No abstract

No abstract

No abstract

Mathematics is more than just basic skills. Mathematical thinking should be an important aspect of mathematics education. In the Netherlands, higher-order thinking skills like mathematical problem solving, reasoning, modelling and communicating mathematics have been part of the examination program since 1989. To assess these skills in an authentic and open way, the Mathematics A-lympiad, a competition for teams in upper secondary school, was designed. Shortly hereafter a Mathematics B-day was developed which showed that open-ended tasks for teams can also be designed within the domain of pure, formal mathematics. As a result of the success of the Mathematics A-lympiad, similar activities have been created for lower secondary and for primary school. The Mathematics A-lympiad assignments fulfil specific requirements, such as being accessible for all students, eliciting mathematical thinking and providing opportunity for different strategies and solutions. In the wake of these events more attention is paid to higher-order thinking skills in regular mathematics education as well.

This study reports on a way to address twenty-first-century skills in mathematics education by organizing one-day mathematics challenges in the Netherlands. During such a day, students work in teams in school on an open-ended problem which aims to elicit skills like problem-solving, modeling, collaboration, and communication. The framework and the methodological approach of the maker movement are used to describe and analyze the design of these learning spaces for students and the practices they become engaged in. In this study, two design teams are interviewed and two assignments, including student work, are analyzed. The results show that the maker perspective bears similarities with the problem-solving perspective, but also enriches the problem-solving perspective by emphasizing the importance of tinkering, making something, and working as a community of practice. Emerging task characteristics that afford students' making processes are the use of a context that is meaningful for students, the low-floor-high-ceiling character of the open problem, and the request for a product. The extent to which the requested product is more context-related or more mathematical depends on the intentions of the task and the interest of the target group. Maker characteristics of the design teams elicit the importance of brainstorms with professionals, time for tinkering with the problem situation, and time for exploring possible student strategies, before the final assignment is developed.