Which of the following influences a learner's engagement level through external means?

Extrinsic motivation is the correct choice because it refers to external factors that influence a learner’s engagement and drive. This type of motivation is driven by external rewards or incentives such as grades, praise, or tangible rewards that come from outside the individual. When learners are motivated by external factors, they are more likely to engage in the learning process due to the prospect of receiving these rewards.

In contrast, intrinsic motivation stems from within the learner, driven by personal satisfaction or interest in the subject matter rather than external rewards. It is focused on internal satisfaction, such as the joy of learning or personal achievement.

Peer motivation involves influence from fellow learners, where the presence or expectations of peers can enhance engagement but still doesn't fully encapsulate the external nature of extrinsic rewards.

Self-driven motivation, like intrinsic motivation, is characterized by a learner's personal goals and aspirations, rather than incentives provided externally. This kind of motivation is inward-focused and does not rely on external stimuli to prompt engagement.

Thus, extrinsic motivation distinctly highlights how external rewards can shape and increase learners' levels of engagement in educational settings.