Early Mathematical Skills Research Articles

An Analysis of The Effects of The Early Mathematics Intervention Program on Early Mathematics Skills of Pre-School Children at Risk

Supporting all children, particularly children with special needs, in the field of mathematics is important for their development. Therefore, it is necessary to develop and implement the necessary early intervention programs in relation to mathematics education. Studies indicate that early mathematics education intervention programs provide an increase in children’s mathematical knowledge levels improving their mathematics performance. It is also reported that such programs are effective in increasing the mathematical achievement of children at risk and that their effects may last for a longer time. Therefore, it is considered important to support the mathematics skills of the children in the risk group with early mathematics intervention programs, to identify the children whose mathematical skills are deficient or who have not acquired these skills sufficiently in the early period. In this study the is aim to reveal the effectiveness of an intervention program developed in relation to the early mathematics skills to improve such skills of children in the pre-school period between 60-72 months of age, who are in the risk group in terms of mathematics skills. In this study, the multiple probe model inter-subjects, which is one of the single-subject research models, was used. The participants of the study were three kindergarten students from three different schools in Kırşehir, Türkiye. The study was carried out in the special education center located in the said city. The data collection tool is an early mathematics intervention program developed for teaching early mathematics skills. When we look at the findings obtained from the study in general, it appears that the early mathematics intervention program was effective in improving the early mathematics skills of all three students. For this reason, priority should be given to supporting the development of early mathematics skills in all children attending pre-school education institutions.

Implementation of a Scale-Up Model in Early Childhood: Long-Term Impacts on Mathematics Achievement

A follow-up of a cluster-randomized trial evaluated the long-term impacts of a scale-up model composed of 10 research-based guidelines grounded in learning trajectories. Two treatment groups received the intervention during the prekindergarten year, and one of these groups received follow-through support in kindergarten and first grade. Business-as-usual curricula were used in all other cases, including all years for the control group. Early effects on mathematics achievement decreased through fourth grade but reemerged at fifth grade. These results support both a latent trait hypothesis, whereby stable characteristics of students explain differences in achievement, and a latent foundation hypothesis, whereby early mathematical knowledge and skills provide a foundation for competence in mathematics in later years, especially those that involve challenging mathematics.

Teaching Early Mathematical Skills to 3- to 7-Year-Old Children — Differences Related to Mathematical Skill Category, Children’s Age Group and Teachers’ Characteristics

This study explored teaching early mathematical skills to 3- to 7-year-old children in early childhood education and care (ECEC) and pre-primary education. Teachers in ECEC (N = 206) answered a web survey. The first aim was to determine whether teaching frequency or pedagogical awareness of teaching early mathematical skills varied according to the category of skills (numerical skills, spatial thinking skills and mathematical thinking and reasoning skills) and whether children’s age group moderated these differences. The second aim was to explore to what extent teacher-related characteristics and children’s age group explained variations in teaching frequency concerning early mathematical skills. Results from repeated MANOVAs demonstrated that the frequency and pedagogical awareness of teaching early mathematical skills depended on the skill category and that children’s age group moderated these differences. In 5- to 6-year-olds and 6- to 7-year-olds, numerical skills were taught more often than spatial thinking skills, whereas in 3- to 5-year-olds, they were taught as frequently. In all age groups, mathematical thinking and reasoning skills were taught the least. Pedagogical awareness was lowest in teaching spatial thinking skills in all age groups, but only in 6- to 7-year-olds was teachers’ pedagogical awareness in teaching numerical skills higher than in the two other categories. According to a univariate analysis of variance, pedagogical awareness and mathematics professional development programmes were strongly associated with teaching frequency in all skill categories. The results emphasise that children’s opportunities to learn early mathematical skills depend on teachers’ characteristics.

Cross-lagged relationship between home numeracy practices and early mathematical skills among Chinese young children.

