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Cognitive control and rule learning are two important mechanisms that explain how goals influence behavior and how knowledge is acquired. These mechanisms are studied heavily in cognitive science literature within highly controlled tasks to understand human cognition. Although they are closely linked to the student behaviors that are often studied within intelligent tutoring systems (ITS), their direct effects on learning have not been explored. Understanding these underlying cognitive mechanisms of beneficial and harmful student behaviors can provide deeper insight into detecting such behaviors and improve predictive models of student learning. In this paper, we present a thinkaloud study where we asked students to narrate their thought processes while solving probability problems in ASSISTments. Students are randomly assigned to one of two conditions that are designed to induce the two modes of cognitive control based on the Dual Mechanisms of Control framework. We also observe how the students go through the phases of rule learning as defined in a rule learning paradigm. We discuss the effects of these different mechanisms on learning, and how the information they provide can be used in student modeling.