Pre-school children discerning numbers and letters

PLoS ONE, 2011

Although number words are common in everyday speech, learning their meanings is an arduous, drawn-out process for most children, and the source of this delay has long been the subject of inquiry. Children begin by identifying the few small numerosities that can be named without counting, and this has prompted further debate over whether there is a specific, capacity-limited system for representing these small sets, or whether smaller and larger sets are both represented by the same system. Here we present a formal, computational analysis of number learning that offers a possible solution to both puzzles. This analysis indicates that once the environment and the representational demands of the task of learning to identify sets are taken into consideration, a continuous system for learning, representing and discriminating set-sizes can give rise to effective discontinuities in processing. At the same time, our simulations illustrate how typical prenominal linguistic constructions (''there are three balls'') structure information in a way that is largely unhelpful for discrimination learning, while suggesting that postnominal constructions (''balls, there are three'') will facilitate such learning. A trainingexperiment with three-year olds confirms these predictions, demonstrating that rapid, significant gains in numerical understanding and competence are possible given appropriately structured postnominal input. Our simulations and results reveal how discrimination learning tunes children's systems for representing small sets, and how its capacity-limits result naturally out of a mixture of the learning environment and the increasingly complex task of discriminating and representing ever-larger number sets. They also explain why children benefit so little from the training that parents and educators usually provide. Given the efficacy of our intervention, the ease with which it can be implemented, and the large body of research showing how early numerical ability predicts later educational outcomes, this simple discovery may have far-reaching consequences.

Cognitive Development, 2003

From an integrative approach, this work focuses on the role of conceptual mechanisms, such as comparison and conceptual-based inference, and sociopragmatic support in young children's taxonomic categorization. "Experiment 1" assessed whether 3-, 4-, and 6-year-old children succeed in detecting taxonomic relations on their own. A clear developmental trend was found: 6-year-olds succeeded, whereas 4-and 3-year-olds relied primarily on perceptually based categories. "Experiment 2" assessed if 3-year-olds are able to change their perceptual response into a taxonomic categorization as a function of the cooccurrence of contingent category information and feedback in an interactive process with an adult (experimenter). A pretest-posttest training study compared 3-year-olds' performance in four conditions: comparison, conceptual-based, information-only, and feedbackonly. A perceptual-totaxonomic shift was found only in the comparison and conceptualbased training groups. Children who only received either category information or corrective feedback did not make such a shift. The results show that social interaction with supportive adults is a mechanism that drives conceptual understanding in early childhood.

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.

This paper explores preschooler's conception of the relevance of written numerals to numerical questions about sets of items. Participants were asked questions about sets of items labeled with written numerals, and their tendency to treat the numerals as a relevant source of information for answering the questions was assessed. Preschooler's frequently used the numerals to answer the questions, although this was affected by the type of question, and the numbers in the question.

Pharma innovation, 2022

Number concept is defined as a person's general understanding to perform operation on numbers. National Council of Teachers of Mathematics (NCTM, 2002), USA (it is world's largest mathematics organisation), states that "the foundation for children's mathematical development is established in the earliest years". Therefore, preschool age is crucial period of life and considerable amount of attention should be paid to this phase. It is the time when skills are attained which acts as a foundation for all the subsequent years in the lifespan. Studies show that to lead a positive life in future it is necessary to expose children to number concepts in early years of life. Thus, the study aimed at assessing attainment of number concepts in preschool children. The number concepts were assessed in the categories of Number sense, Number representation and Number relation, which are based on the five principles of counting proposed by Gelman and Galistell. The study was carried out on twenty four numbers of preschool children belonging to the age of 3-4 years, selected through purposive sampling method. The investigator developed activities to assess the number concepts formed by preschool children. It was found that the concept of Number sense i.e. naming and matching numbers were better formed in children than Number representation and Number relation. The concept of number relation was not clear in preschool children. Among the three areas of Number relation viz., Sequencing, Cardinality and Magnitude, it was found that children performed well in the activities of sequencing numbers and poor in cardinality of numbers. It is very important for young children to master with the early number concepts for later achievement in mathematics.

Engaging young children in mathematics: Standards …, 2004

British Journal of Developmental Psychology, 2007

The Journal of Mathematical Behavior, 2000

It is the purpose of this paper to present a review of research evidence that indicates the existence of qualitatively different thinking in elementary number development. In doing so the paper summarises empirical evidence obtained over a period of ten years. This evidence first signalled qualitative differences in numerical processing , and was seminal in the development of the notion of procept . More recently it examines the role of imagery in elementary number processing . Its conclusions indicate that in the abstraction of numerical concepts from numerical processes qualitatively different outcomes may arise because children concentrate on different objects or different aspects of the objects which are components of numerical processing.

HAL (Le Centre pour la Communication Scientifique Directe), 2017

The aim of this pilot study is to explore when and how toddlers discern aspects of number in exploratory play and communication. Data for analysis consists of video-observations of 23 1-3year-olds' mathematical activities in preschool, revealing occurrences where toddlers' conceptions of number are challenged. A qualitative analysis informed by Variation theory of learning provides important clues for early mathematics education: toddlers encounter many aspects of number on a daily basis, but their conceptions are rarely challenged. This study will work as a basis for intervention and further studies of the possibility to enhance early mathematics education.

Mathematical Thinking and Learning

In this article we report on a study of children's attention to numerical content in picture books. Specific research questions are 1) how the content in a designed picture book directs children's attention to numbers, and 2) what kind of numerical reasoning the book reading entails. To answer these questions, we conducted an educational design research study in two cycles, with a specially designed picture book and two ways of reading: first without any prompting from the reading teacher, and second with teacher-child interaction. Nineteen preschool children (aged 3-5 years) and three teachers participated in video-observed individual reading sessions. The observations of the reading activities were analyzed with focus on the children's attention to numbers as well as on their numerical reasoning during the book talks. Based on the observations, we suggest that preschool children do direct their attention to aspects of numbers, but that the design of the pictures and the framing of the reading sessions influence which numerical aspects are discerned. Furthermore, teachers' support in transforming empirical clues into mathematical representations and comparisons seems critical for more advanced reasoning about numbers to occur.