By Katie Crozier (March 2022)
The level of conversation we engage in, and the stimulating environment of the maths hub community, have encouraged me to look deeper than the surface features of a good lesson. That has led me to ponder how we develop high-quality teaching and how can we improve it even further.
Good maths subject knowledge
Our own subject knowledge is absolutely crucial in our job, and needs to be a moving and living thing, not static. We can always learn more about the maths for ourselves. We also need to continue to develop our understanding about how children think about the maths and how concepts are learned and applied. By itself, however, good subject knowledge doesn’t result in high-quality teaching.
Being a reflective practitioner
The way to achieve higher levels of quality teaching is for us to ensure we are thinking as practitioners who want to improve. For me, being reflective is absolutely key. If we ‘deliver’ a lesson and walk away without a thought we are unlikely to improve. We have to engage with our lesson, our children, our subject knowledge and all the other complex things that make teaching such a muddy science. We can’t have a single lesson design that will work every time because children are all wonderfully different, and so are maths concepts.
I have found that my reflections, alongside my evolving subject knowledge, are moving me forward. When I think of moments of teaching enlightenment I have experienced, they have come about when I have sat back and thought about something that has happened. The moment may have passed but the thought has not. In their book Professional Capital, Hargreaves and Fullen (2012, p50) write about the importance of having a mixture in each classroom between ‘best practice and next practice’. ‘Best practice’ is defined by them as ‘existing practices that already have a good degree of widely agreed effectiveness’ and ‘next practice’ as ‘innovative approaches that often begin with teachers themselves and that will sometimes turn out to be the best practices of the future’. This ‘next practice’ might develop as part of my own thought process, but it more often occurs when this thought is shared with another person who is also engaged in reflecting on their work. The dialogue and musings around a point of discussion create more things to consider – more questions than answers maybe – but this can then result in a shift in the way we think. The shift creates new things to try, new ways to think about some mathematics, new ways to use a manipulative, etc. Collaboration adds so much more to our busy, but sometimes lonely, teaching environment.
Being mathematically observant
In my school we are starting to use the phrase “mathematically observant” to refer to the way children respond in lessons, which I think is excellent, but I think it can refer to teachers as well. Before you can reflect on something you need to have noticed it in the first place. In the busy classroom it is easy to get caught up in the complexity of the environment. There are so many things happening all at once, many of which are intertwined, and it can be difficult to focus on one particular thing.
When I reflect on a lesson, I try to be aware of the point where I was surprised, curious, baffled by something that happened. This thing didn’t ‘work’ as it was supposed to – why? Or it worked particularly well – why?
This process involves behaving like a camera zoom lens. I need to focus in on exactly which part of a question proved tricky, what prior knowledge was required, what I could do to support the child to understand this and how I can support the child to deepen their mathematical knowledge.
I have been thinking a lot about how to get a window into a child’s mathematical mind and see how they are interpreting my teaching. We can certainly talk to children and get them to explain their reasoning and thinking. I also find that the right task can reveal so much that you wouldn’t necessarily know before. This is likely to be a task that is open enough to be revealing but precise enough to give you an insight into a specific area of maths.
Children’s engagement in the maths lesson
In order to encourage and support children to engage with their mathematics lessons I not only need to think about pedagogy and lesson planning, but also the relationship I have with the class.
I think my lessons with my class improve as the year goes on. I know them better (as mathematicians and as people), I know what to look out for, I have a better idea of how to respond to particular situations, and there is an emerging environment built on mutual respect and trust.
Continuing to develop
I have written above about the important aspects of development that seem important to me as I think about my own teaching. I will continue to think about my development as a mathematics teacher and the process I am going through as I try to create my own ‘next practice’. As a result, for me, every day is a CPD day.