Teach-Primary-Issue-19.7

However, a forward-facing approach is to invest time in exploring area models, first with physical dienes blocks, then with an easily adjustable virtual model (such as Mathsbot.com). This supports a much deeper understanding of multiplicative structure and allows children to make important connections when they use area models again in secondary to explore topics such as quadratic equations. Finally, a Year 6 teacher working on negative numbers could rely entirely on number lines. However, they might also introduce two-colour, double-sided counters, knowing the power of these manipulatives for modelling ‘zero pairs’ in future. (See Fig.1 and Fig. 2 ) Examples The examples we choose should help us expose the full extent of each concept. If we don’t, we risk children developing misconceptions, storing up trouble for the future. A good example of this is the need to present equations in different forms. It is extremely common to see something like 2 + 4 = 6 but do we see 6 = 4 + 2 as much? Subtractions in this form are even less common: how often do primary teachers expose children to 4 = 6 - 2? Failure to face forward with an early maths concept such as this leaves secondary teachers to pick up the pieces, battling to reconfigure students’ incomplete or incorrect mental models that have been embedded over many years. This need to expose children to more ‘unusual’ examples is also apparent in our teaching of shape. What makes a triangle a triangle? What makes a hexagon a hexagon? Using shapes such as those in Fig. 3 will support fruitful discussion of key properties, developing a much fuller understanding. The same can be done for something less visual, like rounding numbers. What is 346 rounded to the nearest 20? Instead of following a fixed algorithm about which digits to look at and change up or down, exploring a question like that will help children to understand that the rounding question is really asking, “which multiple of X is Y closest to?”. A great place to start with this is by chatting to teachers in other year groups. What does the concept you’re about to teach look like at their level? How might that affect the methods, models and examples you choose? Also, reflect on the whole-school culture around maths; all teachers need to feel responsible for all children’s mathematical futures, not just for getting them to the expected standard for their current year group. Finally, keep investing time in developing subject knowledge; to make forward-facing choices, we must have a deep understanding of both the maths at hand and the maths our children will face in future. TP Jo Austen is an assistant headteacher in East London. His book, Small Numbers, Big Ideas: Essential Concepts for Teaching Early Maths (John Catt), is out now. 1. Methods Don’t settle for children getting correct answers. Model and encourage increasingly efficient methods and increasingly fluent calculation. 2. Models Choose powerful models that emphasise mathematical structure and will support the learning of more advanced concepts in future. 3. Examples Include ‘boundary’ examples that expose the full extent of each concept, supporting future learning by avoiding embedding misconceptions. 3 STEPS TO FORWARD - FAC I NG MATHS Fig. 1 +2 -10 -5 -4 -4 2 -2 0 5 10 Fig. 2 -4 + 2 = -2 Fig. 3 A triangle and a hexagon 54 | www.teachwire.net