Teach Primary Issue 18.5

MA THS Gill Cochrane is a former primary school teacher. She is now the lead developer on the specialist literacy and maths courses run by Real Training in partnership with Dyslexia Action. information. The gesturing enhances the processing of the equation as a whole, working from left to right. Re-organising the presentation of a problem, as below, promotes scanning of the whole sum, and examination of the inter- relationships within it. 1. Fill the boxes with = or > or < 4 4 3 2 5 6 22 ÷ 2 22 × 2 23 × 2 23 × 3 2. Fill the boxes with numbers 16= × = × = × In time, with supporting, structured discussion, learners can develop flexibility in strategy use when calculating, which can reduce the need to calculate in some cases. The children will learn to exploit the inter-relations to reduce the cognitive load of computation. Organising numbers and fractions spatially Recent research has shown that lower levels of maths anxiety are found in people who ‘spatialise’, organising sequences from left to right in verbal working memory. Here are some ways we can help children spatialise their mathematical understanding: - Number lines and bar models should be modelled as important organisers of computational thought. - Work on fractions should include their ordering onto number lines to make relative value explicit. - Cross-sectional drawing can provide an additional way to map space to solve word problems. exploration that lead to the solution. Reasoning by anomaly involves working out the rule behind various patterns and then spotting the item that isn’t following it, e.g. Figure 3 . By studying each of the patterns and the interrelations within them, children will start to appreciate how practice in this type of task promotes structured scrutiny of the relationships within and across the set items. Reasoning by antithesis requires learners to identify when a parallel or opposite rule has been applied. This is more complex, as the process must be identified so the sub- item featuring the opposite process can be chosen. Practice with all these types of non-verbal reasoning tasks is done without processing number systems, allowing analytical skills to be strengthened separately from numeric work. There is evidence that this type of reasoning practice can help when it comes to work with numbers. Purposeful scanning A rich body of research demonstrates that purposeful scanning of information can significantly aid the ability to solve problems. There are indications that providing practice in explicitly noticing relationships within written equations can boost performance on similar maths problems. For example, building meaningful gesturing into the appraisal of sums can lead to better performance on tasks involving the equivalence concept. Ask pupils to use their index and middle fingers to touch each number before the equals sign (and any after it) and then to use their index finger to point to the missing There is a causal link between spatial thinking and achievement and confidence in maths. Spatialising maths builds an appreciation of the relations between and within objects and ultimately contributes to a more secure mathematical understanding in the longer term. TP How to build maths understanding • Reduce reliance on memorisation for learning basic number facts; use number relationships and reasoning strategies instead. • Try conceptual instruction using a limited range of numbers (e.g. 1 to 9), their sums and associated subtraction facts. This makes it easier to analyse the relationships between the elements within the sums. • Use exploratory work on factor pairs to help encourage more flexible calculation strategies. • Giant number lines can help young learners to walk through sums and to conceptualise counting as ‘moving on.’ • Gesture and personification have been shown to increase retention and deepen understanding by recruiting a wider range of memory systems. • Use concrete resources for teaching angles, for example, using hinged strips to demonstrate that an angle is a measurement of turn. • Promoting maths oracy should be an important feature of eachmaths lesson. Figure 2. Analogical reasoning: Which shape completes the pattern? Figure 3: Reasoning by anomaly: Which pattern is the odd one out? realtraining.co.uk/maths-courses Download an extended version of this feature, with additional resources, at tinyurl.com/tp-Cochrane www.teachwire.net | 33