Children's Mathematical Development Research Articles

Cognitive Foundations of Early Mathematics: Investigating the Unique Contributions of Numerical, Executive Function, and Spatial Skills.

There is an emerging consensus that numerical, executive function (EF), and spatial skills are foundational to children's mathematical learning and development. Moreover, each skill has been theorized to relate to mathematics for different reasons. Thus, it is possible that each cognitive construct is related to mathematics through distinct pathways. The present study tests this hypothesis. One-hundred and eighty 4- to 9-year-olds (Mage = 6.21) completed a battery of numerical, EF, spatial, and mathematics measures. Factor analyses revealed strong, but separable, relations between children's numerical, EF, and spatial skills. Moreover, the three-factor model (i.e., modelling numerical, EF, and spatial skills as separate latent variables) fit the data better than a general intelligence (g-factor) model. While EF skills were the only unique predictor of number line performance, spatial skills were the only unique predictor of arithmetic (addition) performance. Additionally, spatial skills were related to the use of more advanced addition strategies (e.g., composition/decomposition and retrieval), which in turn were related to children's overall arithmetic performance. That is, children's strategy use fully mediated the relation between spatial skills and arithmetic performance. Taken together, these findings provide new insights into the cognitive foundations of early mathematics, with implications for assessment and instruction moving forward.

French preschool and primary teachers' attitude towards finger counting

Teachers' beliefs and attitudes are known to guide the type of activities they implement in their classrooms. A traditional conception that finger counting is merely a back-up when children fail to use more sophisticated and efficient strategies could therefore prevent teachers from encouraging children's use of fingers in arithmetic tasks. However, the potential benefit of finger counting for young learners has been recently documented and setting aside its practice within classrooms may hinder children's mathematical skill development. It is therefore important to establish whether there is a discrepancy between teacher's beliefs regarding finger counting and the latest discoveries in this field of research. To this aim, we interrogated 413 teachers from preschool to Grade 5. We found that, despite being generally positive towards finger counting, teachers think that finger counting is typical of children who present math difficulties or lack of confidence, even during the first years of learning. These results are discussed considering what is known and what remains to be determined in the current scientific literature.

The sums are larger than their natural number addends: Relation to operands understanding predicts growth in arithmetic/algebraic problem solving.

The relation to operands (RO) principles describe the relation between operands and answers in arithmetic problems (e.g., the sum is always larger than its positive addends). Despite being a fundamental property of arithmetic, its empirical relation with arithmetic/algebraic problem solving has seldom been investigated. The current longitudinal study aimed to address this issue. Two-hundred-and-two Chinese fifth graders (57% boys) were assessed on their RO understanding. Their arithmetic/algebraic problem solving were assessed multiple times over 2 years. Results from latent growth curve modeling showed that RO understanding predicted the growth in arithmetic/algebraic problem solving when other known predictors of arithmetic/algebraic problem solving were controlled. The findings highlight the role of RO understanding in children's mathematical development. Interventions should be developed to enhance children's RO understanding. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Early home learning support and home mathematics environment as predictors of children's mathematical skills between age 4 and 6: A longitudinal analysis using video observations and survey data.

This large-scale and longitudinal study examines early home support for learning, formal/informal home mathematics activities, and their associations with children's mathematical development between age two and six. Data were collected in Germany between 2012 and 2018, N = 1184 (49% girls, 51% boys), and 15% of children had parents with a migration history. Linguistically and mathematically stimulating, attentive, and responsive parent-child engagement at age two predicted children's mathematical skills at age four and six (small-to-medium effect size). Both formal and informal home mathematical activities at age five predicted children's mathematical skills at age six (small effect size), and were associated with children's prior mathematics attainment. This study also provides indicators where individual differences and social circumstances are relevant to understanding different early mathematics outcomes.

The Effects of Music towards the Mathematical Language Development of Children

Mathematical programs should enable children to use mathematics as a tool to explore, find knowledge and solve problems as well as develop language. Mathematical abilities are the basis of the skills required for the Basics of children's mathematical development starting from the experience of children related to concrete bends or objects containing quantities and qualities of objects such as different colors, sizes, and shapes as well as the numbers around them. Thus, this research successfully identified three main objectives such type of music can increase children’s mathematical development, the effect of music on children’s mathematical development in terms of cognitive and literacy and to identify challenges and barriers toward mathematical children’s development. As can be concluded, music does a lot of good to the mathematical development of children. Which is a factor influencing the development of a child's mathematical language.

