The continuous advancement of natural user interfaces (NUIs) allows for the development of novel and creative ways to support collocated collaborative work in a wide range of areas, including teaching and learning. The use of NUIs, such as those based on interactive multi-touch surfaces and tangible user interfaces (TUIs), can offer unique opportunities for learning, for automatically capturing digital traces of students' multimodal interactions, and for facilitating multi-user exploration of student data. We used a composite framework to characterize our first-hand experiences and a small number of related deployments. The dimensions of analysis considered include the orchestration activities involved, the phases of pedagogical practice supported, the target actors, the iteration of the LA process, and the levels of impact of the LA deployment. Results from our analysis helped us identify the current trends, gaps, challenges, and pedagogical opportunities of the application of LA and the use of NUIs for supporting learning. [Paper presented at the LAK '16--International Conference on Learning Analytics and Knowledge (6th, Edinburgh, United Kingdom, April 25-29, 2016).]