ABSTRACT
The value placed on derived fact strategies varies markedly across countries and times. Some writings imply a sharp distinction between standard, ‘school-taught’, automatized, usually written strategies, and non-standard, non-school-taught, often mental, derived fact strategies. In fact, derived fact strategies and standard strategies can be best seen as parts of a continuum, rather than as totally distinct entities. Children were given problems requiring the derivation of arithmetical facts of varying levels of difficulty. The particular arithmetical performance measures included in the analysis were as follows: addition level, use of addition principles for derived fact strategies, subtraction level, use of subtraction principles for derived fact strategies and addition estimation. Most young children are not able to describe or explain their estimation strategies effectively, while they usually can describe their derived fact strategies. There have been enormous variations across time and place in educational attitudes to derived fact strategies, ranging from active discouragement to explicit encouragement and teaching.
