How Haylock and Cockburn and the connective model have shaped and inspired our thinking for 25 years

Haylock and Cockburn suggested that when learners engage in mathematical activity, it will involve manipulating some, or all, of the elements of the model and that connecting these experiences is how learners make sense of the mathematics; hence we refer to it as 'the connective model'. A focus on making sense of the mathematics, rather than a focus on answer getting, also appealed to us, fitting with our beliefs and values about mathematics teaching and learning and the importance of conceptual understanding, and we became hooked. [...]for the context of putting shopping in a basket, linked to understanding the additive structure of the counting system, concrete experiences of the context include using a shopping basket in a real shop, a role play experience in a classroom shop and putting objects in a box. Sometimes the set has more than three, but most people opt for the simplest case (Figure 7): We have found itis extremely unusual, in this context, for + to be represented as a number on a number line (Figure 8): Having asked teachers to draw representations of = we then ask them to consider 2 + 3 = and they recognise that none of their drawings match this division.