Does my daughter like math? Relations between parent and child math attitudes and beliefs.

As early as age six, girls report higher math anxiety than boys, and children of both genders begin to endorse the stereotype that males are better at math than females. However, very few studies have examined the emergence of math attitudes in childhood, or the role parents may play in their transmission. The present study is the first to investigate the concordance of multiple implicit and explicit math attitudes and beliefs between 6- and 10-year-old children and their parents. Data from implicit association tasks (IATs) reveal that both parents and their children have implicit associations between math and difficulty, but only parents significantly associated math with males. Notably, males (fathers and sons) were more likely than females (mothers and daughters) to identify as someone who likes math (instead of reading), suggesting gender differences in academic preferences emerge early and remain consistent throughout adulthood. Critically, we provide the first evidence that both mothers' and fathers' attitudes about math relate to a range of math attitudes and beliefs held by their children, particularly their daughters. Results suggest that girls may be especially sensitive to parental math attitudes and beliefs. Together, data indicate that children entering formal school already show some negative math attitudes and beliefs and that parents' math attitudes may have a disproportionate impact on young girls.

Being nice by choice: The effect of counterfactual reasoning on children's social evaluations.

The ability to engage in counterfactual thinking (reason about what else could have happened) is critical to learning, agency, and social evaluation. However, not much is known about how individual differences in counterfactual reasoning may play a role in children's social evaluations. In the current study, we investigate how prompting children to engage in counterfactual thinking about positive moral actions impacts children's social evaluations. Eighty-seven 4-8-year-olds were introduced to a character who engaged in a positive moral action (shared a sticker with a friend) and asked about what else the character could have done with the sticker (counterfactual simulation). Children were asked to generate either a high number of counterfactuals (five alternative actions) or a low number of counterfactuals (one alternative action). Children were then asked a series of social evaluation questions contrasting that character with one who did not have a choice and had no alternatives (was told to give away the sticker to his friend). Results show that children who generated selfish counterfactuals were more likely to positively evaluate the character with choice than children who did not generate selfish counterfactuals, suggesting that generating counterfactuals most distant from the chosen action (prosociality) leads children to view prosocial actions more positively. We also found age-related changes: as children got older, regardless of the type of counterfactuals generated, they were more likely to evaluate the character with choice more positively. These results highlight the importance of counterfactual reasoning in the development of moral evaluations. RESEARCH HIGHLIGHTS: Older children were more likely to endorse agents who choose to share over those who do not have a choice. Children who were prompted to generate more counterfactuals were more likely to allocate resources to characters with choice. Children who generated selfish counterfactuals more positively evaluated agents with choice. Comparable to theories suggesting children punish willful transgressors more than accidental transgressors, we propose children also consider free will when making positive moral evaluations.

Who's the winner? Children's math learning in competitive and collaborative scenarios.

Games are frequently used to promote math learning, yet the competitive and collaborative contexts introduced by games may exacerbate gender differences. In this study, 1st and 2nd grade children in the U.S. (ages 5-8; N = 274; 70% White, 15% Asian, 2% Black, 1% Native American, 14% mixed or other race; 17% Hispanic) played either a competitive, collaborative, or solo game to learn about a challenging novel math concept: proportion. Overall, both social contexts boosted perseverance and task attitudes. However, analyses revealed the competitive condition yielded gender differences in attention to proportion in the presence of competing cues, with older boys underperforming in the competition condition. Potential explanations for these findings, as well as implications for classroom math learning, are discussed.

A counting intervention promotes fair sharing in preschoolers.

Recent work has probed the developmental mechanisms that promote fair sharing. This work investigated 2.5- to 5.5-year-olds' (N = 316; 52% female; 79% White; data collected 2016-2018) sharing behavior in relation to three cognitive correlates: number knowledge, working memory, and cognitive control. In contrast to working memory and cognitive control, number knowledge was uniquely associated with fair sharing even after controlling for the other correlates and for age. Results also showed a causal effect: After a 5-min counting intervention (vs. a control), children improved their fair sharing behavior from pre-test to post-test. Findings are discussed in light of how social, cognitive, and motivational factors impact sharing behavior.

