We brought together maths education experts from around the world for a series of online expert panels and webinars to consider how we can equip maths learners for the future – whatever that future looks like. This series of blog posts aim to highlight the key takeaways to help you empower today’s learners to embark on a lifelong adventure with maths through resilience, connection, curiosity, and creativity.
In this blog we summarise Professor Anne Watson’s webinar sharing her top tips for transforming your primary maths teaching.
Professor Anne Watson taught mathematics in challenging schools for 13 years before becoming a teacher educator and researcher at the University of Oxford, where she taught secondary mathematics PGCE students. She has published books and articles about strategies for teaching mathematics, and has led research into mathematics teaching and learning from primary to tertiary level.
In her webinar, Anne suggested a series of small adjustments that you can make that will transform your primary maths teaching in a way that makes a real difference to children’s learning.
1. A purposeful example
When preparing your lesson, think carefully about what numbers you are going to use. Your example needs to be big enough to think about, but small enough to understand. A purposeful example takes into consideration: the learner’s perspective (what they know already), the context, your intentions, and the key idea that you are teaching. If you prepare the number facts in advance, you are able to be fluent, having already thought ahead to where you want to go next.
2. Plan your language
We sometimes say things in a way that doesn’t convey their mathematical meaning. For example, be careful with prepositions – saying 4 over 5 for a fraction doesn’t convey mathematical meaning. Choose your language so that it is mathematically meaningful and so that it is possible to use the same structure of language as things get more complicated. Match the maths language to your children’s language and the symbolism you are using. The way we become better at using language is by communication with others; it is a two-way learning process. By using it again and again, we reach fluency. Children will only use language that has mathematical meaning if their teacher models it first.
3. Think and talk
Children often think they have to find an answer and become caught up in this rather than the ‘what’ and ‘how’. Help them overcome this by starting with something to think and talk about, rather than something to calculate. Give them the answer to a calculation and ask them why, and what this tells us. It will help them think about what they are going to talk about, not simply wait to be told how to do the calculation.
4. Vary representations
Start new ideas with a variety of symbols and images, showing children different presentations of one relationship. This is a powerful way to help them to understand a structure, and much more powerful than showing them one structure and lots of different numbers. Consider which representations will make the most sense, including some that children will already be familiar with, and that will most support their imaginations.
5. Vary examples to reveal meaning
Begin to vary the numbers in your example to build on where the fluency is, exploiting pattern and repetition. Variation Theory tells us that we notice what changes against an invariant background. This is fundamental to learning, and to the structure of mathematics. Using the language and representation of the original example, children have a structure that they begin to understand. They can use it again and again, building on and extending the work done already and revealing meaning as things get increasingly complicated. You can expect your learners to notice and accept without question something that follows on from their previous work. Encourage them to make their own examples.
You can watch the full webinar ‘Five top tips for transforming your primary maths teaching’ here. (Note: you will be taken to a sign-up page and asked to enter your details in order to access the recording).
For the next blog in this series ‘Maths in Early Years: How to build solid foundations for Primary’ by Dr Helen J Williams click here.
Choice of examples: Rowland, T. (2008). The purpose, design and use of examples in the teaching of elementary mathematics. Educational studies in mathematics, 69(2), 149-163.
Mathematical language: Austin, J. L., & Howson, A. G. (1979). Language and mathematical education. Educational studies in mathematics, 10(2), 161-197.
Spatial images: Mulligan, J., Woolcott, G., Mitchelmore, M., & Davis, B. (2018). Connecting mathematics learning through spatial reasoning. Mathematics Education Research Journal, 30(1), 77-87.
Variation: Marton, F. (2014). Necessary conditions of learning. Routledge.
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