In this article, the authors share a European perspective on teaching linear equations in Finland, Flanders, and Hungary. They begin with an assertion that it is through observation, in its broadest sense, and opportunities for participation, that people assimilate themselves into the culture in which they are raised. They discuss three approaches to mathematics teaching and reflect on the one characteristic common to these approaches. They compare that commonality with what they have seen in other European countries. This interesting commonality is that trainees have always begun their formal treatment with arithmetic equations; equations with the unknown on one side that they know their students can solve mentally.