brought to you by


Supporting children to secure a deeper understanding of fractions


By Rebecca Holland, Lead Maths consultant at Oxford University Press


What makes fractions difficult to understand?


‘Fractions’ is often a topic area that many children (and adults) find particularly challenging, leading to uncertainty and maths anxiety. For many of us, if we reflect on our childhood experience of learning about fractions, it was mostly abstract procedural-based learning of tips and tricks (with very little understanding, in many cases). Models, when used, were often a linear fraction wall, pizzas or other circular images - the relatable context was often linked to food. The relationships between these models were not always explored and therefore the connections and relationships were often missed or confused.


Fractions, decimals, ratios and percentages are essentially different forms of notation for the same ‘rational numbers’ - we represent them in several ways. Often these different forms are taught at different times or using different representations, resulting in children not making the connections.


As well as this, we now have children in our primary schools who have had at least two years of disrupted teaching and who may have missed core understanding.


The Numicon learning theories and pedagogy


Many of us are familiar with Numicon Shapes, which are often seen as an integral part of a developed mathematical understanding for the youngest children in school. The Numicon Shapes (800229) are one element of the Numicon approach; a way of teaching mathematics that grew out of a classroom-based research project conducted by Ruth Atkinson, Romey Tacon and Dr. Tony Wing.


There are two main learning theories that underpin the Numicon approach: Jerome Bruner’s enactive-iconic- symbolic representations, often referred to as concrete- pictorial-abstract (or the CPA approach) and Numicon’s own pedagogy.


In Numicon, we interpret Bruner’s representations as follows:


• Concrete: the children engage with a physical resource that can be manipulated


• Pictorial: both the development of visualisation that stems from using the concrete resource that can be recalled subsequently, and/or a jotting or drawing


• Abstract: both the spoken word whilst discussing the concrete or pictorial representation, and/or the recording of mathematical understanding using symbols and numerals.


We do not see this as a progressively linear theory. Rather, we believe that by engaging in a concrete activity the children will also be developing their visualisation and describing their mathematical understanding. Sometimes the children might use a concrete resource to prove their thinking after they have worked using abstract notation.


This theory links into the Numicon pedagogy wheel:


• Communicating mathematically: being active, illustrating, talking. This clearly links to Bruner’s theory. It is also worth noting that all partners (children and adults) are actively involved in the dialogue - not just passively hearing or waiting to speak. This often leads to a lesson structure that has a short teacher input - sometimes just a question - and (as illustrated below) children often begin to reason from the outset.


• Exploring relationships (in a variety contexts): children explore a variety of connections and relationships through reasoning. If they know 7 ones and 3 ones make 10 ones, they will eventually know what to add to 0.7 to make 1.


• Generalising: in doing mathematics, exploring relationships, and looking for patterns, children will make new situations predictable. This also links to Benjamin Bloom’s Taxonomy and higher-order thinking.


10


Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20