This paper presents a novel methodological approach of how to design, conduct and analyse robot-assisted play. This approach is inspired by non-directive play therapy. The experimenter participates in the experiments, but the child remains the main leader for play. Besides, beyond inspiration from non-directive play therapy, this approach enables the experimenter to regulate the interaction under specific conditions in order to guide the child or ask her questions about reasoning or affect related to the robot. This approach has been tested in a long-term study with six children with autism in a school setting. An autonomous robot with zoomorphic, dog-like appearance was used in the studies. The children's progress was analyzed according to three dimensions, namely, Play, Reasoning and Affect. Results from the case-study evaluations have shown the capability of the method to meet each child's needs and abilities. Children who mainly played solitarily progressively experienced basic imitation games with the experimenter. Children who proactively played socially progressively experienced higher levels of play and constructed more reasoning related to the robot. They also expressed some interest in the robot, including, on occasion, affect.