Early Mathematics Research Articles

Problem-Solving Skills, Memory Power, and Early Childhood Mathematics: Understanding the Significance of the Early Childhood Mathematics in an Individual’s Life

Problem-Solving Skills, Memory Power, and Early Childhood Mathematics: Understanding the Significance of the Early Childhood Mathematics in an Individual’s Life

Can peers help sustain the positive effects of an early childhood mathematics intervention?

Our study assessed whether the peer environment in kindergarten and first grade affected student learning following an early mathematics intervention. We leveraged longitudinal data from a cluster-RCT to examine whether math achievement in kindergarten (n = 1,218) and first grade (n = 1,126) was affected by either the share of high-achieving classmates or the proportion of classroom peers who received a preschool math curriculum intervention. Analyses indicated that exposure to treated peers in first grade, but not kindergarten, was significantly associated with small gains in end-of-year achievement. Some analyses also suggested that average peer math achievement was positively related to children's kindergarten and first-grade achievement across conditions, though these results were less robust. We did not find consistent evidence to suggest that the proportion of treated peers coincided with better teaching practices. Taken together, these findings suggest that classroom peer effects may play only a limited role in sustaining early intervention effects.

Early Childhood Mathematics Curriculum in the light of the standards of the National Council of Mathematics Teachers

Early Childhood Mathematics Curriculum in the light of the standards of the National Council of Mathematics Teachers

Pelaksanaan Kemampuan Matematika Awal Melalui Pemanfaatan Media Konkrit Pada Anak Kelompok B Di Tk Xaverius Kalianda

This research is motivated by the existence of conditions related to the early mathematical ability is still low. Therefore it is necessary an effort to improve the mathematical ability of children in group B in TK Xaverius Kalianda. This study aims to know that the use of concrete media in learning can improve early mathematical ability in children group B in TK Xaverius Kalianda. This study is a classroom action research consisting of four stages namely, planning, action implementation, observation and reflection. At the beginning of observation of early group math ability in TK Xaverius Kalianda still not developed, as indicator of low early child mathematics ability in kindergarten, this can be seen from 15 children of group B which have progressed development especially in the case of early mathematics only 3 children or 20%, and the rest as many as 12 children or 80% have not been able to develop properly. After the reflection through the use of concrete media there is an increase. The results of this study indicate that through the utilization of concrete media can improve the early mathematical ability of the previously not developed at the time of pre-survey to start developing in the first cycle reached 72% and developed as expected in the second cycle reached 82%. Thus the method of utilizing concrete media can be one of the methods or ways that can be used in learning, especially in improving early math skills.

Best Practices in STEM Education for Preschool Children: A Case Study in Malaysia

Previous research has demonstrated that since 1967, the Malaysian government has set a target percentage rate of 60:40 for student involvement in the science stream compared to literature. This ratio policy has been followed throughout the national school system ever since. However, such a ratio appears to be impossible to maintain year after year. Therefore, the empowerment of science education needs to be explored from an earlier. This study was conducted to (i) explore best practices in Early Science in relation to the implementation of STEM activity in preschool; (ii) explore best practices in Early Mathematics in relation to the implementation of STEM activity in preschool; (iii) explore technology-assisted teaching tools in relation to the implementation of STEM activity in preschool; and (iv) explore engineering activity in relation to the implementation of STEM activity in preschool. This qualitative study employed a case study approach, with data triangulation based on interviews, observations, and document analysis serving as the exploratory method. This study was conducted independently in three Malaysian preschools in Perak and Selangor respectively, with four teachers and 39 children participating as study participants. ATLAS.ti version 8 software was used to generate, arrange, and organise the themes from the three research instruments described utilizing descriptive analysis with the flow of coding processes. The results show that there are nine STEM education best practices, with play-based learning being identified by participants the most frequently. Thus, this study's most significant contribution is the potential to bridge the gap between the Ministry of Education Malaysia's goals to advance STEM education globally, starting in the early years.