Children strategically conceal selfishness.

Can children exploit knowledge asymmetries to get away with selfishness? This question was addressed by testing 6- to 9-year-old children (N = 164; 81 girls) from the Northeastern United States in a modified Ultimatum Game. Children were assigned to the roles of proposers (who offered some proportion of an endowment) and responders (who could accept or reject offers). Both players in the Informed condition knew the endowment quantity in each trial. However, in the Uninformed condition, only proposers knew this information. In this condition, many proposers made "strategically selfish" offers that seemed fair based on the responders' incomplete knowledge but were actually highly selfish. These results indicate that even young children possess the ability to deceive others about their selfishness.

Children's gesture use provides insight into proportional reasoning strategies.

Children struggle with proportional reasoning when discrete countable information is available because they over-rely on this numerical information even when it leads to errors. In the current study, we investigated whether different types of gesture can exacerbate or mitigate these errors. Children aged 5-7 years (N = 135) were introduced to equivalent proportions using discrete gestures that highlighted separate parts, continuous gestures that highlighted continuous amounts, or no gesture. After training, children completed a proportional reasoning match-to-sample task where whole number information was occasionally pitted against proportional information. After the task, we measured children's own gesture use. Overall, we did not find condition differences in proportional reasoning; however, children who observed continuous gestures produced more continuous gestures than those who observed discrete gestures (and vice versa for discrete gestures). Moreover, producing fewer discrete gestures and more continuous gestures was associated with lower numerical interference on the match-to-sample task. Lastly, to further investigate individual differences, we found that children's inhibitory control and formal math knowledge were correlated with proportional reasoning in general but not with numerical interference in particular. Taken together, these findings highlight that children's own gestures may be a powerful window into the information they attend to during proportional reasoning.

Intuitive symbolic magnitude judgments and decision making under risk in adults.

Performance on an intuitive symbolic number skills task-namely the number line estimation task-has previously been found to predict value function curvature in decision making under risk, using a cumulative prospect theory (CPT) model. However there has been no evidence of a similar relationship with the probability weighting function. This is surprising given that both number line estimation and probability weighting can be construed as involving proportion judgment, that is, involving estimating a number on a bounded scale based on its proportional relationship to the whole. In the present work, we re-evaluated the relationship between number line estimation and probability weighting through the lens of proportion judgment. Using a CPT model with a two-parameter probability weighting function, we found a double dissociation: number line estimation bias predicted probability weighting curvature while performance on a different number skills task, number comparison, predicted probability weighting elevation. Interestingly, while degree of bias was correlated across tasks, the direction of bias was not. The findings provide support for proportion judgment as a plausible account of the shape of the probability weighting function, and suggest directions for future work.

Talking about proportion: Fraction labels impact numerical interference in non-symbolic proportional reasoning.

Across two experiments, we investigated how verbal labels impact the way young children attend to proportional information, well before the introduction of formal fraction education. Five- to seven-year-old children were introduced to equivalent non-symbolic proportions labeled in one of three ways: (a) a single, categorical label for multiple fractions (both 3/4 and 6/8 referred to as "blick"), (b) labels that focused on the numerator [e.g., 3/4 labeled as "three blicks" (Experiment 1) or "three-fourths" (Experiment 2)], or (c) labels that had a complete part-whole structure ("three-out-of-four"). Children then completed measures of non-symbolic proportional reasoning that pitted whole-number information against proportional information for novel proportions. Across both experiments, children who heard the categorical labels were more likely to match non-symbolic displays based on proportion than children in any of the other conditions, who demonstrated higher levels of numerical interference. These findings suggest that fraction labels have the potential to shape children's attention to proportional information even in the context of non-symbolic part-whole displays and for children who are not familiar with formal fraction symbols. We discuss these findings in terms of children's developing understanding of proportional reasoning and its implications for fraction education.

