Fraction Ball impact on student and teacher math talk and behavior.

We assessed the impacts of Fraction Ball-a novel suite of games combining the benefits of embodied guided play for math learning-on the math language production and behavior of students and teachers. In the Pilot Experiment, 69 fifth and sixth graders were randomly assigned to play four different Fraction Ball games or attend normal physical education class. The Efficacy Experiment was implemented to test improvements made through co-design with teachers with 160 fourth through sixth graders. Researchers observed and coded for use of math language and behavior. Playing Fraction Ball resulted in consistent increases of students' and teachers' use of fraction (SDs = 0.98-2.42) and decimal (SDs = 0.65-1.64) language and number line arithmetic, but not in whole number, spatial language, counting, instructional gesturing, questioning, and planning. We present evidence of the math language production in physical education and value added by Fraction Ball to support rational number language and arithmetic through group collaboration.

A cultural lens on Yucatec Maya families' COVID-19 experiences.

Health guidance during the COVID-19 pandemic led families around the world to spend more time isolated together, disrupting leisure activities, schooling, social interactions, and family work (UNICEF, 2021). Using the lens of Yucatec Maya families' cultural values and practices, semi-structured interviews were conducted with 18 Yucatec Maya rural women in Mexico (Mage  = 32; and for comparison, 13 middle-class European-American women (Mage  = 41)), with children 6-7 years old, to analyze families' experiences during the pandemic. Faced with the same isolation as in the United States, our exploratory analysis revealed Maya families experienced external stresses but at the same time were generally comfortable with their children's everyday activities and their social-emotional well-being, illuminating consequences of the communities' cultural theories about development.

Bias and sensitivity to task constraints in spontaneous relational attention.

Two experiments examined factors that predicted children's tendencies to match objects versus relations across scenes when no instruction was given. Specifically, we assessed the presence of higher relational responding in children by (a) age, (b) greater presumed experience in generating relations through socialization in China versus the United States, and (c) in children with greater manipulated experience via a relational priming task. Experiment 1 showed that Chinese and U.S. children across all ages showed an initial bias to match objects versus relations across scenes. However, older children in both regions were more likely to notice features of the task that indicated attending to relational matches was a more reliable solution, and shifted their responding toward relations over the course of the task. Experiment 2 replicated the object-mapping bias and age effects within U.S. children while also examining the impact of directly manipulating children's relational experiences to test the malleability of the bias. Before the main scene-mapping task, children did a relation generation task known to prime attention to relations. This did not override the initial bias toward object mapping, but it magnified the role of age, making older children increasingly sensitive to task features that prompted relational matches, further shifting their responding toward relations over the course of the task.

Working memory predicts children's analogical reasoning.

Analogical reasoning is the cognitive skill of drawing relationships between representations, often between prior knowledge and new representations, that allows for bootstrapping cognitive and language development. Analogical reasoning proficiency develops substantially during childhood, although the mechanisms underlying this development have been debated, with developing cognitive resources as one proposed mechanism. We explored the role of executive function (EF) in supporting children's analogical reasoning development, with the goal of determining whether predicted aspects of EF were related to analogical development at the level of individual differences. We assessed 5- to 11-year-old children's working memory, inhibitory control, and cognitive flexibility using measures from the National Institutes of Health Toolbox Cognition battery. Individual differences in children's working memory best predicted performance on an analogical mapping task, even when controlling for age, suggesting a fundamental interrelationship between analogical reasoning and working memory development. These findings underscore the need to consider cognitive capacities in comprehensive theories of children's reasoning development.

Problem solving is embedded in context so how do we measure it?

Problem solving encompasses the broad domain of human, goal-directed behaviors. Though we may attempt to measure problem solving using tightly controlled and decontextualized tasks, it is inextricably embedded in both reasoners' experiences and their contexts. Without situating problem solvers, problem contexts, and our own experiential partialities as researchers, we risk intertwining the research of information relevance with our own confirmatory biases about people, environments, and ourselves. We review each of these ecological facets of information relevance in problem solving, and we suggest a framework to guide its measurement. We ground this framework with concrete examples of ecologically valid, culturally relevant measurement of problem solving.

