Recent work has probed the developmental mechanisms that promote fair sharing. This work investigated 2.5- to 5.5-year-olds' (N = 316; 52% female; 79% White; data collected 2016-2018) sharing behavior in relation to three cognitive correlates: number knowledge, working memory, and cognitive control. In contrast to working memory and cognitive…

In this article we aim to deepen our understanding of the content and nature of the early childhood teacher's knowledge, focusing on those aspects which might promote students' algebraic thinking. Approaching arithmetic from the viewpoint of algebra as an advanced perspective and considering the analytical model "Mathematics Teachers'…

Barriers to learning can affect educators and students in achieving learning objectives. One of them is the epistemological obstacle caused by the limited context used when a concept is first learned. The purpose of this study was to explore the epistemological obstacles of mathematics students in the concept of limits and functions during online…

In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes,…

Research Findings: The aim of this study was to investigate U.S. preschool teachers' math pedagogical content knowledge in number comparison. Seventy-four in- and pre-service teachers completed a set of scenario-based questions from a researcher-designed questionnaire that is composed of learning scenarios. Through a mixed-method approach, the…

Learning to count and to produce the correct sequence of number words in English is not a simple process. In NSW government schools taking part in "Early Action for Success", over 800 students in each of the first 3 years of school were assessed every 5 weeks over the school year to determine the highest correct oral count they could…

Urban and rural children have different levels of performance in arithmetic processing. This study investigated whether such a residence difference can be explained by phonological processing. A total of 1,501 Chinese primary school students from urban and rural areas were recruited to complete nine cognitive tasks: two in arithmetic performance…

Purpose: Previous studies examining the inter-relations between serial and discrete naming with reading have found that the ability to efficiently process multiple items presented in a sequence (indexed by serial naming) is a unique predictor of word- and text-reading fluency. However, conclusions have been tempered by the concurrent nature of the…

The aims of this article are to document the types of signs that young children make to represent their mathematical thinking, and to determine the extent to which features of usage-based language acquisition are evident in children's early graphical communications made in mathematical contexts. Studies of young children's symbolic principles in…

In this article we outline the role evidence and argument plays in the construction of a framing theory for Proof Based Teaching of basic operations on natural numbers and integers, which uses tiles to physically represent numbers. We adopt Mariotti's characterization of a mathematical theorem as a triple of statement, proof and theory, and…

How does improving children's ability to label set sizes without counting affect the development of understanding of the cardinality principle? It may accelerate development by facilitating subsequent alignment and comparison of the cardinal label for a given set and the last word counted when counting that set (Mix et al., 2012). Alternatively,…

Many related studies have studied many different models in the teaching of the concept of integer, which have reported that counters failed to completely help with the understanding of the concept of and operation modeling in integers. The purpose of the present research is presenting the "opposite model", which is a quantitative model,…

Replication studies play a critical role in scientific accumulation of knowledge, yet replication studies in mathematics education are rare. In this study, the authors replicated Thanheiser's (Educational Studies in Mathematics 75:241-251, 2010) study of prospective elementary teachers' conceptions of multidigit number and examined the main claim…

At the early stages of concept acquisition, physical properties are inseparable of the concepts they form. With development, the concept seems to depart from the physical entities from which it emerged and seems to exist beyond its physical attributes. Numerosity is an abstract concept; however, physical properties such as diameter, area, and…

This chapter considers psychological and neuroscience research on how people understand the integers, and how educators can foster this understanding. The core proposal is that new, abstract mathematical concepts are built upon known, concrete mathematical concepts. For the integers, the relevant foundation is the natural numbers, which are…