The present study examined the cross-lagged relationship between home numeracy practices (e.g., formal teaching, number games, and number application) and early mathematical skills (basic number processing, and arithmetic skills) among Chinese young children. A total of 155 children (82 boys; mean age = 67.49 months, SD = 3.58 months) were assessed with basic number processing and arithmetic skills at three timepoints during the kindergarten year, and their parents reported the frequency of parent-child numeracy activities. Main results from random-intercept cross-lagged panel models showed that, at the within-family level, earlier basic teaching activities uniquely predicted subsequent basic number processing, while both advanced teaching activities and number game activities at earlier timepoints predicted the following arithmetic skills. These results indicated a unidirectional effect from home numeracy practices on early mathematical skills during the early years.

Small number enumeration processes of deaf or hard-of-hearing students: A study using eye tracking and artificial intelligence.

Students who are deaf or hard-of-hearing (DHH) often show significant difficulties in learning mathematics. Previous studies have reported that students who are DHH lag several years behind in their mathematical development compared to hearing students. As possible reasons, limited learning opportunities due to a lesser incidental exposure to numerical ideas, delays in language and speech development, and further idiosyncratic difficulties of students who are DHH are discussed; however, early mathematical skills and their role in mathematical difficulties of students who are DHH are not explored sufficiently. In this study, we investigate whether students who are DHH differ from hearing students in their ability to enumerate small sets (1–9)—an ability that is associated with mathematical difficulties and their emergence. Based on a study with N = 63 who are DHH and N = 164 hearing students from third to fifth grade attempting 36 tasks, we used eye tracking, the recording of students' eye movements, to qualitatively investigate student enumeration processes. To reduce the effort of qualitative analysis of around 8,000 student enumeration processes (227 students x 36 tasks), we used Artificial Intelligence, in particular, a clustering algorithm, to identify student enumeration processes from the heatmaps of student gaze distributions. Based on the clustering, we found that gaze distributions of students who are DHH and students with normal hearing differed significantly on a group level, indicating differences in enumeration processes, with students who are DHH using advantageous processes (e.g., enumeration “at a glance”) more often than hearing students. The results indicate that students who are DHH do not lag behind in small number enumeration as compared to hearing students but, rather, appear to perform better than their hearing peers in small number enumeration processes, as well as when conceptual knowledge about the part-whole relationship is involved. Our study suggests that the mathematical difficulties of students who are DHH are not related to difficulties in the small number enumeration, which offers interesting perspectives for further research.

The home mathematics environment of dual-language learning children and their early mathematics skills

The home mathematics environment (HME) can foster children’s mathematics skills. Little is known about this association for children from culturally diverse backgrounds. Using Head Start FACES dataset we categorize children into three groups: English monolingual (n = 949); Spanish-speaking Dual Language Learners (DLLs) fluent in English (n = 346); and Spanish-speaking DLLs not-yet-fluent in English (n = 192), to examine whether the HME is related to children’s early mathematics abilities above and beyond their vocabulary skills. Using multi-group analyses with a structural equation-modeling framework, we found that measurement invariance test supports the factorial equivalence of HME construct between groups. However, while HME positively and significantly predict children’s mathematics skills for the English monolingual group, HME did not significantly predict mathematics skills among the Spanish-speaking DLL groups regardless of their English proficiency. We discuss our findings in relation to the need for additional HME items that are sensitive to diverse cultural contexts.

Preschool Classroom Libraries in Turkey: Are They Used to Support Early Mathematics Skills?

The two studies in this paper considered the use of the classroom library as a means of socializing mathematics development in Turkish preschoolers. Study 1 (n = 80) documented whether classes had a library, its contents, and whether/how teachers encouraged children to use the library. Study 2 (n = 47) investigated the teachers’ confidence in teaching mathematics and the means that they used. Both studies used online surveys that were distributed via social media sites. There were four noteworthy findings. One, the Turkish preschool teachers reported viewing mathematics instruction as important to the development of children and were confident in their abilities to teach their students mathematics. However, they relied upon their general knowledge of children and their general pedagogical knowledge, rather than on their knowledge of mathematics, to do so. Two, the preschool teachers in Turkey had classroom libraries that they encouraged their students to use by having a set library time each day and by modeling how to sit and read in the library. They also encouraged family involvement in reading. However, these classroom libraries had fewer mathematics books than other types of texts. Three, while libraries were consistently present in Turkish preschool classrooms, they were not seen as venues for children’s mathematics development. Four, preschool mathematics instruction in Turkey appears typically to use whole groups and explicit instruction, and particularly during circle time/the morning meeting.

