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Prior research shows that when parents monitor, check, and assist in completing homework without an invitation, their children's motivation and academic achievement often decline. We propose that intrusive support from parents might also send the message that children are incompetent, especially if they believe their intelligence is fixed. We tested whether children's mindsets moderate the negative link between parents' intrusive homework support and achievement among first- and second-grade students followed for one academic year (Study 1, N = 563) and middle and high school students for two academic years (Study 2, N = 1,613). The samples were obtained from large urban areas in the United States. In both studies, intrusive homework support more strongly predicted a decrease in achievement over time for children with a fixed mindset. These findings suggest that the belief that intellectual ability cannot be changed may exacerbate the detrimental effects of uninvited help on academic work.

Fractions are a challenging mathematics topic for many elementary and middle school students, and even for adults. However, a growing body of developmental research suggests that young children can reason about visually presented proportions, well before fraction instruction, providing insight into how fractions might be introduced to improve learning. We designed a card game to teach first and second grade children (N = 195, including a racially and economically diverse sample from the United States) about fractions in one of three ways. In the Actively Divided condition we iteratively divided an area model into equal-sized units, in the Predivided condition we used an area model with the end-state of the Actively Divided condition, and in the Nondivided condition we used a continuous representation of the fraction magnitude that was not divided into unit-sized parts. Children in the actively divided condition demonstrated larger improvements matching symbolic fractions and visual fractions (i.e., pie charts) than children in the other two conditions. Posthoc analyses of children's gameplay revealed that the actively divided condition may have provided a more optimal level of difficulty for young children than the predivided condition, which was particularly difficult, and the nondivided condition, which was trivially easy. These differences in gameplay performance provide insights into possible mechanisms for our results. We discuss open research questions highlighted by this work and implications of these findings for both the development of proportional reasoning and fraction learning.

Personal narrative is decontextualized talk where individuals recount stories of personal experience 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--that is, 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[subscript 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 show remarkably sophisticated abilities to evaluate others. Yet their abilities to engage in proportional moral evaluation undergoes protracted development. Namely, young children evaluate someone who shares "absolutely" more as being "nicer" than someone who shares "proportionally" more (e.g., sharing 3-out-of-6 is nicer than sharing 2-out-of-3, because 3 > 2, even though 3/6 < 2/3), whereas adults think the opposite. We investigate the hypothesis that this prior work underestimates children's proportional social reasoning by relying on discrete and spatially separated quantities (e.g., individual stickers), which can hinder proportional reasoning even outside social contexts. In three experiments we examine whether 4- and 5-year-old children's social evaluations are impacted by the discreteness and spatial separation of the resource and compare their behavior to adults (18 to 63 years; across all samples: 38% girls/women, 62% boys/men; no other demographic data was collected). We find that children are sensitive to these features: when the resource was divided into discrete units (Experiment 1) or spatially separated (Experiment 2) children were more likely to use absolute amount, as opposed to proportion, relative to when the resources were not divided and remained spatially connected. However, adults were highly sensitive to proportion regardless of the display's perceptual features (Experiment 3), and children's use of proportion remained below adult-levels. These results suggest that perceptual features influence children's use of absolute versus proportional information in their social evaluations, which has theoretical and methodological implications for understanding children's conceptions of fairness.

Past research has shown that children's mental rotation skills are malleable and can be improved through action experience--physically rotating objects--or gesture experience--showing how objects could rotate (e.g., Frick, Ferrara, & Newcombe, 2013; Goldin-Meadow et al., 2012; Levine, Goldin-Meadow, Carlson, & Hemani-Lopez, 2018). These two types of movements both involve rotation, but differ on a number of components. Here, we break down action and gesture into components--feeling an object during rotation, using a grasping handshape during rotation, tracing the trajectory of rotation, and seeing the outcome of rotation--and ask, in two studies, how training children on a mental rotation task through different combinations of these components impacts learning gains across a delay. Our results extend the literature by showing that, although all children benefit from training experiences, some training experiences are more beneficial than others, and the pattern differs by sex. Not seeing the outcome of rotation emerged as a crucial training component for both males and females. However, not seeing the outcome turned out to be the only necessary component for males (who showed equivalent gains when imagining or gesturing object rotation). Females, in contrast, only benefitted from not seeing the outcome when it involved producing a relevant motor movement (i.e., when gesturing the rotation of the object and not simply imagining the rotation of the object). Results are discussed in relation to potential mechanisms driving these effects and practical implications.

