Engagement is an essential ingredient for students to achieve their learning goals and academic success. In order to increase engagement, instructors update the instructional design (ID) of their courses. With the emergence of learning analytics, log data can be leveraged to find hidden study patterns which give insights into the different ways in which students engage with the learning material of the course. This study explores distinct clusters of online behavioral engagement of students in mathematics courses in the first year of a business bachelors program, their association with academic performance, and whether the study patterns found compare across consecutive academic years with changing ID. We found that courses always have highly disengaged students and highly engaged students but averagely engaged students gravitate towards specific course elements when ID changes.