The Effects of the Mathematics Education Program Supported by Stories on the Mathematical Skills of 48'60-Month-old Children

This study aims to develop a mathematics education program supported by stories for 48–60-month-old children attending pre-school education institutions and examine its effect on children's early mathematics skills. The study group consists of 48–60-month-oldchildren who continue pre-school education in an independent kindergarten affiliated with the Ministry of National Education in Usak province, in 2020-2021.The study was carried out with 33 children, 18 in the experimental and 15 in the control group. A pretest-posttest quasi-experimental design with a control group was used in the study. Test of Early Mathematics Ability -3 (TEMA-3), developed by Ginsburg and Barody, was used to collect data. The test's adaptation, validity, and reliability to 48-60-month-old Turkish children had been conducted by Seker (2013). Regarding data collection, TEMA-3 was administered as a pre-test to the experimental and control group students before implementing the program. After the pre-test, the "Mathematics Education Program Supported by Stories" was instructed to the experimental group three (3) days a week for eight (8) weeks. During the implementation, "Mathematics Education Program Supported by Stories" was instructed to the children in the experimental group by the researcher; the daily education flow specified in the 2013 Pre-School Education Program was continued for the control group children. The data obtained from the research were analyzed with the SPSS statistical program. Independent and dependent t-tests were used to test the difference between the pre-test and post-test between and within groups. Based on the findings obtained from the analyzes, there was no significant difference between the pre-test scores. However, there was a significant difference between the post-test scores in favor of the experimental group. It was concluded that the mathematics education program supported by stories effectively improved children's mathematics skills.

A Pilot Study on the Effectiveness of Kindergarten Games to Enhance Mathematical Skills

Adaptive serious mathematical games in kindergarten were used to investigate whether kindergarteners could grasp mathematics topics. A pretest–posttest-follow up design with two conditions. (Condition 1 educational kindergarten games on the computer, focusing on counting and comparison, Condition 2 educational kindergarten games on the computer, focusing on memory, counting and comparison) and one active control group (playing educational kindergarten games without mathematical content) was set up dealing with 45 preschoolers with a mean age of 68.78 months (SD = 4.46). Children were matched in kindergarten on their early mathematical and language skills as well as on their intelligence before the interventions took place. The study revealed that playing mathematical games in kindergarten had the potential to enhance the early mathematical skills. Children with initial weak mathematical skills in kindergarten caught up with their average performing peers, pointing to the importance of serious numerical games as “opportunities” in kindergarten. Both boys and girls benefitted, with a sustained effect in grade 1, revealing promising potential effects of offering opportunities to focus on mathematics even in very young children.

The role of parent-led and child-led home numeracy activities in early mathematical skills

Existing studies have shown mixed evidence for the role of the home numeracy environment (HNE) in supporting children’s early numeracy skills. To address some of the limitations of the existing literature, the present study used a multi-method approach to assess the parent-led HNE. Parents of children aged 3–5 years completed a questionnaire to assess the frequency of engagement in home numeracy activities and parent and child number talk was coded from play-based observations to assess the quality of engagement. This study also assessed the role of child-led home numeracy activities, including child number talk and Spontaneous Focusing on Numerosity (SFON) on early numeracy skills. Children (n = 164) were assessed on six early number skills (counting, cardinal knowledge, ordering skills, digit naming, arithmetic and symbolic to non-symbolic number mapping). Parent-led activities (questionnaire-assessed HNE activities and parent number talk) were not significantly associated with the composite of these six numeracy skills. There was also no significant association between parent-reported frequency of engagement in HNE activities and parent number talk. Child-led skills (SFON and child number talk) were not significantly associated with the composite numeracy score. Children’s and parents’ use of cardinal number talk was associated with children’s performance on the cardinality task, although associations were small (rs =.22 to.31). This study adds further moderate evidence that parent-led home numeracy activities may not be associated with overall early numeracy skills, and we consider next steps for researchers seeking to understand the role of the HNE.