In a previous study, parent-child praise was observed in natural interactions at home when children were 1, 2, and 3 years of age. Children who received a relatively high proportion of process praise (e.g., praise for effort and strategies) showed stronger incremental motivational frameworks, including a belief that intelligence can be developed and a greater desire for challenge, when they were in 2nd or 3rd grade (Gunderson et al., 2013). The current study examines these same children's (n = 53) academic achievement 1 to 2 years later, in 4th grade. Results provide the first evidence that process praise to toddlers predicts children's academic achievement (in math and reading comprehension) 7 years later, in elementary school, via their incremental motivational frameworks. Further analysis of these motivational frameworks shows that process praise had its effect on fourth grade achievement through children's trait beliefs (e.g., believing that intelligence is fixed vs. malleable), rather than through their learning goals (e.g., preference for easy vs. challenging tasks). Implications for the socialization of motivation are discussed.

Understanding measurement units is critical to mathematics and science learning, but it is a topic that American students find difficult. In 3 studies, we investigated the challenges underlying this difficulty in kindergarten and second grade by comparing performance on different versions of a linear measurement task. Children measured crayons that were either aligned or shifted relative to the left edge of either a continuous ruler or a row of discrete units. The alignment (aligned, shifted) and the measuring tool (ruler, discrete units) were crossed to form 4 types of problems. Study 1 showed good performance in both grades on both types of aligned problems as well as on the shifted problems with discrete units. In contrast, performance was at chance on the shifted ruler problems. Study 2 showed that performance on shifted discrete unit problems declined when numbers were placed on the units, particularly for kindergarteners, suggesting that on the shifted ruler problems, the presence of numbers may have contributed to children's difficulty. However, Study 3 showed that the difficulty on the shifted ruler problems persisted even when the numbers were removed from the ruler. Taken together, these findings suggest that there are multiple challenges to understanding measurement, but that a key challenge is conceptualizing the ruler as a set of countable spatial interval units.

Recent studies reveal that children can solve proportional reasoning problems presented with continuous amounts that enable intuitive strategies by around 6 years of age but have difficulties with problems presented with discrete units that tend to elicit explicit count-and-match strategies until at least 10 years of age. The current study tests whether performance on discrete unit problems might be improved by prompting intuitive reasoning with continuous-format problems. Participants were kindergarten, second-grade, and fourth-grade students (N = 194) assigned to either an experimental condition, where they were given continuous amount proportion problems before discrete unit proportion problems, or a control condition, where they were given all discrete unit problems. Results of a three-way mixed-model analysis of variance examining school grade, experimental condition, and block of trials indicated that fourth-grade students in the experimental condition outperformed those in the control condition on discrete unit problems in the second half of the experiment, but kindergarten and second-grade students did not differ by condition. This suggests that older children can be prompted to use intuitive strategies to reason proportionally.

This study examines the role of a particular kind of linguistic input--talk about the past and future, pretend, and explanations, that is, talk that is decontextualized--in the development of vocabulary, syntax, and narrative skill in typically developing (TD) children and children with pre- or perinatal brain injury (BI). Decontextualized talk has been shown to be particularly effective in predicting children's language skills, but it is not clear why. We first explored the nature of parent decontextualized talk and found it to be linguistically richer than contextualized talk in parents of both TD and BI children. We then found, again for both groups, that parent decontextualized talk at child age 30 months was a significant predictor of child vocabulary, syntax, and narrative performance at kindergarten, above and beyond the child's own early language skills, parent contextualized talk and demographic factors. Decontextualized talk played a larger role in predicting kindergarten syntax and narrative outcomes for children with lower syntax and narrative skill at age 30 months, and also a larger role in predicting kindergarten narrative outcomes for children with BI than for TD children. The difference between the 2 groups stemmed primarily from the fact that children with BI had lower narrative (but not vocabulary or syntax) scores than TD children. When the 2 groups were matched in terms of narrative skill at kindergarten, the impact that decontextualized talk had on narrative skill did not differ for children with BI and for TD children. Decontextualized talk is thus a strong predictor of later language skill for all children, but may be particularly potent for children at the lower-end of the distribution for language skill. The findings also suggest that variability in the language development of children with BI is influenced not only by the biological characteristics of their lesions, but also by the language input they receive.

