Student engagement during learning serves as a critical predictor of academic success and plays a pivotal role in nurturing interest and readiness for future careers. As digital platforms become increasingly important to learning, it is essential that we understand how the interactions that students have with them reflects their engagement with learning. Previous research has often modeled engagement in a fully online context, where students pursue lessons independently and outside the influence of the classroom, paced and structured by digital systems. However, in STEM (Science, Technology, Engineering, and Math) subjects—and many others—learning more frequently happens in a physical classroom setting, under the guidance of a teacher, and involves interactions with other students and tangible objects. Here digital materials are used to scaffold and support learning but are not typically the focus of where learning happens. To study how student interactions with digital materials in these settings might allow us to measure, evaluate and help teachers enhance engagement, we have developed and deployed a smart digital learning platform that guides instruction and captures real-time multimodal student learning events in the physical STEM classroom. Previously we have shown that a subset of student interactions measured with this platform can be used to model student learning and generate human-like insights into engagement. Here we report on the significant influence that teachers have on student interactions with our smart platform in the STEM classroom, and the impact that this has on evaluating their engagement with learning. In an analysis of 108 high school students that used the platform to complete a 19-lesson data science curriculum in 5 different classrooms, we found significant differences between teachers both in the measured time students spent on the lesson and the percentage of the lesson they completed. In this setting, taking teacher influence into account improves the outcomes of our machine learning clustering models that group students based on their level of engagement. These findings inform how we develop smart classroom technology and machine learning applications that are globally informed but locally relevant, and support teachers to enhance student engagement and learning outcomes in dynamic and highly variable STEM classroom learning environments.