Why I Write Puzzles
Ever since I started teaching I’ve really struggled with challenging the highest ability students. Often they’d grasp a concept quickly, and after two or three correct answers they were clearly fine with the topic. Textbooks offered few, if any remedies. Skip a question, skip a column, or worse, move onto a topic I haven’t taught yet. Most ‘challenge’ came in the form of using decimals, or negative numbers to perform the same algorithm. Were these students ready to move on? No, they needed to embed the technique, perfect it and see it from all sides. But I’ve never felt that you get that from performing the same action over and over again, albeit with ‘harder’ numbers to input.
A few years later, the ‘challenge’ box started appearing in textbooks at the end of an exercise. A worded question that more often than not referred to a weird child who liked to collect meaningless data because … well never mind because. Everyone does right? But pick through the bizarre ‘link’ to the real world, and it was the same problem as before, just… “contextual”. Students know it’s going to use the same technique, and putting it in a different pastel shaded box in the book isn’t going to change that.
Roll on a few more years and, as my experience grew, I decided to ditch the textbook altogether. I don’t have them, I don’t use them, I never will again. I’ve learnt that challenge for students often means obscurity, vagueness, opportunity, creativity and choice. I write puzzling questions that purposefully minimalise the amount of information explicitly given (there’s hardly ever more than one measurement provided). There’s no guidance, and there’s no fixed path. There are many different ways to approach each problem, some more efficient than others, but all nonetheless valid. I often use messy numbers with nasty decimals in them simply because that’s what life gives you. Shitty numbers. Why learn about rounding and estimates if all your text book problems are nice integers? Real measurements are frequently NOT integers.
These problems aren’t topic specific. They rely heavily on shape, but under the surface they often require algebra, fractions, simultaneous equations, sequences, anything from the entire tool set a GCSE student should have. I like that. I like the not knowing. I like watching students test the water in different ways to explore which part is shallowest. Isn’t that the exact thing we’re trying to achieve as teachers? To nurture an ability that allows students to approach a problem that seemingly has no clear route, but to persevere and chip away until a route is made by them? I think it is. I also think that the way questions are structured in schools doesn’t allow for that most of the time. Don’t tell them the tool, let them evaluate their toolbox. That’s also why I don’t print the answers. It’s too easy to think for a second then move on, rather than have it consume your every thought for ten minutes, half an hour or longer.
I have been amazed at how even twelve year olds and students from middle sets have taken to these (and other) puzzles in the schools I’ve taught in. For them, finding the answer isn’t even the goal, it’s trying to see if there’s a way through. Seeing those faces completely absorbed in thought fuels my teaching. I’ve seen that same face in teachers, PGCE students, and maths enthusiasts. That frustration, and unwillingness to give up, because there IS an answer, and there IS a way to get there. That’s my love of maths.
I’ve been told on a few occasions by teachers that the best thing about these puzzles is that they made them, after years of teaching the same curriculum over and over, love maths again. These puzzles are that same curriculum. They don’t require any skills outside of GCSE. I hope they inspire you, or your department, or your students, or their parents around the dinner table. I hope they get people talking about maths. If not, well, I’m going to keep writing them anyway.
You can contact me at firstname.lastname@example.org if you have a query or want to book me in for some school-based maths training.
Alternatively you can find me on twitter here.