This type of engaged learning is referred to as active learning.
In contrast to the traditional, mostly passive ways of teaching (one-way lecturing), nowadays there's a trend to active learning.
Active learning is any approach to instruction in which all students are asked to engage in the learning process. Active learning stands in contrast to "traditional" modes of instruction in which students are passive recipients of knowledge from an expert.
Markant et al (2016) explain in a review article that active learning leads to better outcomes than passive forms of instruction. They summarize that the opportunity to control the information while learning leads to improved memory. Mechanisms involved in this effect include the formation of sensorimotor associations, adaptive selection of material and metacognitive monitoring.
Active control over a learning situation results in large areas of the brain being recruited and interconnected during active exploration (source: Psych Central). For example, active exploratory behavior during the observation of objects enhances memory recall (Voss et al., 2011), resulting in enhanced activity in the dorsolateral prefrontal cortex, the cerebellum and the hippocampus is higher and more coordinated after active learning (source: Illinois News Bureau).
- Markant et al Mind, Brain, and Education Society (2016); 10(3): 142-52
- Voss et al., Nat Neurosci (2011); 14(1): 115-20