Varieties of concretisation: an illustrative case study

This paper illustrates, compares and contrasts a variety of different constructions that can be viewed as serving a role in concretisation – the process of developing concrete artefacts to support a learner in understanding abstract concepts. Our illustrative examples are based around the theme of introducing simple number-theoretic notions by representing operations on integers by actual or simulated operations carried out on two liquid containers (so-called “jugs”). Different varieties of concretisation are discussed with reference to phenomenalisation, visualisation and physical embodiment, and in their broader relation to constructionism and learning in cultural context. The importance of concretisations that are both accessible in everyday situations and offer rich experiential potential is highlighted.