Computational thinking (CT) can be considered a 21st century core skill and, accordingly, it should be taught to students at an early age. Nevertheless, the implementation of CT in school curricula is still in an experimental stage, given that different performance metrics remain unclear, including the appropriate age for learning each skill, the significant and achievable computational concepts for each school year, teaching strategies, learning effectiveness, and strategies for assessing development. Based upon constructivist problem-solving learning strategies and supported by a three-dimensional framework, a game-based environment with both individual and collaborative playing modes has been developed as a learning and an assessment tool via learning analytics. Moreover, an exploratory case study has been carried out involving 176 primary school students. Results suggest that this environment is suitable as a learning and assessment tool for CT skills in primary school, providing enduring learning, particularly when it engages the collaborative playing mode. It seems to be better adapted to early primary school stage students, who showed greater improvements and who were able to assimilate more computational concepts than expected. Likewise, special needs or low percentile students benefit even more greatly from the learning tool and especially from the collaborative playing mode. The combination of different assessment methodologies—including CT pre- and posttests, data-driven analytics, direct observation, and questionnaires—provides assessment for each of the framework computational dimensions.