Building students' understanding of cardinality is fundamental for working with numbers and operations. Without these early mathematical foundations in place, students will fall behind. Consequently, it is imperative to build on students' strengths to address their weaknesses with the notion of cardinality.

Understanding a mathematical concept in real-world situations is of practical importance and would be helpful to learn the concept in depth. One potential way to help students learn mathematical concepts in real-world situations would be to engage them with contextual problems. Exponential and logarithmic concepts are essential topics in higher…

Background: Foundation phase teachers are encouraged to develop learners' number sense skills in their teaching and learning activities. Despite the significance of teaching number skills in mental mathematics activities, there are inadequate guidelines that could assist teachers in developing number sense skills through technology-enhanced mental…

Persistent difficulties in learning abstract algebraic concepts--particularly among preservice mathematics teachers--continue to hinder students' mathematical development. While prior studies have documented general misconceptions, few have grounded their analysis in comprehensive learning theories. Addressing this gap, the present study adopts…

It is widely acknowledged that the transition from informal, everyday knowledge to formal, school-taught knowledge is a critically important stage in children's mathematical development. Research highlights the importance of making connections between the different representations of mathematics and the value of children's own mathematical…

The number line estimation task is widely used to investigate mathematical learning and development. The present meta-analysis statistically synthesized the extensive evidence on the correlation between number line estimation and broader mathematical competence. Averaged over 263 effect sizes with 10,576 participants with sample mean ages from 4…

A pivotal information about the structure of students' comprehension underlying from which the knowledge is gained can be identified through the mental model. This study aimed at describing the six levels of students' mental model in comprehending the concept of the integer. The subject of this research was 40 students consisting of 20 students…

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…

Representations of the fingers are embodied in our cognition and influence performance in enumeration tasks. Among deaf signers, the fingers also serve as a tool for communication in sign language. Previous studies in normal hearing (NH) participants showed effects of embodiment (i.e., embodied numerosity) on tactile enumeration using the fingers…

Background: Studies in Down syndrome (DS) and Williams syndrome (WS) have suggested that mathematical abilities are impaired. However, it is unclear which domain-general or domain-specific abilities impact on mathematical development in these developmental disorders. Method: The current study examined the foundations of mathematical development…

In this note, I present an 'easy-to-be-remembered' shortcut for promptly solving the ubiquitous integral [line integral] x[superscript n] e[superscript alpha x] dx for any integer n>0 using only the successive derivatives of x[superscript n]. Some interesting applications are indicated. The shortcut is so simple that it could well be included…

The purpose of the current pilot study was to examine the effects of a teacher-designed and teacher-led numerical board game intervention. Fifty-four 4- to 6-year-olds were randomly assigned to either the number board game intervention or an active control group. Relative to the control group, children who received the number game intervention…

Previous studies suggest that tasks dependent on the mental number line may be difficult for Williams Syndrome (WS) and Down Syndrome (DS) groups. However, few have directly assessed number line estimation in these groups. The current study assessed 28 WS, 25 DS and 25 typically developing (TD) participants in non-verbal intelligence, number…

This research project focuses on identifying the difficulties that children between 6-7 years-old have in learning natural numbers, when working a teaching model with a Von Neumann formal mathematical basis. In this study, we present the analysis of the experimentation with a first-grade class in the construction of zero and one numbers,…

Reasoning about fraction magnitude is an important topic in elementary mathematics because it lays the foundations for meaningful reasoning about fraction operations. Much of the research literature has reported deficits in preservice elementary teachers' (PSTs) knowledge of fractions and has given little attention to the productive resources that…