The Mathematical Development of Children with Down Syndrome: The Adapted Cuisenaire Material as a Learning Facilitator

With this study, we tried to understand how the adaptation of a manipulative material can facilitate the learning of the decomposition of natural numbers in a child with Down Syndrome. Many authors defend the use of manipulative materials to teach Mathematics to children with Down Syndrome and, also, recommend the Cuisenaire material to promote the learning of mathematical initiation concepts. However, we found that the child we study presents difficulties in terms of fine manipulation and abstraction. We promoted the adaptation of the Cuisenaire material to this student and developed an intervention program of twenty sessions, divided into three phases: manipulation of the adapted Cuisenaire; manipulation of conventional Cuisenaire and the performance of exercises. In all sessions, the child worked on the decomposition of natural numbers and the exploration of the train game. After analyzing the data collected, we found that the dimensions and textures of the adapted Cuisenaire allowed us to overcome some of the difficulties felt in terms of manipulation and abstraction and facilitated the learning of decomposing natural numbers to ten. However, the adapted Cuisenaire did not facilitate the manipulation of the conventional Cuisenaire.

Erken Matematik Ölçeği’nin Türkçeye uyarlanması: Geçerlik ve güvenirlik çalışması

Matematiksel kavram ve becerilerin gelişiminde erken çocukluk döneminin son derece etkili ve önemli olduğu bilindiği için çocukların matematik becerileri okulda ve evde sistemli matematik programlarıyla desteklenmelidir. Dolayısıyla öğretmenlerin ve ebeveynlerin işbirliği içinde çalışmaları gerekmektedir. Ebeveynlerin matematik etkinliklerine katılımları çocukların matematiksel gelişimlerine katkı sağlamaktadır. Ebeveynlerin matematik etkinliklerine katılımlarının yanı sıra ebeveynlerin matematik inançları da çocukların matematiksel gelişimlerini etkilemektedir. Bu araştırmanın amacı Missall ve diğerleri (2015) tarafından geliştirilen ve orijinal adı “Early Math Questionnaire” olan Erken Matematik Ölçeği’ni Türkçeye uyarlamak ve ölçeğin geçerlik ve güvenirliğini test etmektir. Araştırmanın çalışma grubunu okul öncesi dönemde çocuğu olan ve araştırmaya gönüllü olarak katılan 205 ebeveyn oluşturmuştur. Erken Matematik Ölçeği’nin orijinali, Matematik Etkinlikleri ve Matematik İnançları olmak üzere iki bölümden oluşmaktadır. Yapılan Doğrulayıcı Faktör Analizi (DFA) sonucunda Matematik Etkinlikleri Bölümünün dört alt boyut ve 36 maddeden oluştuğu bulunmuştur. Ölçeğin Matematik Etkinlikleri Bölümünün genel Cronbach Alfa (α) ve McDonald Omega (ω) güvenirlik katsayıları sırasıyla .966 ve .988 olarak bulunmuştur. Matematik İnançları Bölümünün iki alt boyut ve sekiz maddeden sekiz maddeden oluştuğu bulunmuştur. Ölçeğin Matematik İnançları Bölümünün genel Cronbach Alfa (α) ve McDonald Omega (ω) güvenirlik katsayıları sırasıyla .842 ve .883 olarak bulunmuştur. Bu sonuçlar Erken Matematik Ölçeği’nin Türkçe formunun geçerli ve güvenilir bir ölçme aracı olduğunu göstermektedir.

