1 ON THE EQUIVALENCE RELATION IN STUDENTS ’ CONCEPT IMAGE OF EQUATION

The concept of equation is, in principle, very elementary in mathematics. One can say that any mathematical expression of the form A = B, where A and B are relevant mathematical objects belonging to the same category, is an equation. However, a large variety of vague and incorrect conceptions about equation exists among mathematics teachers and student teachers. Only a minority of students can state a mathematically satisfactory definition for equation. (Attorps & Tossavainen, 2007a, 2007 b). Seen from the point of view of mathematics and language of mathematics, a student’s concept definition of equation can be wrong basically only for three different reasons: failure of understanding the equivalence relation = ; misconceptions related to the truth value of the statement including the = sign; or the confusion about choosing A and B from incompatible mathematical categories. With respect to mathematics at school, the latest reason is, nevertheless, only marginal. We already have reported on the preliminary results on how teachers ’ and students ’ misconceptions related to the understanding of the properties of the equivalence relation are related to the misconceptions that teachers and students possess about equation (Attorps & Tossavainen, 2007a) and that the belief that the equation must always convey a true statement affects strongly ho