Design and Investigation of a Touch Gesture for Dividing in a Virtual Manipulative Model for Equation-solving

Thomas Janßen,Estela Vallejo-Vargas,David A Reid,Angelika Bikner-Ahsbahs

doi:10.1007/s40751-020-00070-8

Thomas Janßen, Estela Vallejo-Vargas + Show 2 more

Open Access

https://doi.org/10.1007/s40751-020-00070-8

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Abstract

Physical models for equation solving typically lack feedback regarding their appropriate use. Such feedback is possible in virtual environments and could be implemented in hybrid models. Based on an epistemological analysis, this article presents a touch gesture as a way for users to signal they want to divide both sides of an equation and a design for feedback on the use of this so-called ‘division gesture’. The design is investigated by contrasting a case study, in which students used an app with the division gesture, with a preparatory study where students had to perform corresponding actions on physical manipulatives. This investigation revealed insight into feedback functions, steps of understanding dividing with this touch gesture and, furthermore, showed problems that students have with the boundary case where the dividend is 0. The study informs possible improvements of the design of the division gesture and of the overall learning environment. The results are reflected on, in order to illuminate known problems of learning how to solve linear equations, and theorized to contribute to the wider discussion around the design of digital and physical manipulatives, in particular the design of modes of interaction enabled by new technologies.

Highlights

Physical models for equation solving typically lack feedback regarding their appropriate use
To investigate the students’ adoption of the division gesture, we focused on their actions in Tasks 4–10
One can observe a strong tendency to subtract first. This was expected for some tasks, but proved somewhat surprising for Tasks 9 and 10, which were formulated to invite division first as a more effective approach

Summary

Introduction

Physical models for equation solving typically lack feedback regarding their appropriate use. Such feedback is possible in virtual environments and could be implemented in hybrid models. The design is investigated by contrasting a case study, in which students used an app with the division gesture, with a preparatory study where students had to perform corresponding actions on physical manipulatives. This investigation revealed insight into feedback functions, steps of understanding dividing with this touch gesture and, showed problems that students have with the boundary case where the dividend is 0. The results are reflected on, in order to illuminate known problems of learning how to solve linear equations, and theorized to contribute to the wider discussion around the design of digital and physical manipulatives, in particular the design of modes of interaction enabled by new technologies

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Conclusion