The national curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum – cognitively, socially and linguistically. The quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof. They must be assisted in making their thinking clear to themselves as well as others and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions.
– Primary National Curriculum 2014
In order for children to think mathematically they need to build a deep understanding of mathematics. Sometimes this understanding is shallow and presents as ‘rules without reasons’. These rules can provide answers to routine problems, but when faced with non-routine questions children may flounder. A connected understanding allows children to see maths as an interconnected discipline, and gives them the opportunity to manipulate known facts.