Understanding Equations in Schema-oriented Education☆

Abstract In the past five years our research team has studied and elaborated a teaching method called the schema-oriented education. Pupils do not receive mathematical knowledge from the teacher. Instead, they build own mathematical schemata through problem-solving and class discussion. Problems are nested in various semantic and structural teaching environments. This article describes in detail the building of a schema in relation to the solution of a system of two linear equations x + y = a, x – y = b in three of such environments.