Explaining early moral hypocrisy: Numerical cognition promotes equal sharing behavior in preschool-aged children.

Recent work has documented that despite preschool-aged children's understanding of social norms surrounding sharing, they fail to share their resources equally in many contexts. Here we explored two hypotheses for this failure: an insufficient motivation hypothesis and an insufficient cognitive resources hypothesis. With respect to the latter, we specifically explored whether children's numerical cognition-their understanding of the cardinal principle-might underpin their abilities to share equally. In Experiment 1, preschoolers' numerical cognition fully mediated age-related changes in children's fair sharing. We found little support for the insufficient motivation hypothesis-children stated that they had shared fairly, and failures in sharing fairly were a reflection of their number knowledge. Numerical cognition did not relate to children's knowledge of the norms of equality (Experiment 2). Results suggest that the knowledge-behavior gap in fairness may be partly explained by the differences in cognitive skills required for conceptual and behavioral equality.

Even bees know zero is less than one.

Across three elegant experiments, Howard, Avarguès-Weber, Garcia, Greentree, & Dyer (2018) demonstrate that honey bees spontaneously generalize an ordinal rule to empty sets, treating zero as less than other whole numbers. Their findings provide strong evidence that bees have a nonsymbolic concept of zero similar to that found in monkeys and human children, suggesting that this capacity may have important evolutionary significance.

The effect of multimodal information on children's numerical judgments.

Although much research suggests that adults, infants, and nonhuman primates process number (among other properties) across distinct modalities, limited studies have explored children's abilities to integrate multisensory information when making judgments about number. In the current study, 3- to 6-year-old children performed numerical matching or numerical discrimination tasks in which numerical information was presented either unimodally (visual only), cross-modally (comparing audio with visual), or bimodally (simultaneously presenting audio and visual input). In three experiments, we investigated children's multimodal numerical processing across distinct task demands and difficulty levels. In contrast to previous work, results indicate that even the youngest children (3 and 4 years) performed above chance across all three modality presentations. In addition, the current study contributes two other novel findings, namely that (a) children exhibit a cross-modal disadvantage when numerical comparisons are easy and that (b) accuracy on bimodal trial types led to even more accurate numerical judgments under more difficult circumstances, particularly for the youngest participants and when precise numerical matching was required. Importantly, findings from this study extend the literature on children's numerical cross-modal abilities to reveal that, like their adult counterparts, children readily track and compare visual and auditory numerical information, although their abilities to do so are not perfect and are affected by task demands and trial difficulty.

A divergence of sub- and supra-second timing abilities in childhood and its relation to academic achievement.

Work with adult humans and nonhuman animals provides evidence that the processing of sub-second (<1 s) and supra-second (>1 s) durations are modulated via distinct cognitive and neural systems; however, few studies have explored the development of these separate systems. Moreover, recent research has identified a link between basic timing abilities and academic achievement, yet it is unclear whether sub-second and supra-second temporal processing may play independent roles in this relation. In the current study, we assessed the development of sub- and supra-second timing across middle childhood and examined how each ability may relate to academic achievement. Child participants (6- to 8-year-olds, n = 111) completed reading and math assessments and a temporal discrimination task that included comparisons in both the sub- and supra-second ranges. Results revealed that younger children performed comparably across the sub- and supra-second ranges, whereas 8-year-olds and adults (n = 72) were relatively better at discriminating durations in the supra-second range. Although discrimination performance in these distinct duration ranges did not uniquely predict math or reading achievement, overall timing abilities were related to math, but not reading, when controlling for age. Together, these data provide evidence for a divergence in timing abilities across sub- and supra-second durations emerging around 8 years of age; however, at least during this stage of development, the relation between children's timing and math achievement is unrelated to this divergence.

Children's understanding of fraction and decimal symbols and the notation-specific relation to pre-algebra ability.

