Watching videos of a drawing hand improves students' understanding of the normal probability distribution.

Understanding normal probability distributions is a crucial objective in mathematics and statistics education. Drawing upon cognitive psychology research, this study explores the use of drawings and visualizations as effective scaffolds to enhance students' comprehension. Although much research has documented the helpfulness of drawing as a research tool to reveal students' knowledge states, its direct utility in advancing higher-order cognitive processes remains understudied. In Study 1, qualitative methods were utilized to identify common misunderstandings among students regarding canonical depictions of the normal probability distribution. Building on these insights, Study 2 experimentally compared three instructional videos (static slides, dynamic drawing, and dynamic drawings done by a visible hand). The hand drawing video led to better learning than the other versions. Study 3 examined whether the benefits from observing a hand drawing could be reproduced by a dynamic cursor moving around otherwise static slides (without the presence of a hand). Results showed no significant learning difference between observing a hand drawing and a moving cursor, both outperforming a control. This research links the cognitive process of drawing with its educational role and provides insights into its potential to enhance memory, cognition, and inform instructional methods.

Representational-mapping strategies improve learning from an online statistics textbook.

Using multiple representations is an important part of learning and problem-solving in science, technology, engineering and mathematics fields. For students to acquire flexible knowledge of representations, they must attend to the structural information within each representation and practice making relational connections between representations. Most studies so far have only attempted to help students connect between multiple representations in the lab or short-term classroom interventions, with the intervention largely separated from students' authentic learning. The present study developed a representation-mapping intervention designed to help students interpret, coordinate, and eventually translate across multiple representations. We integrated the intervention into an online textbook being used in a college course, allowing us to study its impact in a real course over an extended period of time. The findings of this study support the efficacy of the representation-mapping intervention for facilitating learning and shed light on how to implement and refine such interventions in authentic learning contexts. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Instructed Hand Movements Affect Students' Learning of an Abstract Concept From Video.

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.

Making hidden resources visible in a minority serving college context.

OBJECTIVES: Navigating pathways of higher education means uncovering hidden "rules" about how to be successful in university systems that privilege dominant ways of knowing. To unpack these rules, universities have attempted a range of approaches from enrolling students in semester-long courses focused on the transition to college to more cost-effective psychological interventions that use stories to highlight pathways for navigating the transition. These cost-effective approaches are of increased interest to universities and effective in promoting student outcomes. Yet, their effects have mostly been examined in predominantly White institutions leaving open the question of how to tailor these interventions in less-resourced institutions serving a more diverse student body. We examined the effect of making these hidden resources known in concrete ways and of contextualizing these resources with student stories through a scalable online video-based assignment. METHOD: Across 2 large-scale experiments at a minority serving institution, participants watched either resource videos only or resource videos coupled with students' stories. RESULTS: Compared to a no-treatment control group, we found that first-generation-to-college students benefited from receiving both types of resource information. Continuing-generation-to-college students benefited the most when resources were coupled with student stories. CONCLUSIONS: We speculate that first-generation students at minority serving institutions have concrete concerns that need to be addressed alongside identity and social belonging needs. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Exploring the practicing-connections hypothesis: using gesture to support coordination of ideas in understanding a complex statistical concept.

In this article, we begin to lay out a framework and approach for studying how students come to understand complex concepts in rich domains. Grounded in theories of embodied cognition, we advance the view that understanding of complex concepts requires students to practice, over time, the coordination of multiple concepts, and the connection of this system of concepts to situations in the world. Specifically, we explore the role that a teacher's gesture might play in supporting students' coordination of two concepts central to understanding in the domain of statistics: mean and standard deviation. In Study 1 we show that university students who have just taken a statistics course nevertheless have difficulty taking both mean and standard deviation into account when thinking about a statistical scenario. In Study 2 we show that presenting the same scenario with an accompanying gesture to represent variation significantly impacts students' interpretation of the scenario. Finally, in Study 3 we present evidence that instructional videos on the internet fail to leverage gesture as a means of facilitating understanding of complex concepts. Taken together, these studies illustrate an approach to translating current theories of cognition into principles that can guide instructional design.

Relational Priming Based on a Multiplicative Schema for Whole Numbers and Fractions.

