Remarks on a Modeling Cycle and Interpreting Behaviours

Reported research and practice in mathematical modeling and applications has found it useful to describe student behaviours in terms of activity within a modeling cycle. This has enabled researchers to elucidate and to gain insights into processes deployed by students when faced with problems set in the real world and for which practical outcomes might be achieved by constructing a mathematical model. We consider various modeling cycles and we remark on individual modeling routes and other non-linear behaviours. Models of modeling in education raise questions as to the purpose of mathematical modeling and its assessment. We comment on the assessment of modeling competencies and we consider whether common methods of assessment address the mathematical model itself or more general competencies.