Understanding the way learners engage with learning technologies, and its relation with their learning, is crucial for motivating design of effective learning interventions. Assessing the learners' state of engagement, however, is non-trivial. Research suggests that performance is not always a good indicator of learning, especially with open-ended constructivist activities. In this paper, we describe a combined multi-modal learning analytics and interaction analysis method that uses video, audio and log data to identify multi-modal collaborative learning behavioral profiles of 32 dyads as they work on an open-ended task around interactive tabletops with a robot mediator. These profiles, which we name "Expressive Explorers," "Calm Tinkerers," and "Silent Wanderers," confirm previous collaborative learning findings. In particular, the amount of speech interaction and the overlap of speech between a pair of learners are behavior patterns that strongly distinguish between learning and non-learning pairs. Delving deeper, findings suggest that overlapping speech between learners can indicate engagement that is conducive to learning. When we more broadly consider learner affect and actions during the task, we are better able to characterize the range of behavioral profiles exhibited among those who learn. Specifically, we discover two behavioral dimensions along which those who learn vary, namely, problem solving strategy (actions) and emotional expressivity (affect). This finding suggests a relation between problem solving strategy and emotional behavior; one strategy leads to more frustration compared to another. These findings have implications for the design of real-time learning interventions that support productive collaborative learning in open-ended tasks.