Children vary widely in their number knowledge by the time they enter kindergarten, and this variation is related to their future academic success. Although talk about number predicts children's early understanding of foundational number concepts, we know little about whether interventions can increase this talk nor about the types of number talk…

Teachers and teacher educators have been sharing strategies and resources for implementing mathematics routines in National Council of Teachers of Mathematics (NCTM) journals for years. A less commonly shared mathematics routine, especially with young learners, is "Clothesline Math" (Shore, 2017, 2018). In this routine, teachers create…

The aim of this study was to investigate second-grade elementary school students' performance related to their counting skills, place value understanding, and addition operation in natural numbers. A total of 205 second-grade elementary school students from Turkey participated in this study. The data were collected through a 'Personal Information…

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…

We investigated the effect of conceptual transparency in the physical structure of manipulatives on place-value understanding in typically developing children and those at risk for mathematics learning disabilities. Second graders were randomly assigned to one of three manipulatives conditions: (a) attachable beads that did not make the…

Young children's symbolic magnitude understanding, or knowledge of how written numerals and number words can be ordered and compared, is thought to play an important role in their mathematical development. There is consistent evidence that symbolic magnitude skills predict mathematical achievement in later childhood and adulthood. Yet less is…

Difficulties in mathematics are argued to stem from impairments of a specialized system of numerical magnitude representation. This study investigates whether different measures of numerical magnitude understanding in kindergarten uniquely predict mathematical achievement concurrently and 6 months later, and also examines the relative explanatory…

Infants and toddlers experience the world in interaction with others. Likewise, social interactions are important in learning about math--concepts of number ("one," "two," "three"), space ("on top," "upside-down," "round"), and magnitude ("more," "big,"…

Acquiring abstract Mathematics concepts is often challenging for young children. This study explored young children's use of digital cameras to exhibit their understanding of the addition concept. It investigated how the processes involved in producing the photographs and creating the visual representation that helped to develop the children's…

This chapter focuses on the development of concepts that children draw on as they work toward understanding negative numbers. Framed from a conceptual change lens, I discuss different interpretations children have of minus signs, numerical order, numerical values, and addition and subtraction operations and how children draw on these varied…

Research shows that frequent, high-quality mathematics talk that is shared between parents and children can increase mathematics achievement. This article describes ways in which teachers can support parents in increasing the frequency and quality of parent-child mathematics interactions, leading to better outcomes for students.

The aim of this study is to examine the games in ABCya (https://www.abcya.com/) based on the learning trajectories for the development of number concept. To achieve this aim in the study it was examined which ABC educational game application support the learning trajectory and the development level related to number concept of games. This research…

To promote reversibility and strengthen number sense, the authors created an engaging and novel rational number exploration--Quotient Quandary Reversibility task (QQRT)--which promoted flexible and reflective thinking. A class of fifth-grade students took an active role in a collaborative learning task, discussed their strategies, revisited the…

Many students face difficulties with fractions. Research in mathematics education and cognitive psychology aims at understanding where and why students struggle with fractions and how to make teaching of fractions more effective. Additionally, neuroscience research is beginning to explore how the human brain processes fractions. Yet, attempts to…

A recently published interview-based test, known by its partly German acronym, MARKO-D SA, is introduced in this article by way of a narrative of its development through various cycles of research. The 48-item test, in 4 South African languages, captures number concept development of children in the 6 to 8-year age group. The authors present their…