Why might it be (at least sometimes) beneficial for adults to process fractions componentially? Recent research has shown that college-educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study examined patterns of relational priming for problems with fractions in a task that required arithmetic computations. College students were asked to judge whether or not multiplication equations involving fractions were correct. Some equations served as structurally inverse primes for the equation that immediately followed it (e.g., 4 × 3/4 = 3 followed by 3 × 8/6 = 4). Students with relatively high math ability showed relational priming (speeded solution times to the second of two successive relationally related fraction equations) both with and without high perceptual similarity (Experiment 2). Students with relatively low math ability also showed priming, but only when the structurally inverse equation pairs were supported by high perceptual similarity between numbers (e.g., 4 × 3/4 = 3 followed by 3 × 4/3 = 4). Several additional experiments established boundary conditions on relational priming with fractions. These findings are interpreted in terms of componential processing of fractions in a relational multiplication context that takes advantage of their inherent connections to a multiplicative schema for whole numbers.

The simple advantage in perceptual and categorical generalization.

Recent research in relational learning has suggested that simple training instances may lead to better generalization than complex training instances. We examined the perceptual-encoding mechanisms that might undergird this "simple advantage" by testing category and perceptual learning in adults with simplified and traditional (more complex) Chinese scripts. In Experiment 1, participants learned Chinese characters and their English translations, performed a memorization test, and generalized their learning to the corresponding characters written in the other script. In Experiment 2, we removed the training phase and modified the tests to examine transfer based purely on the perceptual similarities between simplified and traditional characters. We found the simple advantage in both experiments. Training with simplified characters produced better generalization than training with traditional characters when generalization relied on either recognition memory or pure perceptual similarities. On the basis of the results of these two experiments, we propose a simple process model to explain the perceptual mechanism that might drive this simple advantage, and in Experiment 3 we tested novel predictions of this model by examining the effect of exposure duration on the simple advantage. We found support for our model that the simple advantage is driven primarily by differences in the perceptual encoding of the information available from simple and complex instances. These findings advance our understanding of how the perceptual features of a learning opportunity interact with domain-general mechanisms to prepare learners for transfer.

The Importance of Being Interpreted: Grounded Words and Children's Relational Reasoning.

Although young children typically have trouble reasoning relationally, they are aided by the presence of "relational" words (e.g., Gentner and Rattermann, 1991). They also reason well about commonly experienced event structures (e.g., Fivush, 1984). To explore what makes a word "relational" and therefore helpful in relational reasoning, we hypothesized that these words activate well-understood event structures. Furthermore, the activated schema must be open enough (without too much specificity) that it can be applied analogically to novel problems. Four experiments examine this hypothesis by exploring: how training with a label influence the schematic interpretation of a scene, what kinds of scenes are conducive to schematic interpretation, and whether children must figure out the interpretation themselves to benefit from the act of interpreting a scene as an event. Experiment 1 shows the superiority of schema-evoking words over words that do not connect to schematized experiences. Experiments 2 and 3 further reveal that these words must be applied to perceptual instances that require cognitive effort to connect to a label rather than unrelated or concretely related instances in order to draw attention to relational structure. Experiment 4 provides evidence that even when children do not work out an interpretation for themselves, just the act of interpreting an ambiguous scene is potent for relational generalization. The present results suggest that relational words (and in particular their meanings) are created from the act of interpreting a perceptual situation in the context of a word.

Attention to context: U.S. and Japanese children's emotional judgments.

A growing number of studies suggest cultural differences in the attention and evaluation of information in adults (Masuda & Nisbett, 2001; Markus & Kitayama, 1991; Hedden, Ketay, Aron, Markus, & Gabrieli, 2008). One cultural comparison, between Westerners, such as Americans, and Easterners, such as the Japanese, suggest that Westerners typically focus on a central single object in a scene while Easterners often integrate their judgment of the focal object with surrounding contextual cues. There are few studies of whether such cultural differences are evident in children. This study examined 48 monolingual Japanese-speaking children residing in Japan and 48 monolingual English-speaking children residing in the U.S.A. (40 to 60 month-olds) in a task asking children to complete a picture by adding the proper emotional expression to a face. The key variable was the context and shift in context from the preceding trial for the same pictured individual. Japanese children were much more likely to shift their judgments with changes in context whereas children from the United States treated facial expression in a more trait-like manner, maintaining the same expression for the individual across contexts.

