An Experimental Research on Error Patterns in Written Subtraction

Pupils' mistakes, if suitably analysed, may give useful suggestions for improving the teaching/learning process of mathematics. We present here the main issues of an investigation on a population of 732 Italian pupils (9--12 years old), addressed to determine the typology of errors in performing written subtraction. We compared our results with those emerging from a study carried out in Brazil on pupils of the same age, concerning the errors in performing the usual algorithm of written subtraction. In our study, one group of Italian pupil utilized the usual algorithm and another group utilized an algorithm also called "Austrian subtraction", which was commonly taught in the primary schools of Trieste (Italy) up to the sixties and is still taught in Austria. We attempted to assess whether certain error patterns depend on different ethnic--cultural situations, teaching methods and algorithm used, and to what extent. We briefly present results from the experimental research and subsequent developments.