Differences in Students' Mathematical Communication Ability and Self-Efficacy Between Open Ended and Contextual Learning Approach

This study aims to: (1) differences in students' mathematical mathematical communication skills and self-efficacy between students who were given an Open Ended Learning Approach with a Contextual Teaching and Learning Approach; (2) the interaction between KAM and the Open Ended Learning Approach and Contextual Teaching and Learning Approach on Mathematical Communication skills; (3) the difference in Self Efficacy between students who were given an Open Ended Learning Approach and a Contextual Teaching and Learning Approach; and (4) the interaction between KAM and the Open Ended Learning Approach and Contextual Teaching and Learning Approach on Self Efficacy. This research is a quasi-experimental research. The research population was all students of class VIII SMP Negeri 1 Stabat, Academic Year 2021/2022 with a sample of class VIII A who was given an Open-Ended Learning Approach and class VIII B who was given a Contextual Teaching and Learning approach. Each class consists of 32 students. The research instrument used was a student's Mathematical Communication ability test and a Self-Efficacy questionnaire. Data analysis was performed by two-way analysis of variance (ANAVA). The results of the study indicate that: (1) There are differences in students' Mathematical Communication abilities who are given learning with the Open Ended Learning Approach and Contextual Teaching and Learning Approach; (2) There is no interaction between the learning model and early mathematics skills on students' Mathematical Communication abilities; (3) There is a difference in Self Efficacy between students who are given an Open Ended Learning Approach and a Contextual Teaching and Learning Approach; (4) There is no interaction between the learning model and the initial ability of mathematics on Self Efficacy. Keywords: Mathematical Communication, Self Efficacy, Open-Ended Approach, Contextual Approach DOI: 10.7176/JEP/13-7-03 Publication date: March 31 st 2022

Mathematical skills of 11-year-old children born very preterm and full-term

Preterm birth affects the academic development of children, especially in mathematics. Remarkably, only a few studies have measured specific effects of preterm birth on mathematical skills in primary school. The aim of this study was to compare 11-year-old children, with an IQ above 70, born very preterm (N = 64) and full-term (N = 72) on a variety of 5th grade mathematical skills and cognitive abilities important for mathematical learning. The measures were spontaneous focusing on numerosity (SFON), spontaneous focusing on quantitative relations (SFOR), arithmetic fluency, mathematics achievement, number line estimation, rational number magnitude knowledge, mathematics motivation, reading skills, visuospatial processing, executive functions, and naming speed. The children born very preterm and full-term differed in arithmetic fluency, SFON and SFOR. Domain general cognitive abilities did not fully explain the group differences in SFON and SFOR. Retrospective comparisons of the samples at the age of five years showed large group differences in early mathematical skills and cognitive abilities. Despite lower early mathematical skills, the children born very preterm reached peer equivalent performance in many mathematical skills by the age of 11 years. Nevertheless, they appear less likely to focus on implicit mathematical features in their everyday life.

Relating mathematical abilities to numerical skills and executive functions in informal and formal schooling

