Abstract
The chapter summarises results of qualitative research based on interviews with 35 mathematics teachers whose gaol was to find out which parts of lower secondary mathematics are seen by teachers as critical from the point of view of pupils. For each identified critical place, the nature of pupils’ problems and their possible causes are given (from the teachers’ viewpoint) and didactic approaches the teachers use to overcome these problems are described.
For each critical place, a huge body of research exist (at least in international literature). We have mostly chosen research of the experimental versus control group type which enables us to put the used didactic approaches into the research contexts.
The teachers spoke most about problems in arithmetic (namely fractions and negative numbers), in algebraic expressions, in word problems. In geometry they mentioned construction geometry and calculations in geometry.
The chapter is summed up by more general considerations stemming from the teachers’ statements about the nature of critical places in mathematics.