Learning mathematics and demonstrating understanding of mathematics involves connecting real experiences, contexts, mathematical images/pictures, language and symbols.

A pupil really understands a mathematical concept, idea or technique if he or she can:

• describe it in his or her own words;
• represent it in a variety of ways (e.g. using concrete materials, pictures and symbols);
• explain it to someone else;
• make up his or her own examples (and non-examples) of it;
• see connections between it and other facts or ideas;
• recognise it in new situations and contexts;
• make use of it in various ways, including new situations.

Teaching for Mastery booklets NCETM adapted from John Holt ‘How Children Fail’ 1964