I work at Oslo and Akershus University College where I teach physics to pre-service science education teachers (primary and middle school level). I use LC in all of my physics classes with non-majors that have a wide variety of academic backgrounds and experiences.
I use Learning Catalytics in several different ways. Before class, I use it to deliver a pre-test prior to class, in the style of Just-in-Time-Teaching, both to encourage the students to do their pre-reading and to guide me in terms of what to focus on in class. At the end of the pre-test I ask students to pose a "wonder question," to get them to think about the possible implications to their known world of the physics material they have read.
During class, I use Learning Catalytics for Peer Instruction; instead of just asking students to respond to questions, I also have them discuss their responses with a peer. What I particularly like about Learning Catalytics is the opportunity to pair students with different responses. This not only makes for more productive discussions, it has also improved the social environment in class, because students are forced to talk to peers they wouldn't necessarily interact with otherwise.
Data from my course evaluations support this notion: on a scale of 1-5 (with 5 indicating highest agreement), students very strongly agreed with the statement "Regularly discussing with different peers chosen by Learning Catalytics has positively affected the class environment" (mean 4.32) and disagreed with the statement "A traditional course would have been better" (mean 2.09). When asked to rate the value of different course components to their learning, the Peer Instruction component rated higher than reading the textbook or the lecture (means 4.36 vs 3.91).
This video illustrates how I use Peer Instruction with Learning Catalytics in class.