Developing Functional Thinking: From Concrete to Abstract through an Embodied Design

In addressing the challenge of fostering functional thinking (FT) in secondary school students, our research centered on the question of how an embodied design can enhance FT's different aspects, including input-output, covariation, and correspondence views. Drawing from embodied cognition theory and focusing on an action- and perception-based task design that uses light ray contexts and different function representations, we developed a digital-embodied learning environment, using the nomogram as a central representation. Our pilot study involving four eighth-grade students provided insights into their physical interactions with these modules through a multi-touch digital interface. Analysis of video and audio recordings from the pilots, including students' hand gestures and verbal expressions, was guided by comparing hypothetical learning activities with the actual learning activities. The results show that (1) a concrete light ray context enables students to ground the abstract mathematical function concept; (2) the bimanual coordinating motion tasks, incorporating the covariation aspect of FT, allow students to connect their bodily experience with function properties; and (3) our embodied and dragging tasks support insight in the conversion between nomograms and graphs of functions, encouraging students' correspondence thinking by providing multiple perspectives to understand, reason about, and manipulate the function. In conclusion, our findings suggest the potential of digital-embodied tasks in fostering FT, evident in students' diverse strategies and reasoning.