The Connective Model
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
Below are resources which explain The Connective Model and provide support with making connections, with a particular focus on the use of mathematical images to aid and demonstrate understanding.
It is important to understand that children need to play with any image that is going to be used for teaching understanding of mathematical concepts, so that they can become familiar with the resource and how it is structured, otherwise they may not be able to attend to features of the resource as the teacher intends. As a result of play, mathematical ideas and questions will arise.