Origins of Students' Errors in Writing Equations

Kaye Stacey and Mollie MacGregor

Institute of Education, University of Melbourne, Australia

 

A set of test items was designed to eliminate as far as possible the factors believed to cause the errors in the formulation of simple linear equations.  The test items were given to 281 year 9 students in seven schools.  The high incidence of errors in the students' responses could not be attributed to the causes widely documented in the literature.  A theory of cognitive models was proposed to account for the errors as well as for the various forms of correct equations.  According to the theory, cognitive models of relations between two variables represent contrast between large and small entities and do not conform with the structure of algebraic notation.  Students frequently make errors when they try to represent these cognitive models directly.