Background: The growing necessity of providing better education, notably through the development of Adaptive Learning Systems (ALSs), leveraged the study of several psychological constructs to accurately characterize learners. A concept extensively studied in education is engagement, a multidimensional construct encompassing behavioral expression and motivational backgrounds. This metric can be used to not only guide certain pedagogic methodologies, but also to endow systems with the right tutoring techniques. As such, this article aims to inspire improved teaching styles and automatic learning systems, by experimentally verifying the influence of in-class behaviors in students' engagement. Results: Over 16 math lessons, the occurrence of students' and instructors' behaviors, alongside students' engagement estimates, were recorded using the COPUS observation protocol. After behavior-profiling the classes deploying such lessons, significant linear models were computed to relate the frequency of the students' or instructors' behaviors with the students' engagement at different in-class periods. The models revealed a positive relation of students' initial individual thinking and later group activity participation with their collective engagement, as well as a positive engagement relation with the later application of instructor's strategies such as giving feedback and moving through class, guiding on-going work. Conclusions: The results suggest the benefit of applying a workshop-like learning process, providing more individual explanations and feedback at the beginning of an interaction, leaving collective feedback and students' guidance of on-going work for later on. Based on the relations suggested by our models, several guidelines for developing ALSs are proposed, and a practical illustrative example is formulated.