Early executive function predicts reasoning development.

Analogical reasoning is a core cognitive skill that distinguishes humans from all other species and contributes to general fluid intelligence, creativity, and adaptive learning capacities. Yet its origins are not well understood. In the study reported here, we analyzed large-scale longitudinal data from the Study of Early Child Care and Youth Development to test predictors of growth in analogical-reasoning skill from third grade to adolescence. Our results suggest an integrative resolution to the theoretical debate regarding contributory factors arising from smaller-scale, cross-sectional experiments on analogy development. Children with greater executive-function skills (both composite and inhibitory control) and vocabulary knowledge in early elementary school displayed higher scores on a verbal analogies task at age 15 years, even after adjusting for key covariates. We posit that knowledge is a prerequisite to analogy performance, but strong executive-functioning resources during early childhood are related to long-term gains in fundamental reasoning skills.

Measuring the building blocks of everyday cognition: executive functions and relational reasoning.

Measurement of the building blocks of everyday thought must capture the range of different ways that humans may train, develop, and use their cognitive resources in real world tasks. Executive function as a construct has been enthusiastically adopted by cognitive and education sciences due to its theorized role as an underpinning of, and constraint on, humans' accomplishment of complex cognitively demanding tasks in the world, such as identifying problems, reasoning about and executing multi-step solutions while inhibiting prepotent responses or competing desires. As EF measures have been continually refined for increased precision; however, they have also become increasingly dissociated from those everyday accomplishments. We posit three implications of this insight: (1) extant measures of EFs that reduce context actually add an implicit requirement that children reason using abstract rules that are not accomplishing a function in the world, meaning that EF scores may in part reflect experience with formal schooling and Western, Educated, Industrialized, Rich, Democratic (WEIRD) socialization norms, limiting their ability to predict success in everyday life across contexts, (2) measurement of relational attention and relational reasoning have not received adequate consideration in this context but are highly aligned with the key aims for measuring EFs, and may be more aligned with humans' everyday cognitive practices, but (3) relational attention and reasoning should be considered alongside rather than as an additional EF as has been suggested, for measurement clarity.

Children's Early Spontaneous Comparisons Predict Later Analogical Reasoning Skills: An Investigation of Parental Influence.

Laboratory studies have demonstrated beneficial effects of making comparisons on children's analogical reasoning skills. We extend this finding to an observational dataset comprising 42 children. The prevalence of specific comparisons, which identify a feature of similarity or difference, in children's spontaneous speech from 14-58 months is associated with higher scores in tests of verbal and non-verbal analogy in 6th grade. We test two pre-registered hypotheses about how parents influence children's production of specific comparisons: 1) via modelling, where parents produce specific comparisons during the sessions prior to child onset of this behaviour; 2) via responsiveness, where parents respond to their children's earliest specific comparisons in variably engaged ways. We do not find that parent modelling or responsiveness predicts children's production of specific comparisons. However, one of our pre-registered control analyses suggests that parents' global comparisons-comparisons that do not identify a specific feature of similarity or difference-may bootstrap children's later production of specific comparisons, controlling for parent IQ. We present exploratory analyses following up on this finding and suggest avenues for future confirmatory research. The results illuminate a potential route by which parents' behaviour may influence children's early spontaneous comparisons and potentially their later analogical reasoning skills.

Why do children struggle on analogical reasoning tasks? Considering the role of problem format by measuring visual attention.

Given the importance of analogical reasoning to bootstrapping children's understanding of the world, why is this ability so challenging for children? Two common sources of error have been implicated: 1) children's inability to prioritize relational information during initial problem solving; 2) children's inability to disengage from salient distractors. Here, we use eye tracking to examine children and adults' looking patterns when solving scene analogies, finding that children and adults attended differently to distractors, and that this attention predicted performance. These results provide the most direct evidence to date that feature based distraction is an important way children and adults differ during early analogical reasoning. In contrast to recent work using propositional analogies, we find no differences in children and adults' prioritization of relational information during problem solving, and while there are some differences in general attentional strategies across age groups, neither prioritization of relational information nor attentional strategy predict successful problem solving. Together, our results suggest that analogy problem format should be taken into account when considering developmental factors in children's analogical reasoning.

