Going Down the Abstraction Stream with Augmented Reality and Tangible Robots: the Case of Vector Instruction

TL;DR

The study addresses persistent misconceptions in vector addition by implementing concreteness fading through a joint AR and tangible-robot learning environment. A three-stage gamified scenario gradually transitions learners from enactive to iconic to symbolic representations, using Cellulo robots and AR visuals to encode wind and river currents. Experimental results show significant learning gains and reveal nuanced relationships between tool usage, level design, and performance, suggesting that embodied learning with AR can bridge concrete experiences and abstract reasoning. The findings highlight practical implications for designing AR-tangible curricula that support collaborative, differentiated learning and pave the way for adaptive, technology-enhanced mathematics and physics education.

Abstract

Despite being used in many engineering and scientific areas such as physics and mathematics and often taught in high school, graphical vector addition turns out to be a topic prone to misconceptions in understanding even at university-level physics classes. To improve the learning experience and the resulting understanding of vectors, we propose to investigate how concreteness fading implemented with the use of augmented reality and tangible robots could help learners to build a strong representation of vector addition. We design a gamified learning environment consisting of three concreteness fading stages and conduct an experiment with 30 participants. Our results shows a positive learning gain. We analyze extensively the behavior of the participants to understand the usage of the technological tools -- augmented reality and tangible robots -- during the learning scenario. Finally, we discuss how the combination of these tools shows real advantages in implementing the concreteness fading paradigm. Our work provides empirical insights into how users utilize concrete visualizations conveyed by a haptic-enabled robot and augmented reality in a learning scenario.

Figures (20)

• Figure 1: Activity Flow. The main working sheet (shown as C) contains 10 game levels located across a river (labeled A, B, ..., I) on the working sheet. For each of the levels, participants need to set the correct velocity to reach the gold (yellow circles with gold plates on the main working sheet). The velocity is set on a separate paper sheet (shown in A). The participant grabs the robot with their hand and moves it in the direction they want to set. The direction is shown in AR (below as a green arrow). Next, the robot is placed at the starting point (dock) of the level (shown in B), and the robot moves in the direction determined by the velocity, and also by the wind and the river's current. The tablet screens below the main sheet show the three stages of concreteness fading.
• Figure 2: Illustration of concreteness fading. The physical/enactive representation refers to an actual moving ship. The pictorial/iconic representation refers to the notion of a moving ship, and the idealized/symbolic representation refers to the velocity vectors of the wind (brown), the river (blue) and the boat (green).
• Figure 3: Software architecture using the qml-AR library and libdots Hostettler for the tablet and robot localisation respectively
• Figure 4: Top: screenshot of the level "A" in the game showing the ship (robot) at the dock (bottom left), leaves and waves showing the direction of the wind and the current. Bottom: screenshot of the level G in the game showing arrows (brown for the wind, and blue for the current, green for ship's velocity)
• Figure 5: Two teams using the AR on the tablet. The activity sheet on the floor contains two Cellulo robots