This classroom-based investigation sought to document how, in real time, STEM teachers and students attempt to locate the invariant mathematical relations that are threaded through the range of activities and representations in these classes, and how highlighting this common thread influences student participation and learning. The authors conducted multimodal discourse analyses of teacher–student interactions during multiday observations in 3 urban high school STEM classes. The focal lessons were in electrical engineering and mechanical engineering (within Project Lead the Way), and precollege geometry. Across 3 cases, teachers and students actively built and maintained cohesion of invariant mathematical relations across activities and representations. Pre- and postlesson interviews revealed that teachers intentionally managed cohesion to provide the continuity across the curricular activities that teachers believed would promote student understanding. The findings contribute to ways of fostering STEM integration and ways of grounding abstractions to promote meaning making and transfer. © 2017 Taylor & Francis.
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