The Norm: Maths is an interconnected web of knowledge. Teachers intellectually understand this, but shy away from the implications and continue teaching topics in isolation.
Target 9 Maths: I take full advantage by beginning with the basics, with the dual aim of filling any gaps in knowledge and ensuring that students start thinking in very particular ways about topics, so that every method learnt can be extended later on to turn topics which are generally considered difficult into simple extensions of this foundational knowledge.
This also ensures that all students can progress together at the same rate, as I make no assumptions about prior knowledge and cover everything.
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The Norm: Most teachers will tell you that they have high expectations for all of their students, but in reality teachers spot who is struggling, think it is going to take a huge effort to help them, and so mentally place them in a ‘just-get-them-through-it’ bucket whilst feeding them easier work than the ‘talented’ students.
Target 9 Maths: Natural talent is a myth though. The only difference between ‘struggling’ and ‘gifted’ students is their level of prior knowledge. So I focus straight away on ensuring that everyone knows what they need to, which rapidly closes the gap between them.
And I never lower my expectations or demoralise a student by giving them easier work. Everyone does the same work, with the same expectations; and by working with small class sizes, every student is given the attention they need to fully unlock their potential.
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The Norm: Too many students are also taught to rotely follow methods, without knowing why they work. The problem with this is that if they then forget the method, they are lost. And when they are being asked to remember lots of methods, they will forget some (perhaps many).
Target 9 Maths: I teach everything for understanding, explaining why maths works as it does, which both increases long-term retention of information and helps students connect different topics for a deeper level of comprehension. So when my students occasionally forget something, they can logically rework out the methods because they knew why they worked in the first place. Sometimes they even work out different methods, which I have not even taught them, because they can understand why they would work (this happens more often than you might think).
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The Norm: In life, there are certain things everyone does, which if you stop to think about make little sense. Following government designed learning pathways for Key Stage 3 and Key Stage 4 (i.e. they should know this in this year, and that in the next year, etc.), as almost everyone does, is one of these nonsensical things.
Target 9 Maths: There are many topics which students are ‘not supposed’ to learn until year 11 which actually follow on logically from topics in year 7, and make a lot more sense to students if they are taught much earlier; thereby turning ‘tricky’ topics into obvious ones.
Understanding this, I sequence topics in a unique order so that they flow smoothly from one-to-the-next, revealing hidden connections which allow students to reutilise their prior knowledge to learn faster and easier. Topics are taught when it makes the most sense to, not when an official document says they should be.
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The Norm: A particularly wise quote is: “Hard choices, easy life. Easy choices, hard life.”
Most teachers make easy choices, spending lots of time on topics they think are likely to turn up in the exams, and only a cursorily moment on topics which turn up less often; imagining that they are helping their students focus on what is most important. But the result is big gaps in knowledge and students coming unstuck on quite simple questions because they were not taught them well enough.
Target 9 Maths: I make hard choices, assuming any topic could turn up in its most challenging form, and prepare accordingly. This is why my students tend to get 90% or more of the marks in the exams: because every topic has been covered in equal depth, with a wide variety of questions, so they are ready for any problem they might encounter.
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The Norm: There is also a curious general blind spot in even the best teaching. Whilst great teachers utilise effective approaches based on up-to-date educational and psychological research; they still don’t apply any of this knowledge to homework.
Target 9 Maths: I have thought about what homework would look like if it had never existed before and was designed from scratch. The result is a unique approach which more effectively consolidates learning, whilst also allowing students to practice with less frustration and complete more advanced work than would otherwise be possible.
Exactly how it works is for students on the course only; but it is both familiar and different, and simple enough that someone else really should have thought about it before now.