School mathematics has typically focused on developing students’ knowledge of mathematical concepts and procedural skills. However, a broader notion of mathematical mastery, involving a range of competencies, has evolved in the last few decades. This new notion of mathematical competence has influenced curriculum reforms both in Norway and across the world. This thesis aims to investigate mathematical tasks used in Norwegian secondary education and teachers’ knowledge of these tasks from this new competency perspective.
A first study involved tasks from two mathematics assessments and investigates the competency demands of the tasks and teachers’ ability to recognise these demands. Teachers’ ratings of task demands with regards to six mathematical competencies were analysed using estimates of reliability and agreement as well as descriptive statistics. Furthermore, psychometric modelling was used to examine the extent to which the teachers’ ratings could explain the variance in task difficulty. A second study investigates teachers’ considerations of the demands of tasks they had used in their teaching practices. These considerations were analysed deductively and inductively through content analysis followed by analysis of the competency demands of the tasks.
The findings suggest that the demands of the assessment tasks and the teacher-submitted tasks are dominated by a few competencies, among which procedural knowledge plays a leading role. The teachers seem to recognise and emphasise the demand for certain competencies, whereas others seem less emphasised and more challenging to recognise. Knowledge about mathematical competencies and their role in mathematical tasks is crucial both with regards to planning and implementing teaching activities and for the development of valid mathematics assessments in line with the new notion of mathematical competence. This thesis contributes such knowledge and discusses further steps toward a competency-oriented mathematics education.
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