While a consensus has emerged to characterize student engagement during learning activities as a three-component construct featuring behavioral, emotional, and cognitive aspects, we propose adding agentic engagement as an important new aspect, which we define as students' constructive contribution into the flow of the instruction they receive. High school students (237 females, 128 males) from Taiwan completed surveys of their classroom motivation and the four hypothesized aspects of engagement while grades were obtained at the end of the semester. Structural equation modeling analyses showed that agentic engagement was both a distinct and an important construct, one that was associated with students' constructive motivation, related to each of the other three aspects of engagement, and predicted independent variance in achievement. The discussion highlights the important, though currently neglected, ways that students contribute constructively into the flow of the instruction they receive, as by personalizing it and by enhancing both the lesson and the conditions under which they learn. (Contains 4 tables and 1 figure.)