Exploring opportunities for math learning within parent–infant interactions

AbstractChildren's mathematical knowledge at school entry varies considerably and predicts long‐term achievement outcomes. Differences in children's exposure to math and number talk at home may help to explain variations in school‐entry math ability. However, nearly all research on exposure to math and number talk has been conducted with parents and preschool‐aged children. This longitudinal study examined to what extent parents talk about math with their 10‐, 14‐ and 18‐month infants during play. Additional analyses examined factors to explain variation in parent math talk at the family level (socio‐economic status), parent level (beliefs about children's mathematical development) and child level (gender). Transcripts of dyadic play sessions were coded for references to numbers and math concepts (e.g., first, many, more). It was found that parents do talk about numbers and math concepts with infants, albeit rarely, and such language increases in frequency and complexity over time. Parents use more statements than questions about math, and most often reference small‐number terms (1–3). Neither socio‐economic status nor beliefs were predictive of parental math talk. However, parents used significantly more math references over time with boys than girls. The results are discussed in terms of the importance of social interactions during infancy in fostering children's mathematical knowledge.

ВЗАИМОДЕЙСТВИЕ ПЕДАГОГОВ И РОДИТЕЛЕЙ В СОВЕРШЕНСТВОВАНИИ МАТЕМАТИЧЕСКОГО РАЗВИТИЯ ДОШКОЛЬНИКОВ

The relevance of the study of the interaction of kindergarten and family in the mathematical development of preschoolers is due to the fact that the unification of the family and kindergarten in one educational space implies the cooperation of teachers and parents. The mathematical development of preschool children will be successful if the teacher interacts with parents. Only cooperation between the kindergarten and the family can ensure the effectiveness of educational activities in the mathematical development of a preschool child. It is necessary to select the forms and methods of organizing this interaction, taking into account the age characteristics of children and the settings of the Federal State Educational Standard (complex tasks, integration of different types of activities, individualization of the child's mathematical development, etc.) in the mathematical development of preschool children. The work of a preschool teacher on the mathematical development of children is particularly time-consuming and requires a lot of pedagogical attention. Mathematical knowledge of preschoolers, such as counting down to ten in ascending and descending order; the ability to recognize numbers in a row and randomly, quantitative (one, two, three...) and ordinal (first, second, third...); to study and present the basic geometric shapes (triangle, square, circle, and others); the basic forms of measurement: the ability to measure length, volume, width, height using a conditional measurement measure; comparison of objects: heavier-lighter, larger-smaller, wider-narrower, higher-lower; the ability to navigate in space and time, etc., will later be the basis for school education.

Falling into line

In extracts taken from her new book, Di Chilvers considers how children's mathematical development unfolds through play and exploration from birth

Використання системи “контролю помилкиˮ за методом Марії Монтессорі в дидактичних матеріалах з формування елементарних математичних уявлень у ЗДО

The article describes one of the Montessori methods known as the system of “error controlˮ in educational materials used for the formation of mathematical concepts in preschool education. The topic is relevant, because at the development of preschool education a special focus is on the logical and mathematical development of children. Mathematical knowledge and skills are the main factors necessary for knowledge of the world around us and life in it. The main educational tasks for the development of mathematical concepts are: the sensory development, logical and mathematical concepts developent, mathematical actions performed by children (arithmetics, measurement, the simplest calculations). Therefore, the logical and mathematical development of children is one of the key elements in the education of personality. The article describes issues of inaccessibility of didactic Montessori materials in Ukrainian preschool education, lack of research in this area, incorrect use of methods of encouragement and evaluation in preschool education. The emphasis of the article is that the method of Maria Montessori is quite popular in the educational space, thus there is a need for new research of the principles of education and training, in particular “the error controlˮ. It gives children the opportunity to independently control their actions and evaluate the result. Each activity of children in educational institutions should be evaluated by a teacher or independently by the children themselves. This concept is known as self-assessment, when students independently assess their activities and capabilities. Formative assessment is described as interactive assessment of the level of students’ knowledge. Montessori materials for the development of students’ math competence are helpful in practical actions and contribute to the development of independence and the ability of co-leadership. The formation of self-assessment ability is a priority in preparing the child for school. Thus, the use of the formative assessment at preschool education is one of the key elements in ensuring education quality. Keywords: Maria Montessori, error control, self-assessment, assessment methods, formative assessment.