Connecting instances to promote children's relational reasoning.

The practice of learning from multiple instances seems to allow children to learn about relational structure. The experiments reported here focused on two issues regarding relational learning from multiple instances: (a) what kind of perceptual situations foster such learning and (b) how particular object properties, such as complexity and similarity, interact with relational learning. Two kinds of perceptual situations were of interest here: simultaneous view, where instances are viewed at once, and sequential view, where instances are viewed one at a time (one right after the other). We examined the influence of particular perceptual situations and object properties using two tests of relational reasoning: a common match-to-sample task, where new instances are compared with a common sample, and a variable match-to-sample task, where new instances are compared with a sample that varies on each trial. Experiments 1 and 2 indicate that simultaneous presentation of even highly dissimilar instances, one simple and one complex, effectively connects them together and improves relational generalization in both match-to-sample tasks. Experiment 3 shows that simple samples are more effective than complex ones in the common match-to-sample task. However, when one instance is not used a common sample and various pairs of instances are simply compared, as in Experiment 4, simple and rich instances are equally effective at promoting relational learning. These results bear on our understanding of how children connect instances and how those initial connections affect learning and generalization.

The education of perception.

Although the field of perceptual learning has mostly been concerned with low- to middle-level changes to perceptual systems due to experience, we consider high-level perceptual changes that accompany learning in science and mathematics. In science, we explore the transfer of a scientific principle (competitive specialization) across superficially dissimilar pedagogical simulations. We argue that transfer occurs when students develop perceptual interpretations of an initial simulation and simply continue to use the same interpretational bias when interacting with a second simulation. In arithmetic and algebraic reasoning, we find that proficiency in mathematics involves executing spatially explicit transformations to notational elements. People learn to attend mathematical operations in the order in which they should be executed, and the extent to which students employ their perceptual attention in this manner is positively correlated with their mathematical experience. For both science and mathematics, relatively sophisticated performance is achieved not by ignoring perceptual features in favor of deep conceptual features, but rather by adapting perceptual processing so as to conform with and support formally sanctioned responses. These "rigged-up perceptual systems" offer a promising approach to educational reform.

Perceptual learning modules in mathematics: enhancing students' pattern recognition, structure extraction, and fluency.

Learning in educational settings emphasizes declarative and procedural knowledge. Studies of expertise, however, point to other crucial components of learning, especially improvements produced by experience in the extraction of information: perceptual learning (PL). We suggest that such improvements characterize both simple sensory and complex cognitive, even symbolic, tasks through common processes of discovery and selection. We apply these ideas in the form of perceptual learning modules (PLMs) to mathematics learning. We tested three PLMs, each emphasizing different aspects of complex task performance, in middle and high school mathematics. In the MultiRep PLM, practice in matching function information across multiple representations improved students' abilities to generate correct graphs and equations from word problems. In the Algebraic Transformations PLM, practice in seeing equation structure across transformations (but not solving equations) led to dramatic improvements in the speed of equation solving. In the Linear Measurement PLM, interactive trials involving extraction of information about units and lengths produced successful transfer to novel measurement problems and fraction problem solving. Taken together, these results suggest (a) that PL techniques have the potential to address crucial, neglected dimensions of learning, including discovery and fluent processing of relations; (b) PL effects apply even to complex tasks that involve symbolic processing; and (c) appropriately designed PL technology can produce rapid and enduring advances in learning.

Simplicity and generalization: Short-cutting abstraction in children's object categorizations.

Development in any domain is often characterized by increasingly abstract representations. Recent evidence in the domain of shape recognition provides one example; between 18 and 24 months children appear to build increasingly abstract representations of object shape [Smith, L. B. (2003). Learning to recognize objects. Psychological Science, 14, 244-250]. Abstraction is in part simplification because it requires the removal of irrelevant information. At the same time, part of generalization is ignoring irrelevant differences. The resulting prediction is this: simplification may enable generalization. Four experiments asked whether simple training instances could shortcut the process of abstraction and directly promote appropriate generalization. Toddlers were taught novel object categories with either simple or complex training exemplars. We found that children who learned with simple objects were able to generalize according to shape similarity, typically relevant for early object categories, better than those who learned with complex objects. Abstraction is the product of learning; using simplified - already abstracted instances - can short-cut that learning, leading to robust generalization.