A computational account of children's analogical reasoning: balancing inhibitory control in working memory and relational representation.

Theories accounting for the development of analogical reasoning tend to emphasize either the centrality of relational knowledge accretion or changes in information processing capability. Simulations in LISA (Hummel & Holyoak, 1997, 2003), a neurally inspired computer model of analogical reasoning, allow us to explore how these factors may collaboratively contribute to the development of analogy in young children. Simulations explain systematic variations in United States and Hong Kong children's performance on analogies between familiar scenes (Richland, Morrison & Holyoak, 2006; Richland, Chang, Morrison & Au, 2010). Specifically, changes in inhibition levels in the model's working-memory system explain the developmental progression in US children's ability to handle increases in relational complexity and distraction from object similarity during analogical reasoning. In contrast, changes in how relations are represented in the model best capture cross-cultural differences in performance between children of the same ages (3-4 years) in the United States and Hong Kong. We use these results and simulations to argue that the development of analogical reasoning in children may best be conceptualized as an equilibrium between knowledge accretion and the maturation of information processing capability.

Personal narrative as a 'breeding ground' for higher-order thinking talk in early parent-child interactions.

Personal narrative is decontextualized talk where individuals recount stories of personal experiences about past or future events. As an everyday discursive speech type, narrative potentially invites parents and children to explicitly link together, generalize from, and make inferences about representations-i.e., to engage in higher-order thinking talk (HOTT). Here we ask whether narratives in early parent-child interactions include proportionally more HOTT than other forms of everyday home language. Sixty-four children (31 girls; 36 White, 14 Black, 8 Hispanic, 6 mixed/other race) and their primary caregiver(s) (M income = $61,000) were recorded in 90-minute spontaneous home interactions every 4 months from 14-58 months. Speech was transcribed and coded for narrative and HOTT. We found that parents at all visits and children after 38 months used more HOTT in narrative than non-narrative, and more HOTT than expected by chance. At 38- and 50-months, we examined HOTT in a related but distinct form of decontextualized talk-pretend, or talk during imaginary episodes of interaction-as a control to test whether other forms of decontextualized talk also relate to HOTT. While pretend contained more HOTT than other (non-narrative/non-pretend) talk, it generally contained less HOTT than narrative. Additionally, unlike HOTT during narrative, the amount of HOTT during pretend did not exceed the amount expected by chance, suggesting narrative serves as a particularly rich 'breeding ground' for HOTT in parent-child interactions. These findings provide insight into the nature of narrative discourse, and suggest narrative potentially may be used as a lever to increase children's higher-order thinking.

Young children's analogical reasoning across cultures: similarities and differences.

A cross-cultural comparison between U.S. and Hong Kong preschoolers examined factors responsible for young children's analogical reasoning errors. On a scene analogy task, both groups had adequate prerequisite knowledge of the key relations, were the same age, and showed similar baseline performance, yet Chinese children outperformed U.S. children on more relationally complex problems. Children from both groups were highly susceptible to choosing a perceptual or semantic distractor during reasoning when one was present. Taken together, these similarities and differences suggest that (a) cultural differences can facilitate better knowledge representations by allowing more efficient processing of relationally complex problems and (b) inhibitory control is an important factor in explaining the development of children's analogical reasoning.

Teaching and Learning Science through Multiple Representations: Intuitions and Executive Functions.

