Teachers often use drawings of the normal distribution to support explanations of related statistical concepts, assuming that the normal curve provides a common language for such discussions. However, we find that students may not understand the basic features of the normal curve. In Study 1, we showed that students who already have studied the normal distribution in a college-level class do not understand basic concepts associated with it. Then, in Study 2, we investigated whether a brief instructional, narrated video could improve students’ understanding of the normal probability distribution. Specifically, we compared three instructional formats: static slides, a video recording of a hand physically drawing those plots, and a screen recording of the hand-drawing. Despite the brevity of the intervention, we found significant improvements in students’ understanding of the normal probability distribution and related probability concepts. The findings are discussed in relation to the dynamic representation and embodied cognition literature.

In recent years, embodied learning has gained significant at- tention as a valuable approach to STEM education. However, previous studies have often focused on highly controlled lab experiments and have failed to consider the unique perspec- tives and backgrounds of learners. The current study aims to replicate the findings of Zhang et al. (2022) by integrat- ing the embodied learning intervention into an online class with students that may differ in important ways from Amer- ican college students (Chinese high school students). Students were introduced to abstract concepts related to randomness and using coding to mimic a shuffling process. Students in sec- tions were randomly assigned to get this introduction through an embodied hands-on video or a less-embodied live-coding video. The learning outcomes were evaluated through authen- tic class assessments (homework and exam). Results showed that students introduced to target concepts with the more em- bodied video outperformed those who watched the less em- bodied video. The benefit of embodiment was observed only on questions related to the topic covered in the intervention videos.

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.