This paper discusses authenticity from the perspective of mathematics education. Often, school mathematics offers students inauthentic word problems, which don’t show the authentic usefulness of mathematics in real life. In some tasks, authentic aspects are combined with inauthentic ones (e.g., an authentic context, but the question is artificial and different from what people within that context would ask). Several studies show that students are more motivated by authentic questions than by authentic contexts. Embedding these findings, I discuss issues associated with defining authenticity in education. A first issue is that philosophers use the term to characterize a person’s existential expressions (e.g., being true to oneself), whereas in education, we use the term for learning environments, artefacts, etc. Second, some researchers define authentic learning environments according to criteria (being open to different approaches, simulate a real-life activity, etc.), but I will illustrate that inauthentic activities can comply with such criteria as well. Alternatively, I suggest using the term for separate aspects in a learning environment (contexts, questions, etc.), and define authenticity as a social construct rather than as a subjective perception. In this way, a community (teachers, students, out-of-school experts) can reach agreement on the nature of this characteristic. For an aspect to be authentic, it needs to have: (1) an out-of-school origin and (2) a certification of originality (e.g., by bringing artifacts physically into a classroom or by testimony of an expert). This approach is illustrated by a study on students’ project work during an excursion to a mathematics research workplace.

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This section sets the stage for the rest of the volume as it discusses purposes, principles, goals and traditions of assessment in mathematics education, with a view to discussing commonalities as well as differences between large-scale and classroom assessment. We recognize and discuss some strong differences between the traditions, practices, purposes, and issues involved in these two forms of assessment. Purposes of AssessmentAssessment has been used for multiple purposes, such as providing student grades, national accountability, system monitoring, resource allocation within a district,

In this paper we explore how students can experience the relevance of mathematical modelling activities. In the literature we found that relevance is a connection among several issues (relevance of what? to whom? according to whom? and to what end?). We framed this concept in terms of Cultural-Historical Activity Theory (CHAT), a theory for analysing how individuals engage in activities within social environments. We designed modelling activities within a mathematics course for engineering students: there were ample mathematical modelling tasks, a guest lecture by an employee from an engine company who used mathematical modelling in his job, and a group work modelling assessment with a presentation to the whole group. After the course, we interviewed ten students with a wide range of final grades in the course. We analysed the interview data in light of the theoretical framing of the concept of relevance. Our analysis showed that, generally, students experienced the modelling activities as relevant, and that they imagined themselves working in professional practices for which mathematics is relevant. However, doing mathematics was also judged as being relevant only to obtain grades, leave school and enter professions for which mathematics might not be needed. We offer recommendations for making mathematics education more relevant to more students.