Beyond the Standardized Assessment of Mathematical Problem Solving Competencies: From Products to Processes

National and international standardised assessments of mathematical competencies challenge students to solve stimulating non-routine problems but, in some sense, they appear to have several limitations exactly in assessing students’ problem solving competencies. In particular, the use of multiple choice or short answer items focuses the assessment on the student’s choice (the product) rather than on how and why the student made that choice (the reasoning, that is, the process). The emersion of the processes appears to be a crucial need for teachers and researchers in order to understand what is involved in students’ answers. In this chapter, we will describe a protocol (developed within an Italian research project) for getting data to understand – at a micro level – the educational macro phenomena illustrated by standardised assessment quantitative results. This approach – that involves educational researchers and mathematics teachers – makes it possible to foster the development of a critical and productive approach to standardised tests, transforming them in an educational opportunity for teachers and researchers