Using a lens of awareness in phenomenographic research: an example from early mathematics education research

ABSTRACT This paper aims to contribute to the advancement of methodological practice for phenomenographic research by introducing the notion of a lens of awareness, as a device that can enable researchers to zoom into the detail of the research process (the parts of the whole) and out again to the related context of a phenomenographic study (the whole). The lens enables researchers to embrace a reflexive stance to bracket prior assumptions, allowing critical inspection of the whole research process and a thorough retrospective and transparent account of the approaches used. We use a lens of awareness to communicate the component parts of a study that examined preschool children’s understandings of the use of numerals in everyday environments. Through an analytical documentation of processes and decisions, we examine challenges, the powerful affordances and application of a phenomenographic approach to research with young children. We discuss four strands of researcher awareness that we argue are important in the application of phenomenography: the nature of the phenomenon; the operationalization of phenomenographic theoretical notions; the researcher’s versus the participant’s experience of the phenomenon and the applied research processes. The paper closes with explorative strategies that may enhance transparency and trustworthiness in phenomenographic research.

The causal role of numerical and non-numerical order processing abilities in the early development of mathematics skills: Evidence from an intervention study

Understanding the basis of mathematical development is essential for supporting mathematics learning and to develop efficient interventions for remediating early problems. In the past decade, evidence has accumulated in support of the importance of ordering skills (i.e., tasks that tap into children's ability to recall the order of items or to judge the correctness of the order of items) in predicting early mathematics performance. Nevertheless, so far these studies have only provided correlational evidence, and intervention studies are lacking. The aim of the current study was to fill this gap by investigating the potential causal role of three types of ordering abilities (number ordering, daily event ordering and order working memory) in the development of mathematics skills during the first year of primary school. Children participated in six brief training sessions over a three-week period, and their mathematics skills and mathematics anxiety were measured before and after the training. In addition to the three training conditions, an active control group was also involved, with children completing reading comprehension exercises. Our findings showed that children's performance improved substantially on all ordering tasks as a result of training. Additionally, training in daily event ordering and number ordering has led to large increases in children's formal mathematics skills. Mathematics anxiety was not affected by the interventions. The current results provide initial evidence for the usefulness of order processing training in developing children's early mathematics skills. They also show that these results are not specific to the domain of numerical ordering.

Effects of a specific training program for early mathematics learning in early childhood education

Effects of a specific training program for early mathematics learning in early childhood education

신문 기사에 나타난 유아 수학에 대한 인식연구

Objectives In this study, the changes in interest and key words by period related to early childhood mathematics appeared in newspaper articles from January 1, 1990 to December 31, 2020 were examined.
 Methods For this purpose, 7,789 articles related to early childhood education were collected through ‘Big Kinds (www.bigKinds.or.kr)’. and 230 articles related to mathematics for earlychildhood were analyzed using buzz anal-ysis and topic modeling techniques.
 Results First, articles on early childhood education increased abou 13.7 times in the 3rd term compared to the 1st term, and articles related to early childhood mathematics increased 24 times in the 3rd term compared to the 1st term. As a result, it was confirmed that social interest in early childhood mathematics increased significantly. Secondly, the results of topic analysis by period: 1st period - ‘Early entry into elementary school’, ‘Establishment of early childhood public education’, 2nd period - ‘Early private education’, ‘Mathematics education approach’, 3rd period - ‘Mathematics and language’ ‘Relationship between mathematics’, ‘Mathematics education program’, and ‘Connectivity between mathematics and gifted education’ were selected as the main themes.
 Conclusions Through this, it was confirmed that social issues regarding early childhood mathematics changed by time, and there was a slight difference from social interest and research trends in academia.

Pierre Gassendi: Humanism, Science, and the Birth of Modern Philosophy

Pierre Gassendi: Humanism, Science, and the Birth of Modern Philosophy

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.

