Origins of Students' Errors in
Writing Equations
Kaye Stacey and Mollie MacGregor
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.