Recent work has shown that undergraduates at a major public university demonstrate implicit understanding of inverse relations between multiplication problems with fractions, as evidenced by the fact that solving one problem facilitates solving its inverse. The present study investigated whether such implicit understanding of mathematical relations is related to overall math ability. We found that low performers showed relational facilitation only when it was supported by perceptual similarity, whereas high performers showed relational facilitation on both perceptually similar and dissimilar problems. These findings are interpreted in terms of novice-expert differences in the representation of mathematical relations.

This paper introduces A Library for Innovative Category Exemplars (ALICE) database, a resource that enhances research efficiency in cognitive and developmental studies by providing printable 3D objects representing 30 novel categories. Our research consists of three experiments to validate the novelty and complexity of the objects in ALICE. Experiment 1 assessed the novelty of objects through adult participants' subjective familiarity ratings and agreement on object naming and descriptions. The results confirm the general novelty of the objects. Experiment 2 employed multidimensional scaling (MDS) to analyze perceived similarities between objects, revealing a three-dimensional structure based solely on shape, indicative of their complexity. Experiment 3 used two clustering techniques to categorize objects: k-means clustering for creating nonoverlapping global categories, and hierarchical clustering for allowing global categories that overlap and have a hierarchical structure. Through stability tests, we verified the robustness of each clustering method and observed a moderate to good consensus between them, affirming the strength of our dual approach in effectively and accurately delineating meaningful object categories. By offering easy access to customizable novel stimuli, ALICE provides a practical solution to the challenges of creating novel physical objects for experimental purposes.

Research suggests that expert understanding is characterized by coherent mental representations featuring a high level of connectedness. This paper advances the idea that educators can facilitate this level of understanding in students through the practicing connections framework: a practical framework to guide instructional design for developing deep understanding and transferable knowledge in complex academic domains. We start by reviewing what we know from learning sciences about the nature and development of transferable knowledge, arguing that connectedness is key to the coherent mental schemas that underlie deep understanding and transferable skills. We then propose features of instruction that might uniquely facilitate deep understanding and suggest that the connections between a domain’s core concepts, key representations, and contexts and practices of the world must be made explicit and practiced, over time, in order for students to develop coherent understanding. We illustrate the practicing connections approach to instructional design in the context of a new online interactive introductory statistics textbook developed by the authors.

Although improving racial equity in critical college courses such as introductory statistics is a laudable goal, making research-based progress toward that aim in a scalable manner remains a challenge. To translate psychological insights to benefit racially marginalized students, we implemented the “Better Book” approach, where instructors, researchers, and developers work together to improve an online textbook used in introductory statistics. The “Better Book” approach to equity assumes that racially marginalized students are a “canary in the coal mine”, alerting us to systemic issues that can affect a broader array of students. We started by finding places in the textbook where racially marginalized students reported higher perceptions of costs (the effort and time required to learn the content) than non-marginalized students. Then we drew upon suggestions from users to redesign the textbook where gaps in cost perceptions peaked. We then analyzed data from both the original and redesigned versions of the textbook to evaluate the impact on students who were subsequently enrolled in the course. Results showed that perceptions of cost were dramatically reduced in the experience of racially marginalized students but also the redesign resulted in an improved experience for all students.

Producing content-related gestures has been found to impact students' learning, whether such gestures are spontaneously generated by the learner in the course of problem-solving, or participants are instructed to pose based on experimenter instructions during problem-solving and word learning. Few studies, however, have investigated the effect of (a) performing instructed gestures while learning concepts or (b) producing gestures without there being an implied connection between the gestures and the concepts being learned. The two studies reported here investigate the impact of instructed hand movements on students' subsequent understanding of a concept. Students were asked to watch an instructional video-focused on the concept of statistical model-three times. Two experimental groups were given a secondary task to perform while watching the video, which involved moving their hands to mimic the placement and orientation of red rectangular bars overlaid on the video. Students were told that the focus of the study was multitasking, and that the instructed hand movements were unrelated to the material being learned. In the content-match group the placement of the hands reinforced the concept being explained, and in the content-mismatch group it did not. A control group was not asked to perform a secondary task. In both studies, findings indicate that students in the content-match group performed better on the posttest, and showed less variation in performance, than did students in the content-mismatch group, with control students falling in between. Instructed hand movement-even when presented as an unrelated, secondary task-can affect students' learning of a complex concept.