Validating a measure of growing pattern understanding in Chinese preschool children

Recent research has pointed to the importance of patterning skills in early mathematics development. However, there is a lack of psychometrically robust instruments to measure patterning skills, especially growing pattern understanding. In this study, we developed and validated an instrument assessing growing pattern understanding among preschool children. One hundred and thirty-eight preschoolers aged approximately five years in Hong Kong were assessed individually on 10 growing pattern items at two time points over a one-year period. Confirmatory factor analysis showed that a two-factor model (i.e., increasing and decreasing patterns) fit the data best in the second year of preschool (PS2), but a one-factor model (i.e., growing patterns) fit the data best in the third year (PS3). Scale reliability was adequate at both time points. At the item level, Rasch analysis showed that all the items were within an acceptable range of difficulty at both time points. Information curves also suggested that the test items provided the most information (i.e., having high reliability) at high ability levels at PS2 but were a sensitive measure for children of both low and high abilities at PS3. No differential item functioning was detected across boys and girls at PS2 or PS3. Also, expected relations were found between growing pattern understanding and children's performance on repeating patterns and English expressive vocabulary, supporting convergent and discriminant validity. Overall, the results suggest that the growing pattern task has sound psychometric properties and is appropriate for use in preschool children aged five and six years.

Teachers’ mathematics pedagogical content knowledge and quality of early mathematics instruction in Turkey

It is a well-known fact that societies today need to provide quality mathematics education to individuals from their early years in order to compete on a global scale. Although there is a growing interest in early mathematics, there are still some obstacles regarding quality mathematics instruction. Two of the most important obstacles are the mathematics pedagogical content knowledge (MPCK) and early mathematics teacher qualification of pre-school teachers. The purpose of this study was to evaluate the relationship between pre-school teachers’ classroom mathematics practices and their MPCK. The study included 55 pre-school teachers. Classroom Observation of Early Mathematics – Environment and Teaching (COEMET) was adapted into Turkish. The teachers’ MPCK was assessed using the Survey of Pedagogical Content Knowledge in Early Childhood Mathematics (SPECKECM). The results show that the teachers’ MPCK was at a medium level, being most successful regarding shapes and least in patterns. The COEMET scores were positively and statistically significantly correlated to the total score of the SPECKECM. Moreover, teachers’ pedagogical content knowledge (PCK) scores successfully predicted the total COEMET scores.

Early childhood student teachers engaging in a scenario-based professional program: The case of early mathematics

Early childhood student teachers engaging in a scenario-based professional program: The case of early mathematics

Validity and Reliability of Pre-Service Teacher Competency Level in Teaching Early Mathematics Instrument Using the Rasch Model

The Pre-Service Competency Teacher Level in Teaching Early Mathematics Instrument has been developed to measure the competency level and readiness to teach early mathematics in Preschool. This study was conducted to produce empirical evidence on the validity and reliability of this instrument by using the Rasch model. Surveys were conducted in three private universities that offer Early Childhood Education Programmes. A total of 85 pre-service teachers were selected as a sample of the study through simple random sampling. The validity and reliability of the instrument were measured using Rasch's model through Winstep software version 3.68.2. The findings of the unidimensionality test showed 46.1%. The Rasch analysis shows the person reliability index is 0.8 with a separation index is 2.05. The item reliability index is 0.91 and the separation index is 3.18. The item fitness analysis found 29 items in the instruments are in the valid range and one item that falls out of the allowed range. The finding showed that this instrument has a high degree of validity and reliability and can be used to measure the competency level of pre-service teaching in teaching early mathematics.

THE EFFECTS OF DISCOVERY-BASED LEARNING OF DIFFERENTIATED ALGEBRA CONTENT ON THE LONG-TERM KNOWLEDGE OF STUDENTS IN EARLY MATHEMATICS EDUCATION

One of the essential characteristics of knowledge that determines its quality is its durability. The durability of students' knowledge depends, among other things, on the quality of organization and implementation of teaching in the process of acquiring new knowledge, as well as reviewing and repeating old knowledge. More specifically, the durability of students' knowledge depends on the applied methodological approach and the students' activities in the classroom. The aim of this study was to examine the effects of discovery-based learning on differentiated algebra content on the long-term knowledge of students in early mathematics education. To achieve this goal, an experiment was conducted with parallel groups consisting of a sample of 261 fourth-grade students from primary schools. The experiment aimed to investigate whether the methodological approach to algebra instruction based on the principles of discovery learning and content differentiation yields better effects on the durability of students' knowledge compared to traditional learning methods. The results of the research showed that discovery-based learning on differentiated algebra content contributes to better knowledge durability overall and at each of the three achievement levels (basic, intermediate, and advanced).

Generalizability of the effectiveness of a preschool mathematics intervention for low-socioeconomic status Turkish children.

