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Education Sciences
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Exploring Mathematical Thinking in Early Childhood Education
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Exploring Mathematical Thinking in Early Childhood Education

A special issue of Education Sciences (ISSN 2227-7102).

Deadline for manuscript submissions: 31 January 2026 | Viewed by 3275

Special Issue Editors

Dr. Penelope Kalogeropoulos

E-Mail Website
Guest Editor
Faculty of Education, Monash University, Clayton, VIC 3800, Australia
Interests: practices and pedagogies; assessing mathematical competence and dispositions; learning mathematical concepts; teacher beliefs, attitudes, and knowledge; inclusion, equity, social justice, and student engagement
Dr. Ann Downton

E-Mail Website
Guest Editor
Faculty of Education, Monash University, Clayton, VIC 3800, Australia
Interests: young children’s mathematical thinking; student representations of mathematical thinking (drawing, physical representations, use of manipulatives); learning early numeracy through play; affective learning in early mathematics; embodied cognition

Special Issue Information

Dear Colleagues,

The research on early childhood education has increased in recent years. Many would argue that studies have shown a positive relationship between children’s early mathematical knowledge and their later mathematics learning. Another contributing factor is the emphasis placed on preschool education.

We invite you to contribute to this Special Issue with innovative research exploring key topics and issues in early childhood mathematics education. Your contribution should provide readers with insights into the challenges and core issues facing early educators today. Possible themes include the following:

  • The promotion of early-years mathematical structural development;
  • The contribution of multimodality and embodiment to early mathematics learning;
  • Children’s informal mathematical learning experiences;
  • Pedagogies that foster children’s informal mathematics-related experiences;
  • The role of contexts, manipulatives, and/or picture storybooks that support early mathematics learning;
  • Parents’ and carers’ roles in supporting early mathematics learning;
  • Children’s vulnerabilities in mathematics learning;
  • Early-years mathematical reasoning.

Dr. Penelope Kalogeropoulos
Dr. Ann Downton
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a double-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Education Sciences is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • early numeracy
  • pedagogies
  • play-based learning
  • representations

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  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (5 papers)

