Analogy and Arithmetics: An HDTP-Based Model of the Calculation Circular Staircase

Analogical reasoning and its applications are gaining attention not only in cognitive science but also in the context of education and teaching. In this paper we provide a short analysis and a detailed formal model (based on the Heuristic-Driven Theory Projection framework for computational analogy-making) of the Calculation Circular Staircase, a tool for teaching basic arithmetic and insights based on the ordinal number conception of the natural numbers to children in their first years of primary school. We argue that such formal methods and computational accounts of analogy-making can be used to gain additional insights in the inner workings of analogy-based educational methods and tools.