Teach-Primary-Issue-19.7

Jo Austen makes the case for ‘forward-facing’ approaches in primary maths W hat is 673 x 10?" “Just add a zero!” Most teachers know this isn’t a great idea; once decimals are involved, this ‘quick trick’ becomes a real problem (673.4 x 10 does not equal 673.40). ‘Just add a zero’ is probably the most infamous example of an approach that accelerates students towards the current objective but is not ‘facing forwards’ to their mathematical future. In maths (and everything else), we should aim to be forward-facing – looking ahead to the more advanced concepts that pupils will encounter further down the line. I first came across this idea in Mark McCourt’s excellent book, Teaching for Mastery , which reminds us that ‘an effective mathematics education system is one that focuses on teaching approaches that maximise subsequent progression, rather than a pursuit of short-term, superficial success’. Essentially, we need to make choices that our students’ future teachers will thank us for. Let’s break this down into methods, models and examples. Methods We mustn’t simply settle for children getting the right answers; not all mathematical methods are created equal, and moving to better methods matters. For example, a Year 1 child calculating 3 + 8 by taking three blocks, then another eight blocks, then counting the whole lot to reach 11, is an important step, but not something we can settle for. It is a slow, inefficient method and would, if relied on in future, become a problem, clogging up the child’s working memory. Instead, the forward-facing teacher knows the likely progression of methods of early addition, recognising them as steps towards rapid, fluent calculation in future. This is not to say that there is always one ‘best’ method to work towards mastering. Many primary children have the misguided idea that mastering formal written methods for the four main operations is the ultimate aim. Far from it! We should explicitly teach children to choose an appropriate method for the question at hand, depending on the numbers involved. For example, 400,000 – 26 would be a very messy formal column method but is straightforward for those with a sound understanding of place value. Similarly, doing 34 x 102 with a written method would seem unnecessarily slow to those who can use the distributive law of multiplication to do (100 x 34) + ( 2 x 34) = 3400 + 68 = 3468. Teachers need to explicitly model this kind of thinking, knowing that future, more challenging mathematical concepts will be far more accessible to students whose working memory is not consumed by calculation. Models The importance of physical manipulatives and pictorial models to develop deep conceptual understanding is now widely accepted in UK schools. However, the forward-facing teacher goes further, understanding the progression of mathematical concepts well beyond the year group they are currently teaching, and using this knowledge to inform their choices of models and manipulatives. For example, a Year 1 teacher could rely solely on part-whole models to help their class solve simple missing number equations involving addition and subtraction. However, they might also introduce simple bar models, not because they are a necessity for the current objective, but because the teacher knows they will become extremely useful to pupils later on. Similarly, a Year 4 teacher tackling two-digit times two-digit multiplication could use only a grid method and never show an area model. Don’t just ADD A ZERO! “ “We mustn't settle for pupils getting the right answers; not all methods are created equal” www.teachwire.net | 53 MA THS S P E C I A L