Understanding the Teaching of Maths

Over the last 20 years, maths teaching hasn’t really changed in my eyes – has it? Yes – priorities and approaches have shifted (often quite dramatically) but, in a nutshell, teaching maths looks very similar to when I started in Year 2 all those years ago. The direct teaching remains at the heart of maths teaching going off on many tangents along the way and promoting mathematical discussion at every opportunity.  I believe that this discreet teaching element of the lesson is imperative and when intertwined with discovery and mastery approaches, maths lessons really can be magnificent moments of fun and animation!  Those times when you look around the room and think: Yes: This is why I teach!

Department of Education Guidence

“A greater coherence by exposing core concepts in the NC and by demonstrating progress” from year group to year group. 

Department of Education

Recent DfE changes have been a pleasant surprise really! Yes – It is still a statutory requirement that the whole of the curriculum is taught but the priority now seems to be those ‘connections’ that children make when progressing through the skills at their own pace and on their own journey. The DfE want to bring “A greater coherence by exposing core concepts in the NC and by demonstrating progress” from year group to year group.  Greater coherence in any educational area is music to my ears.  Children will make links between what they HAVE learnt, to what they ARE learning and will then hold on to those priceless ‘nuggets of knowledge’ and fundamental maths skills that they will (hopefully) keep with them when they revisit that same mathematical area next time.  It’s kind of like a “Tips & Tricks” memory bank that is repeated and revisited. What is important?  Exploration, explanation, mastery approaches, capturing those light bulb moments, fluency, internalising visual representations and practising mathematical processes along the way – before you move onto to the next step. Tangents are good, but one carefully planned mathematical route needs to be followed in order to lay those foundations of learning & understanding in the right order.  If mathematical concepts and ideas are to be truly understood, they must not only be passively received but must be discussed & revisited as often as possible. 

So, this latest DfE guidance is not particularly anything new, as most teachers DO make links to previous learning and understand too where each child needs to go next within the range of maths areas – and guess what – sometimes this doesn’t need to be written on a plan or an intervention – We just know!  Making mathematical connections should ALWAYS be encouraged and as we stop within a lesson to ‘take the temperature’ of the learning across all ‘groups’ of children, we can promote & celebrate those mathematical processes and applications as well as eventually arriving at the ‘right answers’.

The valuable language and mathematical understanding become apparent as they are discussed and also the little ‘brick walls’ that inhibit mathematical progress are often broken down – even if it is piece by piece over a period of time. Are the children ready to move on – or “Ready to Progress” (DfE). This makes sense. To run before you can walk in any curriculum area is often like walking on quicksand. Knowledge isn’t internalised and is often forgotten when areas are revisited next. Nothing ‘goes in’ it simply sits on the surface and evaporates quite quickly.  So far so good then! We have all been used to standard ‘progression of skills’ grids but the DfE have grouped mathematical skills and concepts which makes it easier to see those fundamental links – previous and forward thinking!

My teaching method

“Pulling the prior knowledge to the forefront of the children’s minds and discussing the skills that we may use that day”

Rebecca Underwood

I love starting a maths lesson by pulling the prior knowledge to the forefront of the children’s minds and discussing the skills that we may use that day; making predictions, celebrating progress and putting our ‘fists up’ to those misconceptions that have forced us to make wrong turnings. But it’s ok to get lost in maths. No one is perfect. It’s a life skill to make mistakes. We learn from them!  Children are inquisitive; they look for patterns and suggest solutions.  Within a safe and encouraging environment, children can take risks and address misconceptions with great resilience. We don’t all get it right first-time around!  We often don’t spend enough time ‘embedding’ what we have taught them.  Children need this immersion to create their very own links (often teachers declaring the connections themselves is not enough).  We can’t assume that a child who can count to 100 has a talent or mastery that others lack. Before that point, the child needs to develop a deeper understanding of quantity and place value and if this is pushed aside in an attempt to prove progression and high attainment, then we may see great gaps at a later stage.

