Elkjær, Morten; Hodgen, Jeremy; (2022) Operationalising Vergnaud’s Notion of Scheme in Task Design in Online Learning Environments to Support the Implementation of Formative Assessment. Implementation and Replication Studies in Mathematics Education , 2 (1) pp. 21-44. 10.1163/26670127-bja10002.

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Abstract

This paper presents an implementation process model for designing and implementing tasks that provide formative feedback in the online learning environment of mathematics classrooms. Specifically, the model operationalises components of Vergnaud’s notion of scheme. The implementation process model features a task sequence guided by controlled variation and a ‘dual scheme idea’. Using such a sequence of tasks, this work illustrates how Vergnaud’s notion of scheme can be used to aid teachers in hypothesising about their learners’ understanding of problems involving linear equations, ultimately providing improved feedback for teachers and improved opportunities for student learning in online environments. In Denmark, the online environment matematikfessor.dk is used by approximately 80% of Danish K-9 students. The impact sheet to this article can be accessed at 10.6084/m9.figshare.19493846.

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