What kind of cook are you?
What kind of mathematics teacher are you?
Two completely unconnected questions you may think.
This morning, as I’m engaging in one of my favourite relaxation activities (baking) I find myself using many maths skills (some estimating, some approximating, a little geometry, some problem solving and quite a bit of creativity) but beyond that, I’ve found myself thinking about maths pedagogy and some things I’ve noticed recently.
My work involves visiting other schools and working with colleagues around the region and country, who do the same. We visit to look at mathematics – how the children are learning, how the adults are teaching and how the leaders are orchestrating both. Something I’ve noticed, especially since Covid struck, with all the restrictions and changes to teaching that brought, is that lots of schools now use schemes. Schemes change the way teachers teach, they change the way children learn. Much depends on which scheme was selected by leaders and why, how that scheme was introduced and is understood and what CPD went alongside this introduction. (See EEF 2021 for guide to implementation.) I’ve noticed in some classrooms, that the adoption of a scheme has changed the teacher and the teaching in unexpected, unplanned for ways. Others have noticed this too.
In some cases the teacher has turned into the presenter – they click on presentation slides, and present mathematical ideas and concepts to children. The children, to play their part, are expected to engage with these ideas, understand these concepts, or at least remember the procedures presented. Some do, some don’t. And the next lesson, is whatever the scheme suggests.
Now I’m returning to my kitchen. This morning I’m baking. I’m baking for myself and some family. I am baking a sponge cake – that’s a simple recipe, I remember it without having to look it up, from when I learnt to cook at school.
However, I know:
· I can’t eat gluten.
· My father is diabetic.
· My son is trying to boost the amount of fruit in his diet.
· My grandson likes lemons.
Do I prepare and bake several different cakes, using different recipes?
No, I really don’t have the time for that – any why would I?
I adjust the recipe, use gluten free flour, low fat spread, less sugar (but not as much as to affect negatively on flavour), add some lemon curd and fresh lemons. This one recipe will work for everyone. And finally, I don’t have the standard sized cake tins, so I adjust the cooking temperature and time – do I know exactly what time they’ll be ready? No, because there’s lots of variety in the ingredients and cookers, so I check, I test, and I use my experience to judge when they’re ready.
There is lots of room for error along the way. Some may not be disastrous, and would still produce cakes, others would be disastrous for specific people and must be avoided, such as using the wrong flour.
What does that have to do with teaching maths? You might ask. Consider a classroom of children, like my family, all with different needs. Do I plan several different maths lessons to teach them at the same time? No, that would involve a lot of time and effort from me and no benefit for the children. I design one maths lesson, one maths concept. Do I present the standard maths as per the scheme? No, based on my knowledge of prior learning, gaps, tricky bits of new learning, individual needs and previous experiences, I make sensible, carefully considered adjustments. Will everyone (get to eat tasty cake) learn the maths they need to in that lesson? Yes, because I am the teacher and I will have designed my lesson to ensure they do.
Could I have baked this way from the beginning, when I very first learned how to cook? No, I couldn’t – at that stage I followed the recipe exactly, I measured every single ingredient precisely and I wasn’t aware of how the size of eggs, adding lemon juice and vanilla essence would impact on the amount of eggs I’d need. I wasn’t aware of how the cake could taste as nice with less sugar or different flour. It is something I have learnt through experience, but also through study – some reading of cookery books, some watching of cookery programmes, some learning from friends/family who cook, some eating out, some trial and improvement – if it didn’t taste right, what needs to change next time? And do I follow exactly the same recipe now every time I cook a sponge cake, no …. It depends on the audience and need.
Maths lessons can be compared to baking. A carefully selected and implemented scheme can be an enormous help, we all need a curriculum as a start point and a scheme can break that down into smaller steps, providing the coherence necessary. But teachers are the ones who make the mathematics understandable for every child in the class. Teachers are the bridge between the scheme and the individual child. Teaching is not just presenting! Teaching involves a range of complex skills and interaction with decisions made at various points before/within/after each lesson, and just like baking, teachers need to continuously developing their skills. Teachers need time to read research, purposefully observe others, reflect, take part in action research, learn from others and continuously strive to improve. Teachers need time and support to build expertise over their careers.
A standard recipe from the book will not suit everyone (it could endanger some), it needs adjusting.
A standard lesson from a scheme will not work for every learner, it needs adjusting – not into a different thing altogether, but in a way to ensure the whole class can learn that key concept.
Does a scheme remove the need for teacher CPD, no, but it does allow more time for the CPD as some of the other aspects of planning the maths have been done for the teacher.
What kind of cook are you, do you just follow the recipe from the book precisely, regardless of who will be eating?
What kind of mathematics teacher are you? Do you just present material, regardless of the individuals in your class?