"Now I Get It!": Eureka Experiences During the Acquisition of Mathematical Concepts

Many famous scientists have reported anecdotes where a new understanding occurred to them suddenly, in an unexpected flash. Do people generally experience such "Eureka" moments when learning science concepts? And if so, do these episodes truly vehicle sudden insights, or is this impression illusory? To address these questions, we developed a paradigm where participants were taught the mathematical concept of geodesic, which generalizes the common notion of straight line to straight trajectories drawn on curved surfaces. After studying lessons introducing this concept on the sphere, participants (N = 56) were tested on their understanding of geodesics on the sphere and on other surfaces. Our findings indicate that Eureka experiences are common when learning mathematics, with reports by 34 (61%) participants. Moreover, Eureka experiences proved an accurate description of participants' learning, in two respects. First, Eureka experiences were associated with learning and generalization: the participants who reported experiencing Eurekas performed better at identifying counterintuitive geodesics on new surfaces. Second, and in line with the firstperson experience of a sudden insight, our findings suggest that the learning mechanisms responsible for Eureka experiences are inaccessible to reflective introspection. Specifically, reports of Eureka experiences and of participants' confidence in their own understanding were associated with different profiles of performance, indicating that the mechanisms bringing about Eureka experiences and those informing reflective confidence were at least partially dissociated. Learning mathematical concepts thus appears to involve mechanisms that operate unconsciously, except when a key computational step is reached and a sudden insight breaks into consciousness.

Spirituality of Science: Implications for Meaning, Well-Being, and Learning

Scientists often refer to spiritual experiences with science. This research addresses this unique component of science attitudes-spirituality of science: feelings of meaning, awe, and connection derived through scientific ideas. Three studies (N = 1,197) examined individual differences in Spirituality of Science (SoS) and its benefits for well-being, meaning, and learning. Spirituality of Science was related to belief in science, but unlike other science attitudes, spirituality of science was also associated with trait awe and general spirituality (Study 1). spirituality of science also predicted meaning in life and emotional well-being in a group of atheists and agnostics, showing that scientific sources of spirituality can provide similar psychological benefits as religious spirituality (Study 2). Finally, Spirituality of Science predicted stronger engagement and recall of scientific information (Study 3). Results provide support for an experience of spirituality related to science, with benefits for meaning, well-being, and learning.

"It kinda has like a mind": Children's and parents' beliefs concerning viral disease transmission for COVID-19 and the common cold

How people reason about disease transmission is central to their commonsense theories, scientific literacy, and adherence to public health guidelines. This study provided an in-depth assessment of U.S. children's (ages 5-12, N = 180) and their parents' (N = 125) understanding of viral transmission of COVID-19 and the common cold, during the first year of the COVID-19 pandemic. The primary aim was to discover children's causal models of viral transmission, by asking them to predict and explain counter-intuitive outcomes (e.g., asymptomatic disease, symptom delay) and processes that cannot be directly observed (e.g., viral replication, how vaccines work). A secondary aim was to explore parental factors that might contribute to children's understanding. Although even the youngest children understood germs as disease-causing and were highly knowledgeable about certain behaviors that transmit or block viral disease (e.g., sneezing, mask-wearing), they generally failed to appreciate the processes that play out over time within the body. Overall, children appeared to rely on two competing mental models of viruses: one in which viruses operate strictly via mechanical processes (movement through space), and one in which viruses are small living creatures, able to grow in size and to move by themselves. These results suggest that distinct causal frameworks co-exist in children's understanding. A challenge for the future is how to teach children about illness as a biological process without also fostering inappropriate animism or anthropomorphism of viruses.

A Model of Scientific Data Reasoning

Data reasoning is an essential component of scientific reasoning, as a component of evidence evaluation. In this paper, we outline a model of scientific data reasoning that describes how data sensemaking underlies data reasoning. Data sensemaking, a relatively automatic process rooted in perceptual mechanisms that summarize large quantities of information in the environment, begins early in development, and is refined with experience, knowledge, and improved strategy use. Summarizing data highlights set properties such as central tendency and variability, and these properties are used to draw inferences from data. However, both data sensemaking and data reasoning are subject to cognitive biases or heuristics that can lead to flawed conclusions. The tools of scientific reasoning, including external representations, scientific hypothesis testing, and drawing probabilistic conclusions, can help reduce the likelihood of such flaws and help improve data reasoning. Although data sensemaking and data reasoning are not supplanted by scientific data reasoning, scientific reasoning skills can be leveraged to improve learning about science and reasoning with data.

Rethinking the "gap": Self-directed learning in cognitive development and scientific reasoning

To improve upon their current knowledge, learners must be able to generate informative data and accurately evaluate this evidence. However, there is substantial disagreement regarding self-directed learners' competence in these behaviors. Researchers in cognitive development have suggested that learners are "intuitive scientists," generating informative actions and rationally coordinating their current observations and prior beliefs from an early age. Conversely, researchers in scientific reasoning report that learners struggle with experimentation and often fail to reach appropriate conclusions from evidence, even as adults. According to the prevailing narrative, these inconsistent findings must be "bridged" to explain the gap between learners' successes and failures. Here, we advocate for an alternative approach. First, we review the research on scientific reasoning and find that there may be less evidence for learners' failures than is typically assumed. Second, we offer a novel interpretation that aims to account for both literatures: we suggest that self-directed learners may be best understood as competent causal reasoners. That is, many seemingly uninformative or irrational behaviors are consistent with the goals of causal learning. This account not only resolves the apparent contradictions in the existing research, but also offers a way forward towards a more accurate and integrated understanding of self-directed learning. This article is categorized under: Psychology > Development and Aging Psychology > Learning Psychology > Reasoning and Decision Making.

Intuitive sociology

How do humans intuitively understand the structure of their society? How should psychologists study people's commonsense understanding of societal structure? The present chapter seeks to address both of these questions by describing the domain of "intuitive sociology." Drawing primarily from empirical research focused on how young children represent and reason about social groups, we propose that intuitive sociology consists of three core phenomena: social types (the identification of relevant groups and their attributes); social value (the worth of different groups); and social norms (shared expectations for how groups ought to be). After articulating each component of intuitive sociology, we end the chapter by considering both the emergence of intuitive sociology in infancy as well as transitions from intuitive to reflective representations of sociology later in life.