogue loses sight of the rich tapestry of research, writing and ideas from the past and instead leaves one open to merely following agendas
The development of intuitive practice is desirable, as then is its deconstruction
As I end both this piece and my introduction as a whole, I realise that it will be of interest to look back upon in the future as my thinking further evolves to see how much of the above I would change or revise, what, if anything, I would remove, and what I would add. I also suspect that, in one way or another, this introduction has previewed everything I will ever write here.
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