Diagrammatic Re-codification of Probability Theory: A Representational Epistemological Study

It is claimed that the current representations used for probability theory provides a poor codification of that knowledge. The limitations of the representations and how they encode the knowledge causes conceptual difficulties and makes problem solving difficult. Probability Space diagrams constitute a new representational system that provides a simpler and more coherent codification of probability theory, which effectively supports problem solving. The two approaches are contrasted, which demonstrates that the effects of representations on advanced forms of cognition extend beyond problem solving and impacts on the conceptual understanding and learning of bodies of knowledge.