Narrative skill in kindergarteners has been shown to be a reliable predictor of later reading comprehension and school achievement. However, we know little about how to scaffold children's narrative skill. Here we examine whether the quality of kindergarten children's narrative retellings depends on the kind of narrative elicitation they are given. We asked this question with respect to typically developing (TD) kindergarten children and children with pre- or perinatal unilateral brain injury (PL), a group that has been shown to have difficulty with narrative production. We compared children's skill in retelling stories originally presented to them in 4 different elicitation formats: (a) wordless cartoons, (b) stories told by a narrator through the auditory modality, (c) stories told by a narrator through the audiovisual modality without co-speech gestures, and (e) stories told by a narrator in the audiovisual modality with co-speech gestures. We found that children told better structured narratives in response to the audiovisual + gesture elicitation format than in response to the other 3 elicitation formats, consistent with findings that co-speech gestures can scaffold other aspects of language and memory. The audiovisual + gesture elicitation format was particularly beneficial for children who had the most difficulty telling a well-structured narrative, a group that included children with larger lesions associated with cerebrovascular infarcts.

Prior studies indicate that children vary widely in their mathematical knowledge by the time they enter preschool and that this variation predicts levels of achievement in elementary school. In a longitudinal study of a diverse sample of 44 preschool children, we examined the extent to which their understanding of the cardinal meanings of the number words (e.g., knowing that the word "four" refers to sets with 4 items) is predicted by the "number talk" they hear from their primary caregiver in the early home environment. Results from 5 visits showed substantial variation in parents' number talk to children between the ages of 14 and 30 months. Moreover, this variation predicted children's knowledge of the cardinal meanings of number words at 46 months, even when socioeconomic status and other measures of parent and child talk were controlled. These findings suggest that encouraging parents to talk about number with their toddlers, and providing them with effective ways to do so, may positively impact children's school achievement. (Contains 2 footnotes, 4 tables, and 5 figures.)

Children with unilateral pre- or perinatal brain injury (BI) show remarkable plasticity for language learning. Previous work highlights the important role that lesion characteristics play in explaining individual variation in plasticity in the language development of children with BI. The current study examines whether the linguistic input that children with BI receive from their caregivers also contributes to this early plasticity, and whether linguistic input plays a similar role in children with BI as it does in typically developing (TD) children. Growth in vocabulary and syntactic production is modeled for 80 children (53 TD, 27 BI) between 14 and 46 months. Findings indicate that caregiver input is an equally potent predictor of vocabulary growth in children with BI and in TD children. In contrast, input is a more potent predictor of syntactic growth for children with BI than for TD children. Controlling for input, lesion characteristics (lesion size, type, seizure history) also affect the language trajectories of children with BI. Thus, findings illustrate how both variability in the environment (linguistic input) and variability in the organism (lesion characteristics) work together to contribute to plasticity in language learning. (Contains 3 tables, 3 figures, and 6 footnotes.)

Previous studies have found that children have difficulty solving proportional reasoning problems involving discrete units until 10 to 12 years of age, but can solve parallel problems involving continuous quantities by 6 years of age. The present studies examine where children go wrong in processing proportions that involve discrete quantities. A computerized proportional equivalence choice task was administered to kindergartners through 4th-graders in Study 1, and to 1st- and 3rd-graders in Study 2. Both studies involved 4 between-subjects conditions that were formed by pairing continuous and discrete target proportions with continuous and discrete choice alternatives. In Study 1, target and choice alternatives were presented simultaneously; in Study 2, target and choice alternatives were presented sequentially. In both studies, children performed significantly worse when both the target and choice alternatives were represented with discrete quantities than when either or both of the proportions involved continuous quantities. Taken together, these findings indicate that children go astray on proportional reasoning problems involving discrete units only when a numerical match is possible, suggesting that their difficulty is due to an overextension of numerical equivalence concepts to proportional equivalence problems. (Contains 2 figures, 4 tables, and 2 footnotes.)

On average, men outperform women on mental rotation tasks. Even boys as young as 4 1/2 perform better than girls on simplified spatial transformation tasks. The goal of our study was to explore ways of improving 5-year-olds' performance on a spatial transformation task and to examine the strategies children use to solve this task. We found that boys performed better than girls before training and that both boys and girls improved with training, whether they were given explicit instruction or just practice. Regardless of training condition, the more children gestured about moving the pieces when asked to explain how they solved the spatial transformation task, the better they performed on the task, with boys gesturing about movement significantly more (and performing better) than girls. Gesture thus provides useful information about children's spatial strategies, raising the possibility that gesture training may be particularly effective in improving children's mental rotation skills.

