De vertaalslag van een situatie naar een wiskundige formule; een studie naar vraagstellingen en leerlingprestaties op het centraal examen wiskunde B1

Tijdschrift voor Didactiek van de Beta-wetenschappen, uitgegeven door het Freudenthal Instituut, Universiteit Utrecht in de periode 1983-2014

Schaap, S. Vos, P. Ellermeijer, T. Goedhart, M. Tijdschrift voor Didactiek van de Beta-wetenschappen 2011 – 28(1), 3-32 Download pdf

The translation from a situation to a mathematical equation; a study into the phrasing of questions and student performance at the central mathematics exam.
The Dutch senior secondary school mathematics curriculum prescribes that students should be able to translate a situation into a mathematical formula (to algebraise). This article reports on a research that verifies to what extent the national exam questions assess this learning goal and to what extent grade 12 students are skilled in algebraisation. We analysed national exams from the period covered by the curriculum goal and we assessed students’ performances through three data sources: scores on exam questions related to algebraisation, written work of students to these questions, and task-based interviews based on these questions with grade 12 students. The analysis of the data reveals that the algebraisation goal was barely assessed in five consecutive years, and only in a format where the formula is given ready made and the students are assigned to reconstruct this formula (reconstructive algebraisation). The score on these questions varied from high to low. High scores occurred for questions in which the authors to a large extent explained how to translate the situation to the ready-made formula. Lower scores occurred on questions that required formula skills (e.g. expanding square roots) or left several translation activities to the students. We found that the ready made formula in questions asking for reconstructive algebraisation gives safety to students, but also reveals problem solving approaches and becomes an aim in itself. The task-based interviews showed that students are able to algebraise, even if a formula is not offered beforehand. We recommend further research into question formats that combine different algebraisation activities, such as simplification, structuring, identifying variables and constructing an algebraic model.