Supporting children's understanding of the everyday, cultural use of written numerals is highly significant, as it is this understanding that gives meaning to classroom conversations on the purposes of written numbers. This paper presents findings from a phenomenographic study of the qualitatively different ways in which 3-5-year-old children…

This study focuses on adults who are neither preschool teachers nor professional caregivers and investigates their beliefs regarding the importance of engaging young children with numerical activities. It also examines the types of numerical activities adults report having observed children engaging with, as well as the types of activities they…

In this article, we direct attention to what becomes critical in teaching activities for toddlers (1-3-year-olds) to learn the meaning of numbers. One activity we thoroughly explore is interactive book reading, based on previous research indicating positive learning outcomes from this type of mathematical activity, as it has shown to…

Recent studies have highlighted the importance of ordinality skills in early numerical development. Here, we investigate individual differences in ordering sets of items and suggest that children might also differ in their tendency to spontaneously recognize and use numerical order in everyday situations. This study investigated the individual…

Mastery of the cardinality principle (CP) is foundational for children's mathematical development. Children's age and subitizing and counting skills contribute to their CP acquisition. This study aimed to investigate the effectiveness of different types of instruction for supporting 3-4-year-olds' CP development and its interplay with child…

The decomposition of numbers when solving subtraction tasks is regarded as more powerful than counting-based strategies. Still, many students fail to solve subtraction tasks despite using decomposition. To shed light upon this issue, we take a variation theoretical perspective (Marton, 2015) seeing learning as a function of discerning critical…

This study investigates the relationship between children's subitizing activity and their construction of arithmetic units. In particular, the study hypothesizes a positive association between children's construction of subitized units and their construction of arithmetic units, and hypothesizes that children who can subitize larger units, such as…

The give-"n" task is widely used in developmental psychology to indicate young children's knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and…

This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students' behavior in these three stages of problem posing, especially focusing on investigating…

This study examines the solutions of 34 kindergarten children as they create equal groups from n bottle caps, where n was equal to 8, 9, 22, and 23. For each n, children were asked to find as many different solutions as possible. The number of solutions they found, i.e., children's fluency, as well as the strategies used to create equal groups,…

Rational numbers, such as fractions and decimals, are harder to understand than natural numbers. Moreover, individuals struggle with fractions more than with decimals. The present study sought to disentangle the extent to which two potential sources of difficulty affect secondary-school students' numerical magnitude understanding: number type…

This study identifies language specific errors made with transcoding tasks to inform possible future pedagogic decisions regarding the language used when teaching early number. We compared children aged 5-7 years from Kuwait and England. The spoken Arabic language of Kuwait gave the opportunity to compare not only languages where the tens and…

Students entering sixth grade operate with three different multiplicative concepts that influence their reasoning in many domains important for middle school. For example, students who are operating with the second multiplicative concept (MC2 students) can begin to construct fractions as lengths but do not construct improper fractions as numbers.…

School reform efforts are situated within social and political contexts and, as such, are susceptible to the commonsense discourses circulating through, and shaping, society. Two discourses prevalent in US education reform are those perpetuating the ideologies of neoliberalism and neoconservatism. These ideologies are inherently…

In this paper, we share details of a South African early grades' number intervention informed by aspects of Davydov's writing on early number teaching and learning. A key part of Davydov's approach to early number teaching involves starting with attention to relationships between quantities rather than with counting. The Structuring Number…