Gnome Gnolf is a mobile augmented reality puzzle game, designed as a playful introduction to spatial geometry transformations for middle and high school students. The game is played by holding up a smartphone to view 3D game levels, which are anchored in real space using AR technology.

Players swing their smartphone (or tablet) to putt a ball through “Gnolf” courses – an analog of golf in the gnome world – while directing gnomes to conduct geometry transformations to reorient obstacles and navigate the ball to its hole. Each gnome specializes in a specific geometry transformation, including translation, rotation, and reflection. Gnomes can also use their magic to walk up walls (they aren’t limited to horizontal planes) while moving objects.

Learning Goals

———

Some students struggle to develop an interest in math or see why it’s worth learning. Gnome Gnolf focuses on rigid transformations in geometry as simple, intuitive concepts with real-world analogs. The game encourages students to reimagine their relationship with learning math, and prioritizes playful aspects of geometry to strengthen curiosity, interest, and real-world transfer.

Students typically study geometry on paper or flat screens, creating abstract barriers to 3D understanding. We leverage AR’s affordances of spatial reasoning and embodiment to make these concepts intuitive to more students. Players translate objects up into the air and rotate them from different perspectives using conceptually grounded gestures, such as physically rotating the phone to conduct transformations.