Adaptive expertise is a highly sought after, but difficult to achieve, outcome of mathematics education. Many teaching methods appear to support the development of adaptive expertise only in a small proportion of students. Game-based learning environments may be useful for supporting adaptive expertise. Therefore, we carried out a…

The study investigates the knowledge profiles of elementary pre-service teachers (PST) concerning numbers and operations before their professional classroom practice. By validating an instrument through exploratory and confirmatory factor analyses, it identifies and categorizes the PST' performance into distinct profiles based on the mathematical…

Children learn the cardinalities of the first numbers one, two, three and four before they learn how counting tracks cardinality for all numbers. It may be that when children start to understand counting, they also discover how numbers relate to one another in a structured number system. Do children who understand that the cardinality of a set is…

The current research aimed to unpack teachers' knowledge of integers by investigating how they used the number line and counter models to represent the two meanings of division (i.e., partitive and measurement). The participants were three middle school mathematics teachers working in different cities in Türkiye. Data consisted of teachers'…

There is growing interest in mathematics learning progressions in early childhood education. Counting is a skill usually developed early in life. The application of the counting principles in early childhood typically entails counting objects. This poses challenges for learning about zero. Indeed, the word "zero" is seldom used in the…

The conceptual development of natural number in preschoolers is well-researched. However, less is known about the conceptual development of zero. Recent studies suggest that children develop an understanding of zero after learning to count. It remains unclear, when a conceptual understanding of "zero" as number word for an empty set…

This study seeks to analyse the awareness of the pre-service teachers on the counting methods, systems and tools used in the prehistoric method and the Ancient period and to examine the distribution of this awareness by gender. A total of 42 sophomore-level students studying at a university in the Western Black Sea region, Turkey, participated in…

Place value is one of the 'big ideas' in number and plays a critical role in helping students develop their number sense, problem solving and computation skills. Yet, the elegant simplicity of our place value system belies the abstract nature of the construct. This paper presents data from 606 Year 3-6 students (ages 8-12) from two metropolitan…

This study investigates how the approximate number system (ANS) and young children's symbolic skills jointly develop and interact. Specifically, the study aims at disentangling the directionality of the association between ANS acuity and a wide range of symbolic skills that reflect 4- to 5-year-olds' symbolic quantitative knowledge (enumeration…

"Place value," which underlies the meanings of multidigits, encompasses the principle of position and base-10 rules. To understand 65, one needs to know that the digits 6 and 5 occupy different positions and thus represent ordered values of different magnitudes (i.e., the "principle of position") and that the value of each…

This study argues that the pattern and timing of ordinal acquisition differs substantially from that of cardinals and is influenced by different language-specific factors, such as (ir)regular ordinal morphology, superlative morphology, and the singular-plural distinction. We discuss data from a Give X task (Wynn 1992) administered to 77 Dutch…

This study aimed to examine whether a computational thinking (CT) intervention related to (a) number knowledge and arithmetic (b) algebra, and (c) geometry impacts students' learning performance in primary schools. To this end, a quasi-experimental, nonequivalent group design was employed, with 61 students assigned to the experimental group and 47…

This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

This research aims to determine second-year university students' understanding in interpreting and representing fractions. A set of fraction tests was given to students through two direct learning interventions. An unstructured interview was used as an instrument to obtain explanations and confirmations from the purposive participants. A total of…

Identifying and addressing the knowledge gap in early numeracy is crucial, given the strong associations between early numeracy skills and later school success. The purpose of this study is to establish current viewpoints and ideas on children's numeracy development via three forms of representation: manipulative, symbolic, and static. The…