Evolutionary processes in the development of errors in subtraction algorithms

Abstract

[EN] The study of errors made in subtraction is a research subject approached from different theoretical premises that affect different components of the algorithmic process as triggers of their generation. In the following research an attempt has been made to investigate the typology and nature of errors which occur in subtractions and their evolution throughout primary education. The main aim of the research is to examine whether in our school context systematic errors are made and if these decrease throughout schooling. In order to do this, we carried out a rigorous analysis of over 7140 subtractions done by children of 7 to 13 years of age in 2nd, 3rd, 4th, 5th and 6th years of primary school, using a sample of 357 primary school students who were tested with the VanLehn 20 subtractions test. The SPSS 11.5 computer programme was used to analyze the data generated by the tests. One hundred and twenty-two different errors were analyzed, the results showing systematic errors in 55% of the cases. We likewise found that the evolution of the error throughout primary education shows certain similarities with the results obtained in other teaching contexts. The results obtained are undoubtedly valuable for programming the teaching process.