Researchers have proposed various approaches to increase motivation for learning. However, in many cases, they are designed to boost motivation but fall short of creating learning habits. Gamification and competition between peers are widely used to urge people to, for example, do more steps in a day. E-learning platforms often use leaderboards to visualize peer progress, but their effectiveness is limited to when users open the platform. In this work, we use notifications to inform peers of each other's progress in real-time to increase motivation for learning. In an in-the-wild study with 19 participants, we investigate the impact of peer-awareness on learning by comparing real-time notifications (sent immediately after peers' progress) with interval-based notifications (sent at random intervals). Contrary to our initial expectations, our findings reveal that interval-based notifications are more effective in promoting learning activities. We introduce the Peer-Aware Learning System (PALS), a mobile application designed to simulate peer effects and provide insights from our user study on notification timing strategies for enhancing learning motivation.