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Assessment plays a crucial role in teaching and learning mathematics. The implementation of innovative instructional materials requires well-aligned classroom assessment tasks and student-centered formative assessment. Design research at the Freudenthal Institute has led to new assessment methods that support principles of Realistic Mathematics Education. Realistic assessment that properly reflects the curriculum can be a powerful key to improving mathematics education. The biggest challenge lies in the design of problems that requires more than reproduction of skills to solve, such as making connections, generalization and mathematization.
A model that has emerged from our research is the ‘assessment pyramid’, which classifies mathematical competencies into three levels of reasoning. Tasks at each of these levels also vary in difficulty. That is, tasks designed to assess Level II & III reasoning are not necessarily more difficult than tasks assessing Level I goals.

This model has proven to be helpful to teachers for rethinking assessment design and practice.
More information:
Van den Heuvel-Panhuizen, M. (1996). Assessment and realistic mathematics education. Utrecht: CD-ß Press/Freudenthal Institute, Utrecht University.
Dekker, T. & Querelle, N. (2002). Great assessment problems. Utrecht: Freudenthal Instituut.
Romberg, T. A. (Ed.) (2004). Standards-Based Mathematics Assessment in Middle School - Rethinking Classroom Practice. New York: Teachers College Press.
Webb, D. C. (2009). Designing professional development for assessment. Educational Designer, 1(2), 1-26.
(c) Freudenthal Institute US & Freudenthal Institute for Science and Mathematics Education 2013
FIUS: mathematics education, development and research