A socioeconomic status (SES)-related achievement gap in mathematics emerges in children from many countries before school entry, persists in primary school, and imposes challenges for education systems worldwide. In response, the United Nations' sustainable development goals include universal access to quality preschool education to support universal numeracy. A generalizability study of the effectiveness of an early mathematics intervention was conducted for low-SES Turkish preschool children (33 boys, 27 girls; Mage = 4.32). Classrooms were randomly assigned to treatment (Pre-K Mathematics) or control conditions. Children's early mathematical knowledge was assessed by the Child Math Assessment. A statistically significant positive impact was found (ES = 1.32). This indicates some generalizability of the intervention and supports the feasibility of using early intervention to achieve UN goals.

Addressing Language Diversity in Early Years Mathematics: Proposed Classroom Practices through a Live Brief Assessment

There is a growing emphasis on the role of language in teaching and learning mathematics, most significantly in classrooms with increased language diversity. Consequently, teachers face considerable challenges in accommodating diverse needs and must employ strategies to support all students. It is, therefore, crucial to provide prospective teachers with opportunities to enhance their pedagogical approaches while raising their awareness of the relationship between language and mathematics. In this respect, Live Brief assessments in Higher Education, which involve students working on authentic projects/tasks from a school, may be a promising avenue. This research draws on the 19 Live Brief group presentations prepared by a total of 118 Year 1 prospective primary school teachers, specifically focusing on the language-related challenges faced by a local school in early years mathematics. The data encompassed prospective teachers’ proposed practices, including one-to-one, small group and whole class activities, that aimed to address language diversity. Data analysis was informed by Moschkovich’s three perspectives on the relation between language and teaching and learning mathematics, namely lexicon, register and situated-sociocultural perspectives. While a lexicon perspective was commonly evident in the activities, the manifestation of a situated socio-cultural perspective mainly in the one–to-one activities is noteworthy, given its social and discursive nature. Three themes encapsulated a range of practices suggested in the findings: explicit vocabulary teaching, different strategies of scaffolding and utilising multi-sensory approaches. While the lexicon and register perspectives were commonly evident, the situated socio-cultural perspective was much less commonly manifested in the practices. We offer implications to initial teacher education curriculum, future research and policies about teaching and learning mathematics.

Exploring Chinese Early Childhood Teachers’ Mathematical Belief Profiles and Associated Teacher Characteristics

ABSTRACT Research Findings: This study explored the mathematical belief profiles of Chinese early childhood teachers and examined the associations with teacher characteristics. A total of 391 teachers completed the Early Childhood Teacher Mathematical Belief Scale, of which 36 teachers were interviewed to provide further information. The latent profile analysis identified three distinct mathematical belief profiles: (1) Constructivist profile, (2) Mixed high constructivist and traditional profile, and (3) Mixed low constructivist and traditional profile. Teachers with bianzhi, more than 15 years of teaching experience, and having received professional development in early math were more likely to adopt a Constructivist profile. Practice or Policy: The results showed there are intra-cultural variations in Chinese teachers’ beliefs about early math teaching and learning. This study highlights the need for early childhood teacher educators and policymakers to consider how to help teachers find an appropriate balance between western pedagogies and Chinese traditions.

What is the area of a pig? Problem posing and problem solving in early childhood education

Problem posing and problem solving serve as a crucial element of classroom instruction in early mathematics education, and have long been a topic of study of many practitioners and researchers. Used as a powerful tool for differentiation, they affect the ways in which the practice of mathematics is perceived by students and also help teachers gauge children’s understanding of concepts. In the student-centered approach, problem posing and problem solving can successfully engage students in creative educational situations. This research has been part of a broader design research project, the aim of which was to investigate the relationship between a classroom environment that allows for dialogue and young children’s propensity to design and solve their own tasks. Methodology included taking field notes and photographs, followed by reflection sessions. Turning young mathematicians into independent inquirers helped them gain authentic ownership of their knowledge. Additionally, it aided in the development of the young children’s competencies in effective engagement in problem posing activities. The toolbox of instructional techniques for problem posing in the classroom evolved, transforming mathematical classrooms into inquiry polygons for all learners.