Children's Number Knowledge Research Articles

Less is not always more: Rich and meaningful counting books lead to greater gains in number understanding than sparse counting books.

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).

Get to the point: Preschoolers’ spontaneous gesture use during a cardinality task

Gesture is a powerful learning tool for language, mathematics, and general problem solving, although the specific function of gesture is subject to debate. To address this question, we characterized predictors of preschoolers’ spontaneous gestures while completing a cardinality task. We analyzed video data from 343 preschoolers (158 male, Mage = 4.07y) who participated in the Give-N task (Wynn, 1992), which is used to assess children's number knowledge and understanding of cardinality. Analyses revealed that children’s number knowledge positively predicted gesture use, even when controlling for age, suggesting that as children gain better understanding of the skills necessary to complete the task, they are more likely to use gesture to solve numerical tasks. Moreover, those who had not yet acquired an understanding of cardinality (subset knowers, who are said to not use pointing gestures) were shown to use an effective gestural strategy (pointing and counting). Spontaneous gesture use across all knower-levels was also found to increase as a function of trial difficulty (trials involving larger set sizes), such that children were most likely to gesture on trials that challenged their abilities. Overall, findings indicate that children rely upon gestures as a scaffold during cognitively difficult tasks, and it is their relevant knowledge, not their age, that predicts their likelihood of engaging in gesture.

Early developmental trajectories of number knowledge and math achievement from 4 to 10 years: Low-persistent profile and early-life predictors

Little is known about the development of number knowledge (NK) and the antecedents of low-persistent NK profiles in early childhood. We documented the developmental trajectories of NK across the transition from preschool to elementary school, their predictive validity with respect to later math achievement, and the child and family early-life factors associated with low NK profiles. Children's NK was assessed four times at regular intervals between the ages 4 and 7 years in a large, representative population-based sample. Developmental trajectories of NK were established for 1597 children. These children were also assessed with respect to several features of their family environment at 5, 17, and 29 months, as well as their cognitive skills at age 41 months. Analyses revealed a best-fitting 4-trajectory model, characterized by Low-Increasing (10% of the children), Moderate-Increasing (39%), Moderate-Fast Increasing (32%) and High-Increasing (19%) groups. Children of these trajectory groups differed significantly with respect to math achievement at ages 8 and 10 years, with the Low-Increasing group persistently scoring lower than the other groups throughout these years. Children of Low-Increasing NK group were from household of lower income and father with low educational background, poorer early cognitive development, and more importantly, reduced visual-spatial skills and memory-span. Children displaying reduced cognitive abilities and impoverished living conditions early in life are at greater risk of low NK throughout late preschool and school entry, with ensuing difficulties in math achievement. They deserve early preventive attention to help alleviate later mathematic difficulties.

Thirty-One is a Lot!: Assessing Four-Year-Old Children's Number Knowledge during an Open-Ended Activity

IN EARLY CHILDHOOD EDUCATION, formative assessment should be ongoing and include multiple sources of evidence of children's existing knowledge. Children's understanding of mathematical concepts is highly diverse from a very early age, yet practical strategies to assess children's individual understanding are not always child centred and strengths based. This study explores the diverse ways in which 47 four-year-old children at three different early learning centres in metropolitan Melbourne demonstrated their number knowledge while they traced around wooden numerals, drawing and discussing values of quantity. Examples of children's representations of quantity are illustrated, accompanied by extracts of transcribed conversations. Findings demonstrate that this formative assessment strategy, through attuned prompts and skilled inquiry from the teacher, elicits children's complex understanding of number, located in the everyday experiences of their lives. Embedded in play-based activity, this assessment strategy is both engaging for children and highly productive for educators in documenting children's learning.

