Robust student knowledge: Adapting to individual student needs as they explore the concepts and practice the procedures of fractions

Robust knowledge consists of both conceptual and procedural knowledge. In order to address both types of knowledge, offering students opportunities to explore target concepts in an exploratory learning environment (ELE) is insufficient. Instead, we need to combine exploratory learning environments, to support students acquisition of conceptual knowledge, with more structured learning environments that allow students to practice problem-solving procedures step-by-step, to support students' acquisition of procedural knowledge. However, how best to combine both kinds of learning environments and thus both types of learning activities is an open question. We have developed a pedagogical intervention model that selects and sequences learning activities, exploratory learning activities and structured practice activities, that are appropriate for the individual learner. Technically, our intervention model is implemented as a rule-based system in a learning platform about fractions. The model's decisionmaking process relies on the detection of each individual student's level of challenge (i.e. whether they were under-, appropriately or over-challenged by the previous learning activity). Thus, our model adapts flexibly to each individual student's needs and provides them with a unique sequence of learning activities. Our formative evaluation trials suggest that single components of the intervention model, such as the ELE, mostly achieve their aims. The interplay between the different components of the intervention model (i.e. the outcomes of sequencing and selecting exploratory and structured practice activities) is currently being evaluated.