Numbers are fundamental to mathematics; they play a crucial role in addressing everyday situations and challenges.  Understanding the concept of numbers has a crucial role in education, as it forms the basis for both real-life applications and effective learning. Piaget (1952) described that the number concept first develops by a one-to-one matching stage in which children pair objects with another object. This step is an introductory part of the number conservation. In the development of number conservation, a child knows that even if the position of the objects changes, two paired groups remain equal. Piaget (1952) highlighted that understanding the concept of numbers necessitates the capability to execute logical procedures like classification, seriation (arranging items by size or quantity), and one-to-one correspondence. It was also emphasized that children can actively build numerical understanding by exploring and engaging with the social environment. Thus, these findings significantly affect educational studies, particularly those related to numerical understanding. Investigating how children’s understanding of numerical quantities evolves with age and how this development relates to their mathematical abilities has become a major focus in educational research. 

Researchers characterize a child’s foundational understanding of numerical concepts and their relationships, making sense of operations, and having adaptable, flexible, and practical solutions to numerical situations as a concept of “number sense.” (Berch, 2005; NCTM, 2000; Yang, 2003; Yang & Lin, 2015). Number sense supports children in different aspects like being flexible, creative, and thinking mathematically (Yang & Wu, 2010; Yang, 2019), having powerful estimation and calculation skills (Greeno, 1991), and using numbers efficiently in daily life (Yang, 2005). Therefore, number sense has a great place in the educational studies (Reys & Yang, 1998).

The number sense concept was first used in NCTM’s report (1989) and characterized as understanding the meaning of numbers and relationships between them, identifying their relative sizes, grasping how operations affect numbers, and finding the correct reference point for measurement. Its significance was emphasized as “Instructional programs from prekindergarten to grade 12 should enable all students to (1) understand numbers, ways of representing numbers, relationships among numbers and number system; (2) understand meanings of operations and how they related to one another; (3) compute fluently and make reasonable estimates” (NCTM, 2000, p. 32). Furthermore, Yang and Wu (2010) proposed that number sense provides students with flexibility and logic, allowing them to use numbers and operations efficiently in daily life situations and think mathematically and logically. Therefore, number sense is an essential competency students should possess, and it plays a significant role in K-12 education (NCTM, 2000).

Over the years, although a significant amount of research has emerged concerning number sense that shows its importance for K-12 students, the literature still lacks a review of such studies. Only a few review studies (e.g., Acar & Peker, 2022; Sood & Mackey, 2014)  are encountered, but these studies have regional or contextual limitations. Number sense studies need to be reviewed from a global and international perspective. Thus, it can become possible to identify the trends in number sense studies, point out the gaps and potentials, chart the way for future research, and give a better understanding of how number sense is conceptualized and studied globally. Therefore, this study aims to examine studies that focused on number sense with K-12 students, indexed between 2015 and 2024 in the Web of Science (WoS) database.

Thus, the research question of this study:

How is the distribution of the “number sense” studies involving K-12 students indexed between 2015 and 2024 in the Web of Science (WoS) database regarding their publication years, research methods, sample region, school level, and research purpose?

This qualitative research examined studies on number sense with K-12 students indexed in the Web of Science (WoS) database. The Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) statement by Moher et al. (2009) was used in this study based on inclusion and exclusion criteria. PRISMA includes four steps (identification, screening, eligibility, and inclusion) to select documents for systematic literature review studies. On 17 December 2024, publications were scanned in the “education/educational research” category from the WoS database by setting the criteria as (“number* sense”) (Topic) or (“number* sense”) (Title) or (“number* sense”) (Abstract) and Article or Early Access (Document Types) and English (Languages) and 2024 or 2023 or 2022 or 2021 or 2020 or 2019 or 2018 or 2017 or 2016 or 2015 (Publication Years). A total of 171 articles were obtained. Since this research aims to examine number sense with K-12 students, 171 articles were examined by considering their sample group. Therefore, as a first step, studies that included samples other than K-12 were eliminated. Only articles to which the researcher’s institution had access were included in this study. Thus, a total of 108 studies were left. Then, these 108 studies were analyzed one by one according to their research focus and publication type. It was aimed to include research articles focusing mainly on the “number sense” concept. During this second elimination process, non-English articles, book chapters, literature reviews, position papers, non-empirical research studies, and articles that do not focus on the “number sense” concept were eliminated. Thus, a total of 47 articles were included in this review. One of the qualitative analysis techniques, content analysis, was used to analyze data. Content analysis allows a systematic examination of written documents and requires organizing data according to common themes and categories and interpreting this data systematically and understandably (Yıldırım & Şimşek, 2013). An “Article Review Form” was created in an Excel document to analyze the articles. This document involves categories of analysis criteria: Publication years, research methods, sample region, school level, and research purpose. According to these criteria, each article was analyzed.

Analysis revealed that the number of articles does not have a consistent trend over the years, peaking in 2020 before sharply dropping in 2021. Since 2021, publications have been increased. There are 34 quantitative (72.9%), five qualitative (10.4%), and eight mixed-method studies (16.7%). The samples of articles were taken from a total of 16 regions, with one article not specified. Samples were mostly taken from Türkiye (25.5%) and the USA (21.3%), followed by Taiwan (12.8%) and China (6.4%). Few studies’ samples are from England, Sweden, and Hong Kong (4.3% for each), while Canada, Norway, Cyprus, Egypt, Indonesia, Greece, Malaysia, Hungary, and Tanzania each had the lowest percentage (2.1% for each). Future research can examine under-studied regions. Analysis also revealed that most samples were from primary school (37%), followed by middle school (33.3%) and kindergarten (27.8%). There was only one study on high school. This focus on primary years is crucial because number sense develops during this stage (McGuire et al., 2012; Yang & Li, 2013). Furthermore, most studies used an intervention. These articles generally aim to investigate the effect of an intervention on number sense (29.5%), but there are also some studies that apply a number sense intervention to reveal its effect on other factors, such as self-efficacy and problem-solving (4.9%). Furthermore, some studies focused on students’ number-sense level (14.8%), misconceptions (13.1%), strategies (8.2%), and conceptual understanding (1.6%). Few studies examine the relationship between number sense and different variables such as arithmetic competence and social skills (3.3%) and the factors (e.g., socioeconomic status, achievement, parents’ education level, gender, school location) that affect number sense level (8.2%). There are also instrument development studies (6.6%), but these studies focus only on the middle-school level. The consideration of findings reveals gaps and potentials on number sense studies from a global and international perspective.

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