Reasoning about visual representations in science requires the ability to control one's attention, inhibit attention to irrelevant or incorrect information, and hold information in mind while manipulating it actively-all aspects of the limited-capacity cognitive system described as humans' executive functions. This article describes pedagogical intuitions on best practices for how to sequence visual representations among pre-service teachers, adult undergraduates, and middle school children, with learning also tested in the middle school sample. Interestingly, at all ages, most people reported beliefs about teaching others that were different from beliefs about how they would learn. Teaching beliefs were most often that others would learn better from presenting representations one at a time, serially; while learning beliefs were that they themselves would learn best from simultaneous presentations. Students did learn best from simultaneously presented representations of mitosis and meiosis, but only when paired with self-explanation prompts to discuss the relationships between the graphics. These results provide new recommendations for helping students draw connections across visual representations, particularly mitosis and meiosis, and suggest that science educators would benefit from shifting their teaching beliefs to align with beliefs about their own learning from multiple visual representations.

The origins of higher-order thinking lie in children's spontaneous talk across the pre-school years.

Higher-order thinking is relational reasoning in which multiple representations are linked together, through inferences, comparisons, abstractions, and hierarchies. We examine the development of higher-order thinking in 64 preschool-aged children, observed from 14 to 58 months in naturalistic situations at home. We used children's spontaneous talk about and with relations (i.e., higher-order thinking talk, or HOTT) as a window onto their higher-order thinking skills. We find that surface HOTT, in which relations between representations are more immediate and easily perceptible, appears before-and is far more frequent than-structure HOTT, in which relations between representations are more abstract and less easy to perceive. Child-specific factors (including early vocabulary and gesture use, first-born status, and family income) predict differences in children's onset (i.e., age of acquisition) of HOTT and its trajectory of use across development. Although HOTT utterances tend to be longer and more syntactically complex than non-HOTT utterances, HOTT frequently appears in non-complex utterances, and a substantial proportion of children achieve complex utterance onset prior to the onset of HOTT. This finding suggests that complex language is neither necessary nor sufficient for HOTT to occur; other factors above and beyond complex linguistic skills are involved in the onset and use of higher-order thinking. Finally, we found that the trajectory of HOTT, particularly structure HOTT-but not complex utterances-during the preschool period predicts standardized outcome measures of inference and analogy skills in grade school, which underscores the crucial role that this kind of early talk plays for later outcomes.

Generating Relations Elicits a Relational Mindset in Children.

Relational reasoning is a hallmark of human higher cognition and creativity, yet it is notoriously difficult to encourage in abstract tasks, even in adults. Generally, young children initially focus more on objects, but with age become more focused on relations. While prerequisite knowledge and cognitive resource maturation partially explains this pattern, here we propose a new facet important for children's relational reasoning development: a general orientation to relational information, or a relational mindset. We demonstrate that a relational mindset can be elicited, even in 4-year-old children, yielding greater than expected spontaneous attention to relations. Children either generated or listened to an experimenter state the relationships between objects in a set of formal analogy problems, and then in a second task, selected object or relational matches according to their preference. Children tended to make object mappings, but those who generated relations on the first task selected relational matches more often on the second task, signaling that relational attention is malleable even in young children.

Individual Differences in Relational Learning and Analogical Reasoning: A Computational Model of Longitudinal Change.

Children's cognitive control and knowledge at school entry predict growth rates in analogical reasoning skill over time; however, the mechanisms by which these factors interact and impact learning are unclear. We propose that inhibitory control (IC) is critical for developing both the relational representations necessary to reason and the ability to use these representations in complex problem solving. We evaluate this hypothesis using computational simulations in a model of analogical thinking, Discovery of Relations by Analogy/Learning and Inference with Schemas and Analogy (DORA/LISA; Doumas et al., 2008). Longitudinal data from children who solved geometric analogy problems repeatedly over 6 months show three distinct learning trajectories though all gained somewhat: analogical reasoners throughout, non-analogical reasoners throughout, and transitional - those who start non-analogical and grew to be analogical. Varying the base level of top-down lateral inhibition in DORA affected the model's ability to learn relational representations, which, in conjunction with inhibition levels used in LISA during reasoning, simulated accuracy rates and error types seen in the three different learning trajectories. These simulations suggest that IC may not only impact reasoning ability but may also shape the ability to acquire relational knowledge given reasoning opportunities.

