Embodied Cognition in Learning and Teaching Mathematics: Producing, Observing, and Imagining Actions

• In Event: 43.064 - Exploring Diversity and Synergy Across Research Programs Within Early Algebra

Abstract

Objectives: A growing body of evidence highlights the importance of actions—both real and imagined—in cognitive performance, learning and instruction. A focus on action has far-reaching implications for topics in early algebra learning, including models of learning and design principles for instruction, assessment, and educational technology. In this theoretical talk, we describe a framework for conceptualizing the role of embodied processes in learning that focuses on producing actions, observing actions, and imagining actions, and we consider how this framework applies to learning of early algebra.

Perspective: First, empirical evidence shows that action matters for cognitive performance and learning. Actions that are well aligned with target ideas can promote performance and learning, whereas actions that are not well aligned can interfere (e.g., Lindgren & Johnson-Glenberg, 2013). Second, observing others’ actions can activate action-based knowledge (e.g., Rizzolatti et al., 2001); therefore, learners need not produce actions themselves in order for action to influence performance and learning. Third, imagining or mentally simulating actions can also activate action-based knowledge (e.g., Glenberg et al., 2004), and simulated actions are sometimes manifested in gestures, which are a form of representational action. This framework extends common notions of embodied cognition beyond the individual acting in the moment to consider the influence of others’ actions and how they influence learners’ thoughts and behaviors. The framework also highlights the power of the imagination to simulate behaviors and to replay them outside of the original situation, as well as to generate new action sequences that have never been observed or enacted.

Modes of Inquiry: In considering how this framework applies in the domain of early algebra, we focus on learners’ concepts of equations, and how these concepts are learned via instruction, including instruction that involves opportunities to produce, observe, and imagine actions. We discuss the role of producing actions, including actions with manipulatives (such as balance scales, or buckets and beanbags) in representing equations, equality relationships, and operations on equations (such as subtracting the same amount from both sides). We also consider opportunities for observing others’ actions, including others’ actions on manipulatives and teachers’ gestures. In classroom settings, students may not all have direct access to manipulatives at each lesson; however, they may have opportunities to observe others’ actions and gestures. In this way, the framework can account for vicarious mathematical learning through observing others’ actions and gestures. Finally, we consider imagining actions. We consider evidence that teachers and students sometimes imagine or invoke actions on manipulatives or symbols, even when they are not physically present. When people reinvoke their prior experiences or imagine acting on manipulatives, their simulated actions are sometimes manifested in spontaneous gestures—which provide a window into student thinking, and which are also a form of action in and of themselves.

Significance: This framework has implications for the design of instructional materials and activities (including technological tools) as well as for formative and summative assessment of student learning and knowledge change.

Authors

• Martha W. Alibali, University of Wisconsin - Madison

• Mitchell J. Nathan, University of Wisconsin - Madison

• Andrea Marquardt Donovan, The University of Wisconsin - Madison