Background: The concept of rational numbers is one of the learner's first experiences with a Mathematics concept beyond the basic skills operations on whole numbers. The personal knowledge of fractions that teachers bring to the teaching context is important because teachers mediate the conceptions that their learners construct. Aim: This study…

Problem Statement: Throughout history, many changes have occurred in the field of mathematics education. These changes have also occurred concerning special topics that mathematics educators have constantly been searching. The significance of problem posing in mathematics teaching has increased recently with respect to its contributions to the…

How children play around with new numerical concepts can provide important information about the structure and patterns they notice in number systems. In this chapter, we report on data from 243 second graders who were asked to fill in missing numbers on a number path (encouraging them to play around with numbers less than zero) and to solve…

Howe (2014, Three pillars of first grade mathematics, and beyond. In: Li Y. & Lappan G. (eds), Mathematics curriculum in school education, Springer, Dordrecht, pp 183-207) identified three pillars of first grade mathematics and beyond that described central mathematical and sense-making aspects of major Common Core State Standards Math…

Children and adults show behavioral evidence of psychological overlap between their early, non-symbolic numerical concepts and their later-developing symbolic numerical concepts. An open question is to what extent the common cognitive signatures observed between different numerical notations are coupled with physical overlap in neural processes.…

Although growing evidence suggests a link between children's math skills and their ability to estimate numerical quantities using the approximate number system (ANS), little is known about the sources underlying individual differences in ANS acuity and their relation with specific mathematical skills. To examine the role of intergenerational…

This theoretical paper presents a methodology for instructional design in mathematics. It is a theoretical analysis of a proposed model for instructional design, where tasks are embedded in situations that preserve meaning with respect to particular pieces of mathematical knowledge. The model is applicable when there is an intention of teaching…

"One" anaphora (e.g., "this is a good one") has been used as a key diagnostic in syntactic analyses of the English noun phrase, and "'one'-replacement" has also figured prominently in debates about the learnability of language. However, much of this work has been based on faulty premises, as a few perceptive…

In this article we first review evidence for the approximate number system (ANS), an evolutionarily ancient and developmentally conservative cognitive mechanism for representing number without language. We then critically review five different lines of support for the proposal that symbolic representations of number build upon the ANS, and discuss…

This article addresses access to high-quality education under a neoliberal mentality. It engages at both the discursive and material levels, by mapping how taken-for-granted truths about neoliberal policies circulate through the media. The media--newspapers, network channels, and news websites--have correlated quality education with socioeconomic…

This article presents an analysis of contextual tasks to support the development of counting in Foundation Year classrooms. The tasks allowed the students to engage in authentic and realistic number experiences on which to build their understandings of early number.

This article reconsiders Case's theory of central conceptual structures (CCS), examining the relation between working memory and the acquisition of quantitative CCS. The lead hypothesis is that the development of working memory capacity shapes the development of quantitative concepts (whole and rational numbers). Study I, with 779 children from…

Strategies such as reinforcement and stimulus fading have been shown to be effective in the acquisition of skills, particularly for individuals with developmental disabilities. Teleconsultation is a promising service delivery modality to support teachers and staff in the implementation of effective strategies to address the needs of underserved…

The emergence of visual cortex specialization for culturally acquired characters like letters and digits, both arbitrary shapes related to specific cognitive domains, is yet unclear. Here, 20 young children (6.12 years old) were tested with a frequency-tagging paradigm coupled with electroencephalogram recordings to assess discrimination responses…

The objective of this study is to perform a validity and reliability examination of Number Sense Screener (NSS) by applying it to Turkish children aged 72-83 months. The universe of this general survey model study was constituted by 72-83-month old children showing normal development and studying at primary schools under the authority of the…