The Use of Taught and Invented

Methods of Subtraction.

A. D. Perry and Kaye Stacey

Abstract

This study investigated the methods used by 1370 students in Grades 7 to 12 for carrying out subtractions presented in vertical format. It was found that the percentage of students not using the algorithms taught at school rose exponentially from 1% at Grade 7 to 26% at Grade 12. Invented methods were used significantly more often by students with below average achievement in Mathematics than by others. However, students using invented methods were no more likely to make errors than those using taught algorithms. Older students were more likely to be correct than younger students, regardless of method. Use of invented methods was not associated with score on a lateral thinking test. It is concluded that students generally used invented methods when they had forgotten the taught algorithms. The results support the constructivist recommendation that students, particularly those of below average achievement, should be encouraged to explore and invent a variety of mental and written methods as well as, or instead of, practising an efficient pencil and paper algorithm.