When mathematizing fails

Error processes in modelling contextual problems

Abstract

Mathematisation – the description of real-life situations using mathematical tools – is a key competence in mathematics teaching. Nevertheless, studies show that pupils sometimes experience considerable difficulties in this area. The aim of this study is to analyse possible causes and processes of errors in mathematisation tasks. To this end, a qualitative study was conducted with 486 Year 8 pupils at eight schools in Salzburg. The pupils worked on a task involving deriving a formula for a given real-life situation, documenting their thought processes and solution steps as they went along. The analysis shows that the error processes can be traced back to overarching cognitive and contextual patterns. Common causes include reliance on routine procedures, an insufficient understanding of operations, and difficulties in dealing with mathematical notation. Particularly striking is the incorrect application of the strategy of calculating a unit quantity. The study highlights the diversity of possible error patterns within a single task and emphasises the need for their systematic analysis. For teaching, this implies an increased need for diagnostic sensitivity and targeted support from the teacher.