We analyze data on mathematics students’ understanding of the concept of equation. A majority of the participants (N = 128) studies in teacher education programs in Finland, Sweden and South Africa. The data reveals a variety of fundamentally different concept definitions of equation, of which only a half can be seen to be correct. In the students’ concept image of equation, it is commonly assumed that every equation must possess the truth value ‘true’ in spite of the fact that any considerations related to the truth value only rarely appear in their concept definitions. Also the presence of a variable is regularly assumed in the participants’ concept images. Both a chain of equations and a pair of equivalent equations are surprisingly often seen being a single equation. Finally, the incomplete understanding of the reflexive and symmetric properties of equality often hindersstudents from identifying equations. The study is based on both phenomenographic andquantitative analyses of the students’ answers to a questionnaire.

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