Background/purpose: STEAM (Science, Technology, Engineering, Arts, Mathematics) research and embodied design research have explored the role of full-body movement and multimodal actions in mathematical learning. However, the expressive and dynamic aspects of embodied mathematics learning remain underexplored. This paper aims to address this gap by…

To facilitate multisensory processing, the brain binds multisensory information when presented within a certain maximum time lag (temporal binding window). In addition, and in audiovisual perception specifically, the brain adapts rapidly to asynchronies within a single trial and shifts the point of subjective simultaneity. Both processes, temporal…

This study aimed to reveal the solutions of pre-service teachers to contextual problems related to number bases other than the base ten. Furthermore, it was intended to investigate which issues pre-service teachers discussed about their learning in the problem-solving process, including context, and about student learning in their future teaching…

Studies show that indigenous languages have exhibited enormous impact on the evolution and didactics of counting and place value. However, Ghana systems have different perspectives and pose varied successes on the didactics of counting and place value. In this study, we explored a mixed methods design to examine the mismatch between Ghanaian and…

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction "x/y," children are often taught to use "partitioning": break the whole into "y" parts, and shade in "x" parts. Past research has shown that partitioning on number lines supports children's fraction…

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction x/y, children are often taught to use "partitioning": Break the whole into y parts and shade in x parts. Past research has shown that partitioning on number lines supports children's fraction magnitude knowledge more than partitioning on…

The aims of this article are to document the types of signs that young children make to represent their mathematical thinking, and to determine the extent to which features of usage-based language acquisition are evident in children's early graphical communications made in mathematical contexts. Studies of young children's symbolic principles in…

In this article we outline the role evidence and argument plays in the construction of a framing theory for Proof Based Teaching of basic operations on natural numbers and integers, which uses tiles to physically represent numbers. We adopt Mariotti's characterization of a mathematical theorem as a triple of statement, proof and theory, and…

How does improving children's ability to label set sizes without counting affect the development of understanding of the cardinality principle? It may accelerate development by facilitating subsequent alignment and comparison of the cardinal label for a given set and the last word counted when counting that set (Mix et al., 2012). Alternatively,…

Many related studies have studied many different models in the teaching of the concept of integer, which have reported that counters failed to completely help with the understanding of the concept of and operation modeling in integers. The purpose of the present research is presenting the "opposite model", which is a quantitative model,…

Replication studies play a critical role in scientific accumulation of knowledge, yet replication studies in mathematics education are rare. In this study, the authors replicated Thanheiser's (Educational Studies in Mathematics 75:241-251, 2010) study of prospective elementary teachers' conceptions of multidigit number and examined the main claim…

At the early stages of concept acquisition, physical properties are inseparable of the concepts they form. With development, the concept seems to depart from the physical entities from which it emerged and seems to exist beyond its physical attributes. Numerosity is an abstract concept; however, physical properties such as diameter, area, and…

This chapter considers psychological and neuroscience research on how people understand the integers, and how educators can foster this understanding. The core proposal is that new, abstract mathematical concepts are built upon known, concrete mathematical concepts. For the integers, the relevant foundation is the natural numbers, which are…

Mathematics education researchers have long pursued--and many still pursue--an ideal instructional model for operations on integers. In this chapter, I argue that such a pursuit may be futile. Additionally, I highlight that ideas of relativity have been overlooked; and, I contend that current uses of translation within current integer…

In this commentary, I reflect from a neurocognitive perspective on the four chapters on natural number development included in this section. These chapters show that the development of seemingly basic number processing is much more complex than is often portrayed in neurocognitive research. The chapters collectively illustrate that children's…