On the assessment of procedural knowledge: From problem spaces to knowledge spaces

By generalizing and completing the work initiated by Stefanutti and Albert (2003, Journal of Universal Computer Science , 9 , 1455), this article provides the mathematical foundations of a theoretical approach whose primary goal is to construct a bridge between problem solving, as initially conceived by Newell and Simon (1972, Human problem solving . Englewood Cliffs, NJ: Prentice‐Hall.), and knowledge assessment (Doignon and Falmagne, 1985, International Journal of Man‐Machine Studies , 23 , 175; Doignon and Falmagne, 1999, Knowledge spaces . Berlin, Germany: Springer‐Verlag.; Falmagne et al., 2013, Knowledge spaces: Applications in education . New York, NY: Springer‐Verlag; Falmagne and Doignon, 2011, Learning spaces: Interdisciplinary applied mathematics . Berlin, Germany: Springer‐Verlag.). It is shown that the collection of all possible knowledge states for a given problem space is a learning space. An algorithm for deriving a learning space from a problem space is illustrated. As an example, the algorithm is used to derive the learning space of a neuropsychological test whose problem space is well known: the Tower of London (TOL; Shallice, 1982, Philosophical Transactions of the Royal Society of London B: Biological Sciences , 298 , 199). The derived learning space could then be used for adaptively assessing individual planning skills with the TOL .