Feedback in intelligent tutoring systems has been depicted as an important contributor to encourage exploration. However, few studies have explored learners' interaction patterns associated with feedback and the use of external representations in exploratory learning environments. This study used Fractions Lab, an exploratory learning environment for mathematics, to facilitate children's conceptual understanding of fractions in three Chinese schools. Students (n = 189) from six different classes were invited to use Fractions Lab, and 260,000 event logs were collected. Beyond demonstrating the overall efficacy of the approach, lag sequential analysis supported us in approaching a deeper understanding of patterns of interaction. The findings highlight that the design of three-levels of feedback (Socratic, guidance, and didactic-procedural feedback) played different roles in supporting students to use external representations to perform mathematical tasks in an exploratory learning environment. This study sheds light on how these interaction patterns might be applied to the Fractions Lab system in order to provide increasingly tailored support, based on cultural differences, to enhance students' technology-mediated learning experiences.

The use of massive open online courses (MOOCs) for teacher professional development (TDP) has increased in the past decades. This study explored the key factors that influenced teachers' online course completion as a significant indicator of their success in a TPD MOOC. Participants' selfassessment of Technological Pedagogical Content Knowledge (TPACK), interaction with curriculum content and peers, satisfaction, and overall course score were identified as key influencing factors. Employing a learning model that was constructed as a hypothesis path model based on literature review, we analysed these influencing factors' effects on participants' online learning completion. Results showed that participants' TPACK self-assessment and overall course score had a strong direct effect on their course completion, while their interaction with course content and peers had a significant indirect effect on their course completion. The important role of social activities and formative feedback in the design of MOOC was emphasized in this study. Surprisingly, participants' TPACK self-assessment had a weak negative impact on teachers' online learning completion, which warrants further research. Implications for research and practice are discussed.

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