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Haptic force feedback systems are unique in their ability to dynamically render physical representations. Although haptic devices have shown promise for supporting learning, prior work mainly describes results of haptic-supported learning without identifying underlying learning mechanisms. To this end, we designed a haptic-supported learning environment and analyzed four students who used it to make connections between two different mathematical representations of sine and cosine: the unit circle, and their graph on the Cartesian plane. We highlight moments where students made connections between the representations, and identify how the haptic feedback supported these moments of insight. We use this evidence in support of a proposed theoretical and design framework for educational haptics. This framework captures four types of haptic representations, and focuses on one -- the haptic bridge -- that effectively scaffolds sense-making with multiple representations. 

Embodied, physical interaction can improve learning by making abstractions concrete, while online courses and interactive lesson plans have increased education access and versatility. Haptic technology could integrate these benefits, but requires both low-cost hardware (recently enabled by low-cost DIY devices) and accessible software that enables students to creatively explore haptic environments without writing code. To investigate haptic e-learning without user programming, we developed HandsOn, a conceptual model for exploratory, embodied STEM education software; and implemented it with the SpringSim interface and a task battery for high school students. In two studies, we confirm that low-cost devices can render haptics adequately for this purpose, find qualitative impact of SpringSim on student strategies and curiosity, and identify directions for tool improvement and extension.