This proposal explores relationships between young children's unit development/coordination and young children's subitizing. In particular, this theoretical commentary considers students' degrees of abstraction, students' development of actions on units, and students' operations with units when subitizing. As a result of this commentary, this…

In this chapter, we review two approaches for understanding these national differences in math abilities. The first approach attempts to link cross-national differences in educational input to cross-national differences in test scores. A tacit assumption of this approach is that children's performance on tests of mathematics is a direct effect of…

The acquisition of number conservation is a critical step in children's numerical and mathematical development. Classic developmental studies have established that children's number conservation is often biased by misleading intuitions. However, the precise nature of these conservation errors is not clear. A key question is whether conservation…

It is well documented in literature that rational number is an important area of understanding in mathematics. Therefore, it follows that teachers and students need to have an understanding of rational number and related concepts such as fraction multiplication and division. This practitioner reference paper examines models that are important to…

While understanding rational numbers forms an essential part of mathematical literacy, research has repeatedly shown that they form a stumbling block in education. A big source of difficulty is the inappropriate application of natural number knowledge. The research literature points at three main aspects where natural number knowledge is…

The mental number line metaphor describes how numbers are associated with space. These spatial-numerical associations (SNA) are subserved by parietal structures (mainly intraparietal sulcus [IPS] and posterior superior parietal lobule [PSPL]). Generally, it is assumed that this association is a basic cornerstone for arithmetic skills. In this…

This article sets out to evaluate the English Early Years Foundation Stage Goal for Numbers, in relation to research evidence. The Goal, which sets out to provide "a good foundation in mathematics", has greater breadth of content and higher levels of difficulty than previous versions. Research suggests that the additional expectations…

Recent research on fractions has broadened and deepened theories of numerical development. Learning about fractions requires children to recognize that many properties of whole numbers are not true of numbers in general and also to recognize that the one property that unites all real numbers is that they possess magnitudes that can be ordered on…

When asked to "find three forks", adult speakers of English use the noun "fork" to identify units for counting. However, when number words (e.g. "three") and quantifiers (e.g. "more", "every") are used with unfamiliar words ("Give me three blickets") noun-specific conceptual criteria are unavailable for picking out units. This poses a problem for…

PME, the International Group for the Psychology of Mathematics Education, was founded in 1976, at the "Third International Congress on Mathematical Education" in Karlsruhe, organised by the International Commission on Mathematics Instruction (ICMI). While PME is thus beyond coming of age and is reflecting its further orientation--due to…

Children's drawings are one of the most appropriate approach to knowing children, their individuality and also their perceptions. Child is not always able to express their thoughts precisely, because their vocabulary is still incomplete and is gained just lately. In our paper we concentrate on drawing as a communication means, with which we can…

This paper challenges the emphasis on counting in New Zealand's Numeracy Development Project (NDP), arguing that subitizing provides an alternative pathway to quantification. Longitudinal data is presented showing that children's subitizing skills at the age of five years were a strong predictor of their later success in mathematics at the age of…

Previous evidence has shown that 11-month-olds represent ordinal relations between purely numerical values, whereas younger infants require a confluence of numerical and non-numerical cues. In this study, we show that when multiple featural cues (i.e., color and shape) are provided, 7-month-olds detect reversals in the ordinal direction of…

The residue number system (RNS) has been an important research field in computer arithmetic for many decades, mainly because of its carry-free nature, which can provide high-performance computing architectures with superior delay specifications. Recently, research on RNS has found new directions that have resulted in the introduction of efficient…

Preschoolers' conceptual understanding and procedural skills were examined so as to explore the role of number-words and concept-procedure interactions in their additional knowledge. Eighteen three- to four-year-olds and 24 four- to five-year-olds judged commutativity and associativity principles and solved two-term problems involving number words…