BackgroundThe current evidence on an integrative role of the domain-specific early mathematical skills and number-specific executive functions (EFs) from informal to formal schooling and their effect on mathematical abilities is so far unclear. The main objectives of this study were to (i) compare the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities between preschool and primary school children, and (ii) examine the relationship among the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities among preschool and primary school children.MethodsThe current study recruited 6- and 7-year-old children (Ntotal = 505, n6yrs = 238, and n7yrs = 267). The domain-specific early mathematics as measured by symbolic and nonsymbolic tasks, number-specific EFs tasks, and mathematics tasks between these preschool and primary school children were compared. The relationship among domain-specific early mathematics, number-specific EFs, and mathematical abilities among preschool and primary school children was examined. MANOVA and structural equation modeling (SEM) were used to test research hypotheses.ResultsThe current results showed using MANOVA that primary school children were superior to preschool children over more complex tests of the domain-specific early mathematics; number-specific EFs; mathematical abilities, particularly for more sophisticated numerical knowledge; and number-specific EF components. The SEM revealed that both the domain-specific early numerical and the number-specific EFs significantly related to the mathematical abilities across age groups. Nevertheless, the number comparison test and mental number line of the domain-specific early mathematics significantly correlated with the mathematical abilities of formal school children. These results show the benefits of both the domain-specific early mathematics and the number-specific EFs in mathematical development, especially at the key stages of formal schooling. Understanding the relationship between EFs and early mathematics in improving mathematical achievements could allow a more powerful approach in improving mathematical education at this developmental stage.

Content-rich instruction and cognitive demand in prek: using systematic observations to predict child gains

Currently available measures of PreK classroom quality inconsistently predict gains in children's outcomes. Extant measures may not capture the full range of instructional practices—including the degree to which children are exposed to rich content and cognitively demanding instruction—that are important for supporting the development of early language and mathematics skills. The current study leverages data from systematic observations of classrooms (N = 51) in public schools and community-based organizations implementing the Boston Public Schools prekindergarten program to create reliable measures of content-rich instruction and cognitive demand and explore associations between these constructs and gains in children's (N = 378) language and mathematics skills during PreK. Findings from descriptive analyses revealed that classrooms used content-rich and cognitively demanding practices at moderate levels, and classrooms with higher levels of intervention fidelity generally used higher-quality practices. Classrooms with higher percentages of Black students scored lower on observed cognitive demand. Results from multi-level models revealed that content-rich instruction consistently predicted gains in mathematics skills. There were stronger, positive associations between both content-rich instruction and cognitive demand and gains in mathematics skills for children who started the year with stronger mathematics skills. Neither of the constructs predicted gains in language skills. There was no consistent evidence that associations between either of these constructs and gains in mathematics and language skills varied by children's race/ethnicity, socioeconomic status, or home language. Findings demonstrate that further work to measure and provide supports for exposure to rich instructional content in PreK is warranted.

Early mathematical and receptive language skills of children from different socioeconomic levels: letter knowledge a mediator

ABSTRACT The purpose of this study was to investigate the relation between the early mathematic and receptive language skills while considering letter knowledge as a mediator. Participants included 357 children with a mean age of 64.5 months and their parents. Results suggest that letter knowledge mediates the relation between the early mathematic and receptive language skills. This study revealed the correlation between receptive language, letter knowledge, and early mathematical development, suggesting the need for mathematics to be taught in conjunction with language and early literacy skills to increase the gains out of these skills. Understanding the nature of how these skills relate will help identify children at risk of mathematical difficulties in future years, design individualised teaching activities, and improve the development of math curricula. This study also examined the impact of maternal education level on these three skills and found that children’s performance in these skills improved as mothers’ education level increased. In this context, this result can serve as an important indicator of the maternal education level, and for whom early intervention programmes should be planned and implemented.

Why do early mathematics skills predict later mathematics and reading achievement? The role of executive function

A robust association between young children’s early mathematical proficiency and later academic achievement is well established. Less is known about the mechanisms through which early mathematics skills may contribute to later mathematics and especially reading achievement. Using a parallel multiple mediator model, the current study investigated whether executive function (integration of working memory, inhibition, and cognitive flexibility) can explain the relations between early mathematics skills and elementary school mathematics and reading achievement. Data in this longitudinal study were collected from 243 children during the last year of early childhood education and care (kindergarten ages 5 and 6 years), 1 year later in first grade, and 5 years later when the children were in fifth grade. Background variables (maternal education, age, sex, and immigrant status), kindergarten baseline skills, and mediating effects of first-grade mathematics, phonological awareness, vocabulary, and possible omitted variables were controlled. Results showed that first-grade executive function mediated the effects of kindergarten mathematics on fifth-grade mathematics and on reading achievement. These findings suggest that executive function may work as a mechanism that may help to explain the frequently found strong association between children’s early mathematics skills and later mathematics and reading achievement.