Stereotype Threat Effects on Learning From a Cognitively Demanding Mathematics Lesson.

Stereotype threat-a situational context in which individuals are concerned about confirming a negative stereotype-is often shown to impact test performance, with one hypothesized mechanism being that cognitive resources are temporarily co-opted by intrusive thoughts and worries, leading individuals to underperform despite high content knowledge and ability (see Schmader & Beilock, ). We test here whether stereotype threat may also impact initial student learning and knowledge formation when experienced prior to instruction. Predominantly African American fifth-grade students provided either their race or the date before a videotaped, conceptually demanding mathematics lesson. Students who gave their race retained less learning over time, enjoyed the lesson less, reported a diminished desire to learn more, and were less likely to choose to engage in an optional math activity. The detrimental impact was greatest among students with high baseline cognitive resources. While stereotype threat has been well documented to harm test performance, the finding that effects extend to initial learning suggests that stereotype threat's contribution to achievement gaps may be greatly underestimated.

Executive Function in Learning Mathematics by Comparison: Incorporating Everyday Classrooms into the Science of Learning.

Individual differences in Executive Function (EF) are well established to be related to overall mathematics achievement, yet the mechanisms by which this occurs are not well understood. Comparing representations (problems, solutions, concepts) is central to mathematical thinking, and relational reasoning is known to rely upon EF resources. The current manuscript explored whether individual differences in EF predicted learning from a conceptually demanding mathematics lesson that required relational reasoning. Analyses revealed that variations in EF predicted learning when measured at a delay, controlling for pretest scores. Thus, EF capacity may impact students' overall mathematics achievement by constraining their resources available to learn from cognitively demanding reasoning opportunities in everyday lessons. To assess the ecological validity of this interpretation, we report follow-up interviews with mathematics teachers who raised similar concerns that cognitively demanding activities such as comparing multiple representations in mathematics may differentially benefit their high versus struggling learners. Broader implications for ensuring that all students have access to, and benefit from, conceptually rich mathematics lessons are discussed. We also highlight the utility of integrating methods in Science of Learning (SL) research.

Analogy, higher order thinking, and education.

Analogical reasoning, the ability to understand phenomena as systems of structured relationships that can be aligned, compared, and mapped together, plays a fundamental role in the technology rich, increasingly globalized educational climate of the 21st century. Flexible, conceptual thinking is prioritized in this view of education, and schools are emphasizing 'higher order thinking', rather than memorization of a cannon of key topics. The lack of a cognitively grounded definition for higher order thinking, however, has led to a field of research and practice with little coherence across domains or connection to the large body of cognitive science research on thinking. We review literature on analogy and disciplinary higher order thinking to propose that relational reasoning can be productively considered the cognitive underpinning of higher order thinking. We highlight the utility of this framework for developing insights into practice through a review of mathematics, science, and history educational contexts. In these disciplines, analogy is essential to developing expert-like disciplinary knowledge in which concepts are understood to be systems of relationships that can be connected and flexibly manipulated. At the same time, analogies in education require explicit support to ensure that learners notice the relevance of relational thinking, have adequate processing resources available to mentally hold and manipulate relations, and are able to recognize both the similarities and differences when drawing analogies between systems of relationships.

The pretesting effect: do unsuccessful retrieval attempts enhance learning?

Testing previously studied information enhances long-term memory, particularly when the information is successfully retrieved from memory. The authors examined the effect of unsuccessful retrieval attempts on learning. Participants in 5 experiments read an essay about vision. In the test condition, they were asked about embedded concepts before reading the passage; in the extended study condition, they were given a longer time to read the passage. To distinguish the effects of testing from attention direction, the authors emphasized the tested concepts in both conditions, using italics or bolded keywords or, in Experiment 5, by presenting the questions but not asking participants to answer them before reading the passage. Posttest performance was better in the test condition than in the extended study condition in all experiments--a pretesting effect--even though only items that were not successfully retrieved on the pretest were analyzed. The testing effect appears to be attributable, in part, to the role unsuccessful tests play in enhancing future learning.