Fraction and decimal concepts are notoriously difficult for children to learn yet are a major component of elementary and middle school math curriculum and an important prerequisite for higher order mathematics (i.e., algebra). Thus, recently there has been a push to understand how children think about rational number magnitudes in order to understand how to promote rational number understanding. However, prior work investigating these questions has focused almost exclusively on fraction notation, overlooking the open questions of how children integrate rational number magnitudes presented in distinct notations (i.e., fractions, decimals, and whole numbers) and whether understanding of these distinct notations may independently contribute to pre-algebra ability. In the current study, we investigated rational number magnitude and arithmetic performance in both fraction and decimal notation in fourth- to seventh-grade children. We then explored how these measures of rational number ability predicted pre-algebra ability. Results reveal that children do represent the magnitudes of fractions and decimals as falling within a single numerical continuum and that, despite greater experience with fraction notation, children are more accurate when processing decimal notation than when processing fraction notation. Regression analyses revealed that both magnitude and arithmetic performance predicted pre-algebra ability, but magnitude understanding may be particularly unique and depend on notation. The educational implications of differences between children in the current study and previous work with adults are discussed.

Use of feedback to improve mental number line representations in primary care clinics.

BACKGROUND: As patients become more engaged in decisions regarding their medical care, they must weigh the potential benefits and harms of different treatments. Patients who are low in numeracy may be at a disadvantage when making these decisions, as low numeracy is correlated with less precise representations of numerical magnitude. The current study looks at the feasibility of improving number representations. The aim of this study was to evaluate whether providing a small amount of feedback to adult subjects could improve performance on a number line placement task and to determine characteristics of those individuals who respond best to this feedback. METHODS: Subjects from two outpatient clinic waiting rooms participated in a three phase number line task. Participants were asked to place numbers on a computerized number line ranging from 0 to 1000 in pre-test, feedback, and post-test phases. Generalized estimating equations were used to model log-transformed scores and to test whether 1) performance improved after feedback, and 2) the degree of improvement was associated with age, education level or subjective numeracy. RESULTS: There was an overall improvement in task performance following the feedback. The average percent absolute error was 7.32% (SD: 6.00) for the pre-test and 5.63% (SD: 3.71) for the post-test. There was a significant interaction between college education and post-test improvement. Only subjects without some college education improved with feedback. CONCLUSIONS: Adults who do not have higher levels of education improve significantly on a number line task when given feedback.

Suboptimality in perceptual decision making and beyond.

We concur with the authors' overall approach and suggest that their analysis should be taken even further. First, the same points apply to areas beyond perceptual decision making. Second, the same points apply beyond issues of optimality versus suboptimality.

Numerical intuitions in infancy: Give credit where credit is due.

Leibovich et al. overlook numerous human infant studies pointing to an early emerging number sense. These studies have carefully manipulated continuous magnitudes in the context of a numerical task revealing that infants can discriminate number when extent is controlled, that infants fail to track extent cues with precision, and that infants find changes in extent less salient than numerical changes.

Signal clarity: an account of the variability in infant quantity discrimination tasks.

Infants have shown variable success in quantity comparison tasks, with infants of a given age sometimes successfully discriminating numerical differences at a 2:3 ratio but requiring 1:2 and even 1:4 ratios of change at other times. The current explanations for these variable results include the two-systems proposal - a theoretical framework that suggests that there are multiple systems at play and that these systems do not communicate early in infancy, leading to failure in certain numerical comparisons. An alternative proposal is that infants may be attending to continuous extent dimensions in these tasks rather than number per se. However, neither of these two main proposals is independently capable of accounting for the previously published data. Recently the Signal Clarity Hypothesis was proposed to account for and predict the variability (Cantrell & Smith, 2013). According to this hypothesis, infants' variable success may be understood from a framework of statistical learning taken together with the signal-to-noise ratio generated by control procedures in habituation tasks. Here we test specific predictions made by the Signal Clarity Hypothesis. Across four experiments assessing 9-month old discriminations of small and large sets (2 vs. 4 and 3 vs. 4), we demonstrate that infant success can be predicted by this novel approach and, further, that infants may discriminate smaller ratios of change than previously believed (3:4 numerical change and 2:3 cumulative area change).

