Mathematical modelling is characterised as “solving real world problems by means of mathematics” (Blum, 2015, p. 77). It is the complex process of applying mathematical knowledge to describe, analyse or evaluate real-world situations (Blum, 2015; Niss & Højgaard, 2019).
Particularly, mathematical modelling offers rich potential to link STEM subjects from a mathematical perspective (Hallström & Schönborn, 2019). In addition, mathematical modelling can also pave the way to address sustainability issues in education (cf. Maass et al., 2019).
Types of Mathematical Modelling Tasks
Within the dim²ension project, we distinguish three types of mathematical modelling tasks.
Basic Modelling Tasks
When engaging with and solving model application tasks, the main learning objectives for students are to move beyond using pure mathematics alone and to apply their mathematical knowledge to real-life phenomena (cf. Blum, 2015).
Basic modelling tasks primarily involve using mathematics to solve a problem that is clearly and strongly linked to a real-life situation (cf. Stillman et al., 2019).
Based on given data, derive how much carbon dioxide can still be emitted in order to meet the 1.5°C target.
Task reference: Just et al. (2023)
Fermi Problems
Fermi tasks, also known as Fermi problems in the literature, are a specific type of modelling task that involves making reasonable estimates and educated guesses to perform order-of-magnitude calculations (Ärlebäck & Albarracín, 2022).
One possible definition of a Fermi task is “open, non-standard problems requiring the students to make assumptions about the problem situation and estimate relevant quantities before engaging in, often, simple calculations” (Ärlebäck, 2009, pp. 331–332).
How many tonnes of non-recyclable wrapping paper is used in the European Union every year at Christmas?
Task author: Simon Barlovits
STE(A)M Modelling Tasks
STE(A)M modelling tasks are a specific type of modelling task that uses mathematics to describe phenomena in science, technology, engineering and arts (Goos et al., 2023; Stillman et al., 2023).
When tackling STE(A)M modelling tasks, students are expected to apply mathematics more integrally to address scientific, social, political or economic problems, thereby connecting and combining knowledge from different disciplines.
Atherosclerosis occurs when fat and fibrous tissue build up in the walls of blood vessels, narrowing them. Develop a brochure explaining this phenomenon.
Task reference: Quartieri et al. (2025)