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 unlikely cast of characters, by working collaboratively in a trusting learning community, was able to identify an approach to teaching rational numbers through measuring from the everyday practices of Yup'ik Eskimo and other elders. "The beginning of everything," as named by a Yup'ik elder, provided deep insights into how practical…

In this paper we report on two assessment tasks extracted from a larger study. The tasks involved number-line placements on two different number lines (0-to-10 and 0-to-20) and place-value understanding. Participants were 119 children from four different classes (Years 1-3). Children's placements were more accurate on the 0-to-20 than the 0-to-10…

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…

Children's first mathematics concept is their understanding of the quantities represented by number words (cardinal value), and the age at which they achieve this insight predicts their readiness for mathematics learning in school. We provide the first exploration of the factors that influence the age of becoming a cardinal principle knower (CPK),…

The fifth-grade curriculum presents many opportunities to use students' prior mathematical knowledge as a way to bridge new and more difficult mathematical ideas. In this article, the authors document an area tiling task given to fifth-grade students to connect aspects of area measurement covered in earlier grades to grade-level standards such as:…

Teachers often use number talks at the beginning of class to hear the ways that students understand mathematical topics so that they can base future instruction on student thinking. Students who engage in number talks become accustomed to thinking about mathematics in multiple ways, sharing their thoughts and critiquing the thoughts of others. The…

The purpose of this study was to examine four pre-service middle and high school mathematics teachers' understanding of the directly and inversely proportional relationships presented through hands-on and real-world missing-value word problems. The problems included single and multiple proportions, and the PSTs were provided with plastic gears and…

This investigation examined the degree to which prospective elementary teachers had developed a meaningful and conceptual understanding of what integers are and explored their development of models for multiplication with integers that are related to everyday activities. Additionally, this study explored how these understandings informed…

Using a dog's paw as a basis for numerical representation, sixth grade students explored how to count and regroup using the dog's four digital pads. Teachers can connect these base-4 explorations to the conceptual meaning of place value and regrouping using base-10.

This qualitative research, drawing on the theoretical frameworks by Even (1990, 1993) and Sfard (2007), investigated five high school mathematics teachers' geometric interpretations of complex number multiplication along with the roots of unity. The main finding was that mathematics teachers constructed the modulus, the argument, and the conjugate…