Enhancing preschool children's number knowledge: the suitability of an intervention programme for Saudi practice

This study aimed to present part of a mathematics programme for preschool age, to examine its efficiency in improving children's mathematical abilities in the area of number, and to investigate its suitability for Saudi practice. Pre- and post-tests, using TEMA-2 for one experimental and two control groups were conducted and quantitatively analysed. Teachers' reflection on their practice was sought through reflection forms and every two weeks discussion, which were qualitatively analysed to spot any practical and cultural considerations. Findings revealed that children's number knowledge in the experimental group has significantly improved compared with those of control groups. Teachers' practices have developed through three phases, representing different levels of experience and confidence. The study emphasised the allowing of flexible practices according to learners' needs, and providing professional support with newly implemented mathematics programmes. Some modifications for culturally related tools such as stories and songs were required. However, further investigation is needed to study these cultural issues.

"What counts in the development of young children's number knowledge?": Correction to Levine et al. (2010).

"What counts in the development of young children's number knowledge?": Correction to Levine et al. (2010).

What counts in the development of young children's number knowledge?

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.

A Model of Knower‐Level Behavior in Number Concept Development

We develop and evaluate a model of behavior on the Give-N task, a commonly-used measure of young children's number knowledge. Our model uses the knower-level theory of how children represent numbers. To produce behavior on the Give-N task, the model assumes children start out with a base-rate that make some answers more likely a priori than others, but is updated on each experimental trial in a way that depends on the interaction between the experimenter's request and the child's knower-level. We formalize this process as a generative graphical model, so that the parameters-including the base-rate distribution and each child's knower-level-can be inferred from data using Bayesian methods. Using this approach, we evaluate the model on previously published data from 82 children spanning the whole developmental range. The model provides an excellent fit to these data, and the inferences about the base-rate and knower-levels are interpretable and insightful. We discuss how our modeling approach can be extended to other developmental tasks, and can be used to help evaluate alternative theories of number representation against the knower-level theory.

The development of automated access to symbolic and non‐symbolic number knowledge in children: an ERP study

Infants can visually detect changes in numerosity, which suggests that a (non-symbolic) numerosity system is already present early in life. This non-symbolic system is hypothesized to serve as the basis for the later acquired symbolic system. Little is known about the processes underlying the transition from the non-symbolic to symbolic code. In the current study we investigated the development of automatization of symbolic number processing in children from second (6.0 years) and fourth grade (8.0 years) and adults using a symbolic and non-symbolic size congruency task and event-related potentials (ERPs) as a measure. The comparison between symbolic and non-symbolic size congruency effects (SCEs) allowed us to disentangle processes necessary to perform the task from processes specific to numerosity notation. In contrast to previous studies, second graders already revealed a behavioral symbolic SCE similar to that of adults. In addition, the behavioral SCE increased for symbolic and decreased for non-symbolic notation with increasing age. For all age groups, the ERP data showed that the two magnitudes interfered at a level before selective activation of the response system, for both notations. However, only for the second graders distinct processes were recruited to perform the symbolic size comparison task. This shift in recruited processes for the symbolic task only might reflect the functional specialization of the parietal cortex.

Playing Games and Learning Mathematics: The results of two intervention studies

This article presents the findings of two studies that were designed to improve young children's number knowledge through the use of mathematical games. The first study, with 5‐year‐old children (N = 55), involved parents coming into the classroom to play games with small groups of children. The second study, with 7‐year‐old children (N = 128), explored several ways of incorporating games into school mathematics programmes, including parents playing games with the children. Individual task‐based interviews were used to gather data on the children's number knowledge, and detailed observations were made of selected children's experiences during their normal mathematics lessons and while they were playing the mathematical games. The results showed that games appeared to be most effective as a way of enhancing children's learning when a sensitive adult was available to support and extend the children's learning as they played. The factors that appear to be important when involving parents in games sessions at school are discussed.

A Number Line in the Nursery Classroom: A Vehicle for Understanding Children's Number Knowledge

A Number Line in the Nursery Classroom: A Vehicle for Understanding Children's Number Knowledge