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Research

23 pages, 753 KB  
Article
Analysis of Preschool Teachers’ Dialogue with Children During Combinatorial Activities
by Tatjana Hodnik and Adrijana Mastnak
Educ. Sci. 2025, 15(11), 1489; https://doi.org/10.3390/educsci15111489 - 5 Nov 2025
Viewed by 157
Abstract
This article deals with the quality of dialogue between preschool teachers and children during mathematical activities. Thoughtful and attentive dialogue captures children’s attention and allows them to reason, express thoughts and disagreements, and ask questions. The aim of the study is to determine [...] Read more.
This article deals with the quality of dialogue between preschool teachers and children during mathematical activities. Thoughtful and attentive dialogue captures children’s attention and allows them to reason, express thoughts and disagreements, and ask questions. The aim of the study is to determine how well preschool teachers are able to utilize the potential of a combinatorial problem to ask questions and promote children’s mathematical thinking. Video recordings of eleven preschool teachers formed the basis of the study. Qualitative and quantitative analysis of the transcribed recordings provided an insight into the quality of the dialogues. The results of the study show that the preschool teachers mainly focused on combinatorics during the dialogue, although they also frequently asked the children questions about numbers, as well as questions from a non-mathematical context. In the analyzed dialogues, there was a lack of focusing questions, problem-solving questions, and questions requiring the children to justify their explanations. Unlike other studies that mainly investigate children’s thinking when solving selected combinatorial problems, the present study highlights the role of the teacher as the main actor in the process of children’s mathematics learning. Full article
(This article belongs to the Special Issue Exploring Mathematical Thinking in Early Childhood Education)
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21 pages, 711 KB  
Article
The Role of Spatial Reasoning in Growing and Spatial-Repeating Patterns in First and Second Graders’ Structural Development of Mathematics
by Joanne T. Mulligan
Educ. Sci. 2025, 15(11), 1479; https://doi.org/10.3390/educsci15111479 - 3 Nov 2025
Viewed by 290
Abstract
A cross-sectional qualitative study examined how different pattern types accounted for wide variation in children’s Awareness of Mathematical Pattern and Structure (AMPS), illustrating how spatial and patterning skills are interrelated. An interpretive descriptive analysis of responses was conducted for two interview-based Growing Square [...] Read more.
A cross-sectional qualitative study examined how different pattern types accounted for wide variation in children’s Awareness of Mathematical Pattern and Structure (AMPS), illustrating how spatial and patterning skills are interrelated. An interpretive descriptive analysis of responses was conducted for two interview-based Growing Square Array (GA) and Spatial-Repeating Pattern (SP) tasks with 405 children from Grade 1 (n = 189) and Grade 2 (n = 216). Analysis of developmental levels of AMPS indicated that advanced multiplicative spatial structures were employed in GA patterns for 20% of Grade 1 and 35% of Grade 2 children, respectively. Responses to SP tasks extended beyond the ‘unit of repeat’ to the use of dynamic visualization, and orientation and transformation skills for 60% of children. Responses showing advanced structural features moderately increased at Grade 2 for both tasks. Micro-level analyses of illustrations of interview responses and from a Pattern Construction task, drawn from five case studies, revealed how multiplicative and transformation skills were utilized in forming repetitions and growing patterns in complex and novel ways. While the ‘unit of repeat’ is fundamental, the integration of more complex multi-dimensional patterning with spatial concepts can re-focus learning and pedagogy on establishing interrelationships between patterning and spatial concepts, and broader mathematical knowledge. Full article
(This article belongs to the Special Issue Exploring Mathematical Thinking in Early Childhood Education)
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33 pages, 3248 KB  
Article
Playing Gebeta in Preschool: Informal Pathways to Early Numeracy Through Directionality and Bundling
by Oliver Thiel
Educ. Sci. 2025, 15(10), 1365; https://doi.org/10.3390/educsci15101365 - 14 Oct 2025
Viewed by 705
Abstract
Preschool children develop essential mathematical concepts through play, yet little is known about how traditional board games can support this process. This small-scale microgenetic case study investigates how children unfamiliar with the Ethiopian game Gebeta (a mancala-type game) learn to play the game [...] Read more.
Preschool children develop essential mathematical concepts through play, yet little is known about how traditional board games can support this process. This small-scale microgenetic case study investigates how children unfamiliar with the Ethiopian game Gebeta (a mancala-type game) learn to play the game and what mathematical competencies emerge. Video observations were conducted with 5-year-olds in Norway as they engaged in repeated play sessions. Event logs and transcripts were analysed with a focus on children’s developing strategies and difficulties. The results show that children quickly understood the basic rules but faced challenges with directionality (i.e., maintaining the correct direction of play) and differentiating between different types of game moves. Over time, they demonstrated evident progress in following the rules. They began to treat groups of counters as units, moving from one-by-one counting to bundling and unitising. These developments align with Bishop’s fundamental activities locating and counting. We conclude that Gebeta provides a playful context in which children can practice directionality and bundling, both of which are crucial for avoiding common errors in later school mathematics, such as off-by-one counting errors and misunderstandings of the number system. The study suggests that Gebeta can be introduced in early childhood settings without simplifying the rules, providing an engaging resource for early mathematics education. Full article
(This article belongs to the Special Issue Exploring Mathematical Thinking in Early Childhood Education)
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28 pages, 2046 KB  
Article
Virtual Versus Physical Number Line Training for 6-Year-Olds: Similar Learning Outcomes, Different Pathways
by Eva-Maria Ternblad, Maybi Morell Ruiz and Sonja Holmer
Educ. Sci. 2025, 15(10), 1350; https://doi.org/10.3390/educsci15101350 - 11 Oct 2025
Viewed by 317
Abstract
According to previous research, young children’s numeracy skills may be scaffolded by practicing on the number line. A number line estimation task (NLET) is often conducted with pen and paper, while linear number games are often implemented on a computer or a tablet. [...] Read more.
According to previous research, young children’s numeracy skills may be scaffolded by practicing on the number line. A number line estimation task (NLET) is often conducted with pen and paper, while linear number games are often implemented on a computer or a tablet. If and how the format—physical or digital—influences the accuracy of the estimations is, however, not well-known. If regarding NLET performance as dependent on specific strategies and hypothesizing that these strategies may be affected by the material used, we may also assume that different materials may either support or hinder children’s learning. In this paper, we explore whether training with a physical versus a virtual NLET game will affect children’s strategies when solving NLETs, and if these strategies relate to the accuracy of the estimations. Sixty-two 6-year-old children played an NLET game (virtual or physical) for three sessions, being scaffolded and guided by a researcher. NLET performance was measured by pre- and post-tests, as well as during the intervention. The results show that even if the condition did not significantly affect the children’s overall numeracy skills, the children in the physical condition did express more advanced strategies during the intervention. These strategies, in turn, predicted NLET performance. Full article
(This article belongs to the Special Issue Exploring Mathematical Thinking in Early Childhood Education)
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25 pages, 5460 KB  
Article
Supporting Pre-School Children’s Number Learning Through Embodied Representation
by Jennifer Way and Katherin Cartwright
Educ. Sci. 2025, 15(9), 1170; https://doi.org/10.3390/educsci15091170 - 7 Sep 2025
Viewed by 1023
Abstract
Situated within the Embodied Learning in Early Mathematics and Science project in Australia, this paper explores the relationships between ‘embodied activities’ used by a preschool teacher and the children’s development of number sense over six months. Using an instrumental case study approach, qualitative [...] Read more.
Situated within the Embodied Learning in Early Mathematics and Science project in Australia, this paper explores the relationships between ‘embodied activities’ used by a preschool teacher and the children’s development of number sense over six months. Using an instrumental case study approach, qualitative data from multiple sources including self-reported data from the teacher, activity descriptions, two task-based interviews with nine children, and number-knowledge data extracted from a mathematics achievement assessment (pretest and post-test) was analysed. Pattern searching techniques across text and video revealed connections between the embodied activities implemented by the teacher and the children’s development of subitizing and counting skills, mathematical drawing, and number magnitude knowledge. We propose that attending to specific aspects of children’s physical development, particularly finger dexterity and drawing skills, in experiences that focus on representing number concepts, can support their development of number sense. Full article
(This article belongs to the Special Issue Exploring Mathematical Thinking in Early Childhood Education)
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