Preparation of future educators of preschool institutions for logical and mathematical development of children

Preparation of future educators of preschool institutions for logical and mathematical development of children

Teachers’ knowledge of children’s mathematical development

This research was conducted due to the importance value of mathematics for early childhood and the fact some researches showed the early childhood education (ECE) teachers' low level of basic mathematical knowledge, especially the one related to childhood developmental stages. The participants of this research were 35 ECE teachers from one of the cities in West Java province with teaching experience approximately ten years. In this research, 30 minutes was given to the participants to solve 20 questions, which tested teachers' knowledge related to verbal counting sequence, counting, the ordinal number of words, addition/subtraction, divisions of sets, written number symbols, and words. Besides, the interview was conducted to get more in-depth information from the participants. The quantitative descriptive analysis was used to identify the frequency, percentage, mean value, and standard deviation. The result of the research showed that ECE teachers had limited knowledge of children's mathematical development. It was revealed by the result of the mean value of the teachers’ responses, which were only 33% correct answers and 16% no idea answers. This result can become input for the stakeholders to hold a professional development program which aims to increase the quality of ECE teachers related to mathematical development activity.

The Implicit Contribution of Fine Motor Skills to Mathematical Insight in Early Childhood.

Understanding number magnitude is an important prerequisite for children’s mathematical development. One early experience that contributes to this understanding is the common practice of finger counting. Recent research suggested that through repeated finger counting, children internalize their fingers as representations of number magnitude. Furthermore, finger counting habits have been proposed to predict concurrent and future mathematical performance. However, little is known about how finger-based number representations are formed and by which processes they could influence mathematical development. Regarding the emergence of finger-based number representations, it is likely that they result from repeated practice of finger counting. Accordingly, children need sufficient fine motor skills (FMS) to successfully count on their fingers. However, the role that different types of FMS (such as dexterity and graphomotor skills) might play in the development of finger-based number representations is still unknown. In the current study, we investigated (a) whether children’s FMS (dexterity and graphomotor skills) are associated with their emerging finger-based number representations (ordinal and cardinal), (b) whether FMS explain variance in children’s finger-based number representations beyond the influence of general cognitive skills, and (c) whether the association between FMS and numerical skills is mediated by finger-based representations. We tested associations between preschool children’s (N = 80) FMS (dexterity and graphomotor skills), finger-based number representations, and numerical skills. Furthermore, visuo-spatial working memory and nonverbal intelligence were controlled for. Dexterity was related to children’s finger-based number representations as well as numerical skills after controlling for chronological age, but not after also controlling for cognitive skills. Moreover, the relationship between dexterity and numerical skills was mediated by finger-based number representations. No such associations were observed for graphomotor skills. These results suggest that dexterity plays a role in children’s development of finger-based number representations, which in turn contribute to their numerical skills. Possible explanations are discussed.

The impact of the Promoting Early Number Talk project on the development of abstract representation in mathematics

ABSTRACTIt is widely acknowledged that the transition from informal, everyday knowledge to formal, school-taught knowledge is a critically important stage in children's mathematical development. Research highlights the importance of making connections between the different representations of mathematics and the value of children's own mathematical graphics in bridging the gap between the concrete and the abstract. The Promoting Early Number Talk project explored the effect of ‘Number Talk’ – a resource book to support the development of early number – on teaching and learning in five Year 1 primary school classes in Northern Ireland. This article investigates the impact of the project on the development of abstract representation in mathematics. Findings demonstrate an increased appreciation of the importance of social interaction and the potential value of children's own mathematical graphics. It is recommended that greater prominence is given to the development of children's own mathematical graphics both within curriculum policy and classroom practice.

Maternal cognitive guidance and early education and care as precursors of mathematical development at preschool age and in ninth grade

AbstractFinnish students' international success in mathematics has been largely explained by the high‐quality compulsory basic education system, while increasing evidence suggests that early childhood contexts can also promote development long before formal instruction begins. This study examined, in a sample of 66 mother–infant dyads, 2 early contextual precursors of later mathematical development at preschool age and at the end of comprehensive school. The path analyses showed that maternal autonomy support and scaffolding observed during joint play interactions in infancy, and time spent in various care contexts beyond infancy contributed more to variation in numerical skills than spatial skills tested at preschool age. Maternal autonomy supportive behaviours were related to differences in mathematics and other school grades collected in ninth grade, even after controlling for time spent in various care contexts. Moreover, joint play interactions mediated the relation between mothers' education and children's mathematical outcomes. The findings are discussed in relation to why early developmental contexts can provide an advantageous base for children's mathematical achievement in a society with a high‐quality education system.Highlights Does the quality of mother–infant interaction and amount of early childhood education and care beyond infancy predict children's mathematical development? Mothers' cognitive guidance observed during play predicted children's mathematics skills tested at preschool and assessed by teachers at 9th grade. Autonomy support and scaffolding in early developmental contexts can have far‐reaching influences on children's motivation and school achievement.

