It's Hip to Be Square: A Tangible User Interface for Quadrilateral Learning
Scott George Lambert, Adish Pawar, Taliesin L. Smith, Jennifer Tennison, Emily B. Moore, Jenna Gorlewicz · 2025 · ACM Transactions on Accessible Computing · doi:10.1145/3777899
Summary
This paper presents the Smart Quad, a tangible user interface (TUI) designed to make geometry learning accessible through physical manipulation of four-sided shapes. The Smart Quad pairs via Bluetooth with the PhET Quadrilateral Simulation, creating a multimodal learning environment where students can explore quadrilaterals through touch, sound, and visual feedback simultaneously. The device went through four iterative design cycles with feedback from 23 users, including individuals who are blind or have low vision (BLV). The final design is 3D-printed, costs approximately in materials, and can be assembled in under 10 hours. It measures side lengths and angles through slide potentiometers and relays this data to the paired simulation in real-time, enabling the on-screen shape to mirror physical manipulations. The PhET Quadrilateral Simulation provides customizable accessibility features including Voicing (auditory descriptions of shape properties and changes), Sonification (music that changes based on shape state), keyboard navigation, and visual options like Pan and Zoom. When paired with the Smart Quad, voiced information is delivered in response to physical shape changes rather than requiring keyboard navigation.
Key findings
The researchers conducted a two-part evaluation: classroom sessions with 15 sighted students in grades 6-8, and individual sessions with 5 BLV students in grades 7-9. In shape creation tasks, students using the Smart Quad + Simulation were significantly more successful than those using the Simulation alone—100% correct in the classroom setting versus 55% for Simulation Only on one task. For BLV students specifically, the combined modalities proved essential. Students could quickly create accurate shapes on the Smart Quad but struggled with the same task in the Simulation, often losing track of shape orientation. The tangible device provided immediate tactile feedback about shape size and configuration that was difficult to convey through auditory means alone. However, for precise calculations (perimeter and area), BLV students performed better with the Simulation's Voicing feature, which announced exact side-length values through keyboard navigation. Student feedback highlighted the "engaging" and "fun" aspects of physically manipulating shapes while watching them change on-screen. Teachers observed that younger students (6th grade) explored the device more playfully, while older students used it more purposefully. Nearly all BLV students, at some point during Simulation-only tasks, reached for the Smart Quad to demonstrate their intended shape.
Relevance
This research demonstrates how pairing physical manipulatives with digital simulations can create more inclusive mathematics education. For students with BLV, traditional geometry instruction relies heavily on visual representations that exclude them, while existing tactile manipulatives often lack the dynamic feedback needed for exploring shape transformations. The Smart Quad illustrates key principles for accessible educational technology: multimodal output (haptic, auditory, visual) allows learners to choose the modality that works best for each task; physical-digital pairing provides benefits that neither medium offers alone; and iterative design with disabled users produces genuinely usable tools rather than accessibility afterthoughts. For practitioners developing accessible STEM education tools, the open-source design (files available at printables.com/model/936277) offers a reproducible model. The research also highlights scalability challenges—classroom deployment required significant setup, and wired connections proved fragile—pointing toward areas for future development in accessible educational TUIs.
Tags: tangible user interface · TUI · blind and low vision · mathematics education · geometry · inclusive design · manipulatives · multimodal · sonification · embodied learning