In this article, a cognitive framework for observing learning activities based on human-computer coupling is proposed. The observation is based on the vectorization of a learning situation along with human-computer interaction factors. An evolutionary high-dimensional topology of learning cognitive flow is introduced for human-computer interaction. In addition, the authors have selected a tree topology as the topological structure of a low-dimensional learning space to process the observations for online learning. Furthermore, the mechanism for the BSM (brain cognitive body-situation of coupling-manifold of information) the coupling morphism is presented. The principle for the coupled observation of objects in a cognitive or learning manifold is proposed. Finally, a special system for teaching and learning is programmed to observe and evaluate learning and mental arithmetic training processes. This system not only provides students with a new ergonomic learning model but also records the students' learning processes. Thus, the teachers can summarize the knowledge points automatically rather than manually.