123s and ABCs: developmental shifts in logarithmic-to-linear responding reflect fluency with sequence values.

When placing numbers along a number line with endpoints 0 and 1000, children generally space numbers logarithmically until around the age of 7, when they shift to a predominantly linear pattern of responding. This developmental shift of responding on the number placement task has been argued to be indicative of a shift in the format of the underlying representation of number (Siegler & Opfer, ). In the current study, we provide evidence from both child and adult participants to suggest that performance on the number placement task may not reflect the structure of the mental number line, but instead is a function of the fluency (i.e. ease) with which the individual can work with the values in the sequence. In Experiment 1, adult participants respond logarithmically when placing numbers on a line with less familiar anchors (1639 to 2897), despite linear responding on control tasks with standard anchors involving a similar range (0 to 1287) and a similar numerical magnitude (2000 to 3000). In Experiment 2, we show a similar developmental shift in childhood from logarithmic to linear responding for a non-numerical sequence with no inherent magnitude (the alphabet). In conclusion, we argue that the developmental trend towards linear behavior on the number line task is a product of successful strategy use and mental fluency with the values of the sequence, resulting from familiarity with endpoints and increased knowledge about general ordering principles of the sequence.A video abstract of this article can be viewed at:http://www.youtube.com/watch?v=zg5Q2LIFk3M.

Children underperform following "math" but not "spatial" task framing.

Increasing evidence suggests that success in science, technology, engineering, and math (STEM) fields is not only dependent upon one's actual STEM-relevant abilities but also upon one's STEM-relevant attitudes-in particular, math and spatial attitudes. Here, we examine whether simply mentioning the math or spatial relevance of a task affects children's performance and the moderating role of children's math and spatial attitudes. Further, we examine gender differences in performance given pervasive gender gaps in STEM and early-emerging gender differences in math and spatial attitudes. Participants (221 first- to fourth-grade children from the United States; 113 girls, 108 boys; 52% White, 16% Black, 14% Asian, 9% Hispanic or Latinx, 18% multiple races/ethnicities) were introduced to a novel task framed as tapping into math or spatial abilities (or no framing [control condition]). Children then completed math and spatial anxiety and self-concept measures. Results indicate that children who heard the math task framing were less accurate relative to children in the control condition, and the effect was larger for those with higher math anxiety or lower math self-concept, but it was not different for boys and girls. Children who heard the spatial task framing, however, performed comparably to children in the control condition. Though both math and spatial attitudes revealed identical patterns of gender differences (with higher anxiety and lower self-concept in girls than boys), there were no gender differences in performance. This study highlights the salient role of math attitudes early in development and provides key insights for future work aimed at increasing STEM outcomes. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

How many seconds was that? Teaching children about time does not refine their ability to track durations.

Over development, children acquire symbols to represent abstract concepts such as time and number. Despite the importance of quantity symbols, it is unknown how acquiring these symbols impacts one's ability to perceive quantities (i.e., nonsymbolic representations). While it has been proposed that learning symbols shapes nonsymbolic quantitative abilities (i.e., the refinement hypothesis), this hypothesis has been understudied, especially in the domain of time. Moreover, the majority of research in support of this hypothesis has been correlational in nature, and thus, experimental manipulations are critical for determining whether this relation is causal. In the present study, kindergarteners and first graders (N = 154) who have yet to learn about temporal symbols in school completed a temporal estimation task during which they were either (1) trained on temporal symbols and effective timing strategies ("2 s" and counting on the beat), (2) trained on temporal symbols only ("2 s"), or (3) participated in a control training. Children's nonsymbolic and symbolic timing abilities were assessed before and after training. Results revealed a correlation between children's nonsymbolic and symbolic timing abilities at pre-test (when controlling for age), indicating this relation exists prior to formal classroom instruction on temporal symbols. Notably, we found no support for the refinement hypothesis, as learning temporal symbols did not impact children's nonsymbolic timing abilities. Implications and future directions are discussed.