The ICAP framework defines four cognitive engagement levels: Passive, Active, Constructive, and Interactive, where increased cognitive engagement can yield improved learning. However, personalizing learning activities that elicit the optimal level of cognitive engagement remains a key challenge in intelligent tutoring systems (ITS). In this work, we develop and evaluate a system that adaptively scaffolds cognitive engagement by dynamically selecting worked examples in two different ICAP modes: (active) Guided examples and (constructive) Buggy examples. We compare Bayesian Knowledge Tracing (BKT) and Deep Reinforcement Learning (DRL) as adaptive methods against a non-adaptive baseline method for selecting example type in a logic ITS. Our experiment with 113 students demonstrates that both adaptive policies significantly improved student performance on test problems. BKT yielded the largest improvement in posttest scores for low prior knowledge students, helping them catch up with their high prior knowledge peers, whereas DRL yielded significantly higher posttest scores among high prior knowledge students. This paper contributes new insights into the complex interactions of cognitive engagement and adaptivity and their results on learning outcomes.