This study examined the relation between the amount of mathematical input in the speech of preschool or day-care teachers and the growth of children's conventional mathematical knowledge over the school year. Three main findings emerged. First, there were marked individual differences in children's conventional mathematical knowledge by 4 years of age that were associated with socioeconomic status. Second, there were dramatic differences in the amount of math-related talk teachers provided. Third, and most important, the amount of teachers' math-related talk was significantly related to the growth of preschoolers' conventional mathematical knowledge over the school year but was unrelated to their math knowledge at the start of the school year.

Examined children's and adults' perceptions of facial stimuli that were either systematically exaggerated (caricatures) or de-exaggerated (anticaricatures) relative to a norm face. Found that all ages perceived caricatures as the most distinctive version and anticaricatures as least distinctive; the smallest effect was for 6-year-olds. Caricatures were identified as quickly as veridical faces and faster than anticaricatures. Stimulus familiarity interacted with caricature to determine processing speed and choice of best likeness. (Author/KB)

Tested 3- to 7-year-olds' ability to calculate with whole numbers, fractions, and mixed-numbers, in a task in which an amount was displayed, then hidden. Subjects were to determine the hidden amount resulting when numbers were added or substracted. Found that, although fraction problems were more difficult than whole-number problems, competence on all problem types emerged in the early childhood period. (JPB)

Examined sex differences in 4- to 6-year olds' spatial skill. Found that performance on spatial transformation task showed a substantial male advantage by age 4 years 6 months, with the advantage no more robust for rotation than for translation items. Comparable vocabulary task performance indicated that male advantage on spatial tasks was not attributable to overall intellectual advantage. (Author/KB)

This article examines an important finding from the literature on infant numerical competence. The finding, reported by P. Starkey, E. S. Spelke, and R. Gelman (1990), was that infants looked longer toward a visual display that was equal in number to an auditory set. In Experiment 1, when the procedures described by P. Starkey et al. were followed and duration was held constant across auditory sequences that varied in number, infants looked longer toward the display that was not numerically equivalent to the auditory set. In Experiment 2, when the rate and duration of the auditory sequences were varied randomly within infants, no significant preference for either the equivalent or nonequivalent visual display was shown. These results raise questions about P. Starkey et al.'s claims that infants can represent the numerosity of sets in different modalities and then perform one-one correspondence computations over them.

This study examined the performance of 42 middle- and 42 low-income kindergarten children on arithmetic calculations presented in a nonverbal format as well as in 3 different verbal formats. On the nonverbal task, the child was shown an initial set of disks, which was then hidden with a cover. The set was transformed by adding or removing disks. After the transformation, the child's task was to construct an array of disks that contained the same number of disks as in the final hidden set. A significant interaction between income level and task format was obtained. Although middle-income children performed better than low-income children on each of the verbal calculation tasks, the 2 income groups did not differ in performance on the nonverbal calculation task. The findings suggest that the nonverbal task format is less sensitive to socioeconomic variation than are the verbal task formats.

This study examined the relation between the amount of mathematical input in the speech of preschool or day-care teachers and the growth of children's conventional mathematical knowledge over the school year. Three main findings emerged. First, there were marked individual differences in children's conventional mathematical knowledge by 4 years of age that were associated with socioeconomic status. Second, there were dramatic differences in the amount of math-related talk teachers provided. Third, and most important, the amount of teachers' math-related talk was significantly related to the growth of preschoolers' conventional mathematical knowledge over the school year but was unrelated to their math knowledge at the start of the school year. [ABSTRACT FROM AUTHOR]

Children vary widely in their number knowledge by the time they enter kindergarten, and this variation is related to their future academic success. Although talk about number predicts children's early understanding of foundational number concepts, we know little about whether interventions can increase this talk nor about the types of number talk that are most beneficial to children's number understanding. The current project examines whether embedding number talk in goal-based stories leads to more robust number learning than providing the same numeric input outside of this context. Parent-child dyads ( N = 71; child age = 3 years) were randomly assigned within their preintervention cardinal number understanding levels to one of three conditions: rich counting books (narrative and pictures involving a number goal), sparse counting books (text and pictures that provide opportunities to count and label the same cardinalities as in the rich condition but with no narrative), or nonnumerical control books that involve labeling colors of objects. Children's number knowledge was measured at pretest and at 2 and 4 weeks into the intervention. Findings showed that children randomized to rich counting book condition showed significantly greater cardinal number knowledge and counting skill by the final testing session compared to children in the sparse counting book condition and the color control book condition, which did not significantly differ from each other. Results have implications for the types of number talk that most effectively support children's number learning in the home environment and for the design of interventions. (PsycInfo Database Record (c) 2024 APA, all rights reserved).