ABSTRACT
Perhaps one of the most crucial aspects of arithmetical reasoning is the ability to derive and predict unknown arithmetical facts from known facts, by using arithmetical principles such as commutativity, associativity and the addition/subtraction inverse principle. For example, if we know that 44+23=67, then we can use the commutativity principle to derive the fact that 23+44 must also be 67. Without this ability, children will depend entirely on the facts that they have already learned and will be unable to go beyond them independently. Moreover, the complete inability to derive unknown arithmetical information from known information would seem, a priori, to imply a lack of understanding of the connections and interrelationships between individual number facts. By the same token, the ability to use derived fact strategies can compensate considerably even for quite severe calculation disabilities (Hittmair-Delazer, Semenza, & Denes, 1994; Hittmair-Delazer, Sailer, & Berke, 1995; Warrington, 1982). Derived fact strategies are probably of particular importance in mental calculation (Thompson, 1997a), although they are also used in written calculation.
