Collaboration enhances conceptual learning with multiple representations. However, learning with multiple representations also involves perceptual learning processes. These often-overlooked learning processes are the target of perceptual trainings, which expose students to short nonverbal tasks so that students can induce visual patterns across…

Our civilization recognizes that errors can be valuable learning opportunities, but for decades, they have widely been avoided or, at best, allowed to occur as serendipitous accidents. The present research tested whether greater learning success could paradoxically be achieved through making errors by intentional design, relative to traditional…

Fraction arithmetic facility is fundamental to learning more advanced math topics. However, attaining the ability to add and subtract fractions is hard for many students. The present longitudinal study examined students' growth on simple addition and subtraction word problems between fourth and sixth grades (N = 536). Latent class growth analyses…

The More A-More B intuitive rule has become a research hotspot in the field of mathematical education in recent years. The intuitive rule of More A-More B is often reflected in students' responses to comparison tasks. In such tasks, students are asked to compare 2 objects that differ in a certain salient quantity A (where A[subscript 1] >…

The present study tests whether presenting video modeling examples from the learner's (first-person) perspective promotes learning of an assembly task, compared to presenting video examples from a third-person perspective. Across 2 experiments conducted in different labs, university students viewed a video showing how to assemble an 8-component…

Retrieval practice is a powerful way to promote long-term retention and meaningful learning. However, students do not frequently practice retrieval on their own, and when they do, they have difficulty evaluating the correctness of their responses and making effective study choices. To address these problems, we have developed a guided retrieval…