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Mapping critical cognitive difficulties in mathematical modelling: insights from a comparative study across upper secondary education levels
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DOI：10.1007/s10649-026-10532-2.png)
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Abstract
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This study investigates the cognitive difficulties encountered by upper secondary students when solving mathematical modelling tasks, drawing on the five-phase modelling framework proposed by Stillman et al. (2007). Two complementary instruments were used: the Algorithmic Map of Anticipated Difficulties (AMAD) and the Coded Grid of Cognitive Difficulties in Modelling (CGCDM), both structured around specific cognitive aspects within each phase of the modelling process. The sample comprised 300 students equally distributed across three grade levels—Common Core, first-year Baccalaureate and second-year Baccalaureate—each of whom solved two tasks: a conventional mathematical application task and an authentic mathematical modeling task. Students’ written responses were classified into four performance profiles: Full Success, Partial Success, Unsuccessful with Partial Attempt, and Unsuccessful with No Response. The results indicate that difficulties were more frequent and more pronounced in mathematical modeling tasks, particularly in phases involving mathematisation, interpretation, and validation. Statistical analyses show limited cross-sectional differences among common core, first- and second-year baccalaureate students, while highlighting persistent cognitive difficulties in mathematisation/translation and validation/interpretations across all three educational levels. Key aspects such as contextualisation, hypothesis formulation, and model validation were often absent, indicating stable patterns in students’ reasoning across educational levels. These findings offer a fine-grained account of where difficulties occur within the modelling process and support the relevance of phase-level diagnostic tools for analysing students’ engagement with modelling tasks.
Keywords:
Mathematical Modelling
Mathematical Application
Cognitive Difficulties
Modelling Process
Algorithmic Map of Anticipated Difficulties (AMAD)
Coded Grid of Cognitive Difficulties in Modelling (CGCDM)
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