Cross- and Within-Domain Associations of Early Reading and Mathematical Skills: Changes Across the Preschool Years.

Existing research has mainly examined the role of cognitive correlates of early reading and mathematics from a stationary perspective that does not consider how these skills unfold and interact over time. This approach constraints the interpretation of cross-domain associations and the specificity of domain-specific covariates. In this study, we disentangle the role of these predictors and investigate cross-domain associations between reading, math, and two related domain-specific predictors (phonological awareness and fluency with number sets) over the kindergarten years (n=512, Mage=54months, SDage=3.5, 52% females). Results reveal that the overlap between reading and math skills changes over development. Reciprocal associations between reading and math abilities are observed at earlier stages; then, reading abilities become the lead force. Findings also show that phonological awareness and fluency with number sets are domain-specific predictors that do not contribute to cross-domain gains in academic skills. Indeed, there is a trend for domain-specific skills to be more strongly related to achievement at the beginning of formal education than at the beginning of kindergarten, which suggests an increasing differentiation of domains over the kindergarten years. Such findings have implications for the timing and nature of interventions that aim to support children’s reading and mathematical development.

Effectiveness of the Big Math for Little Kids Program on the Early Mathematics Skills of Children with Risk Group

The aim of this study is to determine the effect of Big Math for Little Kids (BMLK) Program on the early mathematics skills of children with lower socioeconomic level. The participants of the study consist of between 60-72 months of aged children with lower socioeconomic level recruited to kindergartens of Ministry of National Education from Turkey in Diyarbakır in the 2018-2019 academic year. The sample of the study consists of 40 children with above mentioned characteristics. Of these, 20 were assigned to the experimental group and 20 to the control group. Two schools were selected for experimental and control group, and the study was conducted after selecting ten children in a class of each school. In the study pretest-posttest with control group experimental model was used. The data of the study were collected through the Tests of Early Language Development Test (TELD-3) to determine children with adequate language skills of their own age group, and Test of Early Mathematical Ability (TEMA-3) to assess early mathematical development of children. As a result, BMLK program was determined to be effective in the mathematics development of children with lower socioeconomic level. Keywords: early mathematics

Foundations for early mathematics skills: The interplay of approximate number system, mapping ability, and home numeracy activities

This study investigated the conceptual framework of how approximate number system (ANS), mapping ability, and home numeracy activities together contribute to the development of children’s early mathematics skills. Participants were 110 children (58 boys) and their mothers. Children were individually tested on ANS, and their mothers completed the questionnaire of home numeracy activities. One year later, children were administrated the test of intelligence, a test of mapping ability, and the Test of Early Mathematical Ability-3 (TEMA-3). Results indicated that ANS and home numeracy activities directly predicted informal mathematics skills and indirectly predicted formal mathematics skills through mapping ability.

Effect of coding activities on preschool children's mathematical reasoning skills.

The present study was conducted to investigate the effect of coding activities on children’s mathematical reasoning skills. In the study, the pre-test – post-test control group quasi-experimental design was used. The participants of the study consisted of 29 children (17 in experiment group and 12 in control group) aged between 57 – 68 months attending a public kindergarten in Adana, Turkey. Coding Education Program prepared by the researchers was administered to the children in the experiment group while the children in the control group received the regular program. Evaluation Instrument for the Early Mathematical Reasoning Skills was administered to children both in the experimental and control group as pre-test and post-test. Data was collected by individual interviews conducted with the children. Results of the study showed that there is no significant difference between experimental and control group in the pre-test, whereas a significant difference in favor of the experimental group was observed in the post-test. Therefore, it was determined that the coding activities have a significant effect on mathematical reasoning skills of children.