A Theoretical Framework for Designing Digital Assessments

Digital Learning Environments (DLEs) for math are created with the aim of building students’ mathematical thinking, knowledge, and skills. It is therefore critical that such DLEs are grounded in relevant theoretical frameworks. Such frameworks are needed to assess students’ prior knowledge, address misconceptions, promote mathematical ways of thinking, and adopt an evidence-based approach to the design of DLEs for math.

In my previous article on Theory-Driven Digital Learning Environments (DLEs) for Mathematics,[1] I highlighted key features to consider when identifying an appropriate theoretical framework for DLEs for math. Specifically for topics from secondary and high school curricula, a framework that addresses their complex and hierarchical nature and accounts for “how” learners build their mathematical understanding is important. One such framework is the Action, Process, Object, and Schema (APOS) framework[2]. This article describes the APOS framework and how it can be applied to assess student learning in DLEs.

If you’re a teacher, assessment designer, or instructional designer of mathematical learning experiences, this article will provide you with an overview of APOS. It will serve as an introductory guide to understanding and applying APOS to mathematical concepts. More generally, it uses the example of APOS to provide a structure for analyzing students’ problem solving and how they can be applied to inform the design of DLEs.

To learn more about applying the APOS framework to assess student learning and design effective Digital Learning Environments (DLEs) for math, read the full article here.