Conservation of Equation and Function under Transformations of Variable

Tasks that test conservation of equation and function under transformations of variable illustrate an extension of Piaget's conservation methodology to relational concepts. Less than half of the 30 students interviewed in grades 5-12 gave conserving responses to any one of the four tasks. Mathematical background was a significant factor in performance. Students who did not conserve harbored two misconceptions: (a) that changing a variable symbol implies changing the referent and (b) the linear ordering of the alphabet corresponds to the linear ordering of numbers.