Mathematical Competencies in Mathematics Education

Mogens Niss is a Professor of Mathematics and Mathematics Education at Roskilde University, Roskilde, Denmark. Dr. Niss' main field of research is Mathematics Education, where he has published well above a hundred papers in scholarly journals and books, as well as twelve books. His research interests are focused on the justification problem in Mathematics Education, on applications and modelling in the teaching and learning of Mathematics, on assessment, on the nature of Mathematics Education research as a scientific discipline, and on mathematical competencies in Mathematics Education. Tomas Højgaard is Associate Professor of Mathematics Education at Aarhus University, Copenhagen, Denmark. Dr. Højgaard's area of expertise includes relations between educational research and practice didactical modelling as a methodology, descriptions of competencies as an educational tool the structuring of curricula, project work and student autonomy, mathematical problem tackling competency, mathematical symbol tackling competency, textbooks for Mathematics Education and tasks for Mathematics Education.

Background and Setting.- Historical and conceptual background.- Different notions of curriculum and approaches to curriculum development in mathematics education .- What is the task?.- A competence description of mathematical education.- The education of mathematics teachers.- Mathematics teachers: Didactic and Pedagogical competencies.- The mathematical competencies of mathematics teachers.- Competencies and subject matter.- Assessment of competencies.- A characterization of selected central problems.- Recommendations.- Research underpinnings.- Developmental experiences.- Research and development perspectives.