Adaptive expertise is a highly sought after, but difficult to achieve, outcome of mathematics education. Many teaching methods appear to support the development of adaptive expertise only in a small proportion of students. Game-based learning environments may be useful for supporting adaptive expertise. Therefore, we carried out a…

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…

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…

Rational numbers can be represented in multiple formats (e.g., fractions, decimals, and percentages), and a rational number notation can be used to express different concepts in different contexts. The present study investigated the distribution of the multiple concepts expressed by these different rational number notations in real-world contexts…

This paper is part of a broader study which explores South African pre-service teachers' use of the jump strategy on the empty number line for enhancing their confidence to do and teach mental mathematics computation strategies. The focus of this paper is the use of micro-teaching in the form of video recordings by pre-service teachers. Forty…

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…

The Give-N (give-a-number) task has become a popular assessment of children's number words and counting knowledge since Wynn's (1990, 1992) seminal work over 30 years ago. Using the Give-N task, numerous studies have shown that children learn the first few number words slowly, before they understand how counting represents number. This learning…

Multiple studies have reported mathematics underachievement for students who are deaf, but the onset, scope, and causes of this phenomenon remain understudied. Early language deprivation might be one factor influencing the acquisition of numbers. In this study, we investigated a basic and fundamental mathematical skill, automatic magnitude…

This article describes students learning to build their own numbering system by recognizing and identifying patterns with interlocking cubes in different place values. The students used the Egyptian hieroglyphic numeral system in conjunction with this activity to connect learning in other subjects. Students used prior knowledge of place value to…

Assessing implementation allows for a better understanding of an intervention's effects and the mechanisms that influence its impact. Two main areas of implementation are: (1) the quality with which an intervention is delivered; and (2) instructors' adherence to the programmed intervention. The current study used data from a kindergarten…

As students have struggled to use the "chip model" (i.e., red and yellow chips representing positive and negative numbers) to model integer addition and subtraction and have found it confusing, the authors developed a series of activities based on adding and removing opposite objects to and from a boat to better help students in this…

The subjective number-space mapping and, especially, its evolution in young children has been the subject of intense controversy among different competing models. Many studies point out that: (i) young children's innate estimates follow a logarithmic mapping (Weber-Fechner law) and (ii) driven by education, children evolve into a linear mapping.…

This study provides a multidimensional analysis of the structural and semantic peculiarities of phraseological units to identify the general, the similar, and the national-specific, which are different in terms of phraseological figurativeness. Most of the magical images and symbols became the basis of the symbolism of the numerals, which became…

Imaginary latent variables are variables with negative variances and have been used to implement constraints in measurement models. This article aimed to advance this practice and rationalize the imaginary latent variables as a method to detect possible latent deficiencies in measurement models. This rationale is based on the theory of complex…

This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…