I like to think of the next part of the lesson as many ‘small stepping stones’ that lead us all on from our different starting points. These small steps may introduce new learning and concepts using a range of representations and approaches.  Varying the way that a mathematical concept is initially presented to children is key as children learn in a variety of ways using a variety of resources.  Thinking and discussion must always be encouraged and praised.  Mathematical language can be used each day and repetition really is key! Use it and talk about it as much as you can! Working walls, although sometimes frowned upon, really can be useful in maths. Vocabulary and techniques can be ‘stored’ physically for those visual learners to refer to at a later time.

I am a visual learner and always encourage children to create a picture or make jottings to record their mathematical processes, operations and ideas.  They can record their understanding using symbols, diagrams and spoken explanations. Subitising is a recent focus for EYFS/Y1 teachers. Subitising is the recognition of a small number of items without counting i.e. dice images & tens frames etc.. and this skill is often developed at pre-school – sometimes even before! This is a fundamental skill which goes on to consolidate addition and subtraction concepts.

Mathematics introduces children to concepts, skills and logical thinking strategies that are essential in our everyday life and can support learning across the whole curriculum. We DO use maths in our everyday lives (maybe not algebra so much?) and the quick recall of addition facts, times tables and measurement conversions to name but a few is both impressive and, I believe a fundamental skill that most can improve with practice.   

I love the real-life approach whereby ideas are linked to contexts and real scenarios. They help children make sense of the numbers, patterns and shapes that they see in the world surrounding them.  It is then that children delight in using mathematics to solve a problem, especially when it leads them to make new connections or to build on fundamental skills and then project them forward.  Role play is, without doubt, an amazing vehicle for mathematics teaching and not only in EYFS! Think of the all the different scenarios: At the shop, a bit of DIY, making the porridge, measuring the door, counting the money and so many more! Think of the challenge questions to spark discussion!  What would happen if two more came to the party? How many more seats do we need? Can you share the cakes between the 3 dolls? Who has the most money? Quality adult interventions and interactions are key and steer learning and evidence gathering in the right direction.  I believe there is even a place for role play in year 2+ if branded correctly – e.g. enrichment days, becoming the teacher, spending PTA money, arranging an event etc… An office can be set up with maths resources, problems to solve, challenges, open ended tasks and links to home… how exciting would that be!  

In June this year, the Year 4 multiplication tables check was due to become statutory for all Y4 children in the UK. Due to Covid, this did not happen. The tables test is designed to establish the proficiency of children’s quick recall of multiplication facts. Does Rote learning of times tables work?  As someone who was unconfident at times tables at school, I would create links e.g.  12 x 9 question, as 11 x 9 + 9. Also, I saw the crucial link between the 2, 4, 5, and 10 times table and how these facts can support learning of other tables and addition facts.  I can remember the fear of playing games such as fizz buzz and trying to work out what I would have to say.  Has this changed? What is the best way to teach times tables? Again, this links back to the building the foundations of understanding the number system.  So many questions to ask! Let’s see what next year brings.

Personal Judgements

The New EYFS Framework has lost the focus on “shape, space and measures” and “problem solving” which has caused much concern; as has the wording, “automatic recall”. This suggests that concepts are learned by rote without laying the crucial foundations of learning by sequence.  What do you think? What are the corelations between this and the DfE guidance? To recall addition facts, bonds etc.. without meaningful context may further disadvantage some children as concepts become too abstract and those ‘connections’ are lost.

I believe that children should be able to dive deep (pardon the phrase) into each mathematical theme and demonstrate great, conceptual understanding which carefully lay the foundations for their future learning. My favourite words are; explore, discover, challenge, revisit, determination intrigue and inquisitiveness.  When appropriate, share the learning objective. Introduce real-life concepts when possible. Include an element of fluency every day (I do this in morning work sessions) to promote and practise important mathematical skills. Give children opportunities to make those vital connections and apply their mathematical skills in a range of reasoning activities that excite them and make maths magical!  

Read more maths tips and tricks on the Maths Page!

I would love to hear your thoughts and opinions on this matter please leave them below and I will try to respond to as many as possible!

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