The science of learning has generated a wealth of research and theory on how people think and learn. One product of this research is what are known as 'principles of learning' - teaching and learning strategies that have garnered empirical support for their effectiveness at enhancing learning across a range of learners and domains in rigorous lab and classroom tests. For example, the principle of interleaved practice involves mixing problems that can be solved using different solutions -- to support discrimination learning - and spacing problems that can be solved using the same solution over time -- to support long-term memory retention [1]. In the present work, we describe an on-going cluster randomized trial where we attempt to test the efficacy of interleaved practice across multiple schools and geographic regions in a nationally representative U.S. sample. Despite strong evidence that interleaved practice leads to greater math learning than blocking problems [2], blocked practice predominates math curricula [3]. This finding follows a general trend that learning research is underutilized in educational contexts [4]. One reason for this disconnect is that learning takes place within a dynamic system that is highly contextual [5]. What works in one context may not work the same way in another. As a result, scaling learning research remains a major challenge. Although interleaving is seemingly straightforward for application, we describe several challenges we faced in our own work when attempting to scale interleaving in this large-scale study. To address these challenges we outline a process guided by a working implementation model for translating interleaving to concrete materials. We also describe early results of our first (of three) data collection years assessing the impact of a mostly interleaving intervention relative to a mostly blocked intervention on students' math achievement. Although our work is ongoing, the lessons learned even at this early stage can have important implications for scaling interleaved practice as well as learning principles more broadly.

Understanding mathematical equivalence is foundational for developing early algebraic thinking. Despite its importance, many young students struggle with the concept and use incorrect strategies when solving equivalence problems. Immediate, computer-based feedback may help students learn correct strategies. However, designing effective feedback for math equivalence is challenging. In this work-in-progress paper, we discuss usability studies and child-centered design with young students. Our goal is to better understand how students make sense of different kinds of feedback, what kinds of formats they prefer, and what actions they take after receiving the feedback. By centering young students’ perspectives in the design process, we can avoid blind spots created by our adult researcher perspectives and increase the likelihood of student engagement and knowledge gains. We describe the extended iterative process required to help students develop a formal understanding of math equivalence by creating usable and effective computer-based feedback.