The Challenge Of Not Telling, Amongst Others - By Maths Scholar 2024/5
This being the last week of the first term, it is a welcomed opportunity to reflect on the challenges I faced so far and, hopefully, provide useful information for next cohorts or generate discussion amongst our current cohort.
To put things in context, I joined the 2024-25 cohort as a career changer after 40 years in higher education, with the last 22 in research-intensive universities in the UK. My primary education was in Portuguese schools, my secondary education was in a French lycée, and my university studies (up to PhD) at Portuguese universities. This is relevant because one of challenges I have been facing concerns culture – I write cursive, which British students find strange; my ones have an arm, they are not sticks as in the UK; my sevens are crossed (though a considerable number of my students also cross their sevens), so some students confuse my ones with sevens as they write them. More significantly, decimals in the UK are read one by one – for example, 3.14 is “three dot one four” – whereas in French and Portuguese, discounting the fact that there is a comma instead of a point, it is read “three dot (comma) fourteen”. I think I am making good progress in this front, but it is hard to change what has become instinctive.
The major challenge though has been having to unlearn 40 years of preparing and delivering lectures at university. Early on when I started teaching, my mentor told me (I am paraphrasing): “A lesson is not a lecture: what you delivered was a lecture. You worked really hard during the lesson; however, the students didn’t. It’s the students who should be working hard, not you”. This is when I started to make sense of six weeks of observing experienced teachers during their classes – you are given a schedule of classes you should observe but you are not necessarily told what exactly you should be observing. Essentially, and from having read several papers about it, this is about moving from “telling” – direct transmission of facts, or principles, rules, etc – to “asking”, that is, planning a lesson in a way such that, by asking students questions, they are actively engaged in the delivery of the lesson itself and led to discover by themselves what they are meant to be learning. Obviously, if you ask a question, you need to be prepared to do something with the answer, for which the question should be as open as possible to allow for different answers – typically, not “what is the result” but “what could or should we do next”.
“Always have two or more ways of explaining the same thing” was another important advice, together with anticipating misunderstandings or misconceptions when planning a lesson. I have found handling misconceptions – for example, that reducing a quantity by a percentage and then increasing by the same percentage gives the original quantity – to be a particularly good way of leading students to reflect and understand how, in this particular example, multiplicative reasoning works.
In summary, a trainee will always face many challenges but I am finding these to be fascinating and prompting me to learn more, not about mathematics, but the art of teaching mathematics.
By Maths Scholar 2024/5
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