Fermi problems in standardized assessment in grade 8
DOI:
https://doi.org/10.48489/quadrante.23587Keywords:
Fermi tasks, mathematical modelling, task criteria, modelling tasks, test problemsAbstract
Since 2006, Germany has been pursuing a comprehensive educational monitoring strategy that includes comparative and standardized assessment tests (called VERA) in mathematics. These tests are administered state-wide and, with a few exceptions, in the eighth grade of every general education school. Among other competencies, these tests examine the modelling competency of students. In application and modelling tasks, the various requirements associated with testing tasks create specific challenges that often result in word problems rather than real applications. One possible approach to setting a suitable modelling problem for assessment is to use Fermi problems that draw upon a real context. Based on various classifications of mathematical tasks, this paper develops a series of criteria for Fermi problems for assessment purposes. These criteria are applied specifically to Fermi problems contained in the described standardized assessment tool in Grade 8 in Germany. Based on the findings, differences and similarities between Fermi problems are determined and discussed. Fermi problems exhibit a certain homogeneity as specialized modelling tasks, but are also associated with a broad spectrum of difficulties, which seem to be linked to the number of mathematical quantities required for the solution. Various Fermi problems can cover many different aspects of performance and are a good way to incorporate authentic situations into test problems.
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