Does Early Mathematics Intervention Change the Processes Underlying Children's Learning?

ABSTRACTEarly educational intervention effects typically fade in the years following treatment, and few studies have investigated why achievement impacts diminish over time. The current study tested the effects of a preschool mathematics intervention on two aspects of children's mathematical development. We tested for separate effects of the intervention on “state” (occasion-specific) and “trait” (relatively stable) variability in mathematics achievement. Results indicated that, although the treatment had a large impact on state mathematics, the treatment had no effect on trait mathematics, or the aspect of mathematics achievement that influences stable individual differences in mathematics achievement over time. Results did suggest, however, that the intervention could affect the underlying processes in children's mathematical development by inducing more transfer of knowledge immediately following the intervention for students in the treated group.

A Strengths Approach to Supporting early Mathematics Learning in Family Contexts

EARLY CHILDHOOD PROFESSIONALS ARE increasingly being asked to work with children and families using strengths approaches1. However, what does this mean for working with families to support children's mathematical development? Specifically, how can this approach support and engage families, including those who may disengage from their child's mathematics education? This article aims to introduce a strengths framework for supporting children's mathematics learning opportunities in family and community contexts. We apply a Strengths Approach (McCashen, 2005) to an example from an early childhood mathematics program called Let's Count. Let's Count was designed as a means of assisting families to help their young children (aged three to five years) play with, investigate and learn mathematical ideas (Perry & Gervasoni, 2012). Using examples of case studies from Let's Count, we use McCashen's (2005) five-column strengths framework to present ways in which early childhood professionals can support families to explore mathematics with their children, using the unique everyday resources and opportunities of each family.

Understanding and processing numbers among Chinese children.

children learn mathematics using a user-friendly, regular number naming system. Such a number naming system has been suggested to facilitate Chinese children's mathematical development. Recent studies investigated how Chinese children, with such a language advantage, understand and process Arabic numerals. These studies consistently indicate that Chinese children become able to process numerals proficiently and automatically and make sense of the place-value Arabic number system in the first grade, and children who fail to do so are apt to encounter difficulties in later mathematical learning. Moreover, recent findings show that Chinese children with mathematical difficulties have deficits in number-fact retrieval and the place- value concept. These studies prompted the first steps to explore Chinese children's number processing and understanding. Yet, further studies are needed to provide a complete picture of how Chinese children process and understand numerals using a user- friendly number naming system. Keywords: numbers, mathematics, Chinese.

Children’s Mapping between Non-Symbolic and Symbolic Numerical Magnitudes and Its Association with Timed and Untimed Tests of Mathematics Achievement

The ability to map between non-symbolic numerical magnitudes and Arabic numerals has been put forward as a key factor in children’s mathematical development. This mapping ability has been mainly examined indirectly by looking at children’s performance on a symbolic magnitude comparison task. The present study investigated mapping in a more direct way by using a task in which children had to choose which of two choice quantities (Arabic digits or dot arrays) matched the target quantity (dot array or Arabic digit), thereby focusing on small quantities ranging from 1 to 9. We aimed to determine the development of mapping over time and its relation to mathematics achievement. Participants were 36 first graders (M = 6 years 8 months) and 46 third graders (M = 8 years 8 months) who all completed mapping tasks, symbolic and non-symbolic magnitude comparison tasks and standardized timed and untimed tests of mathematics achievement. Findings revealed that children are able to map between non-symbolic and symbolic representations and that this mapping ability develops over time. Moreover, we found that children’s mapping ability is related to timed and untimed measures of mathematics achievement, over and above the variance accounted for by their numerical magnitude comparison skills.