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…

The purpose of this study was to understand children's operations on fragmenting schemes while they are engaged with three different visual models, including circle, rectangle, and length model. This study was a sequential explanatory mixed method, which included two phases that happened sequentially with the dominant use of the quantitative…

Conceptual body movement in education is an external representation mode that research suggests can support children's learning about mathematical phenomena. Children's learning and understanding of mathematical concepts and processes, such as number structure and relationships, number sequencing, position, or geometric properties, may be…

The Tchokwe people lived on the African continent, in Mozambique and Angola. The sona belong to their cultural tradition. The sona are drawings made in the sand by older members of the tribe to tell stories, essential in the youngests' formation. In this article, we show a relationship between the sona and the greatest common divisor (GCD) of two…

Windmill images and shapes have a long history in geometry and can be found in problems in different mathematical contexts. In this paper, we share and discuss various problems involving windmill shapes and solutions from geometry, algebra, to elementary number theory. These problems can be used, separately or together, for students to explore…

In this paper, we focus on two particularly problematic concepts in teaching mathematics: the complex unit i and angles. These concepts are naturally linked via De Moivre's theorem but are independently misused in numerous contexts. We present definitions, notations, and ways of speaking about these terms from mathematics education that are not…

A large and growing body of work has documented robust illusions of area perception in adults. To date, however, there has been surprisingly little in-depth investigation into children's area perception, despite the importance of this topic to the study of quantity perception more broadly (and to the many studies that have been devoted to studying…

Research indicates that establishing a strong foundation in early mathematics is essential for later academic learning. Previous research with students who are deaf or hard of hearing (DHH) has shown varying differences in the performance and achievement when compared to typically hearing (TH) students. While the majority of research in this area…

We examine opportunities and challenges of applying a single, explicit definition of multiplication when modeling situations across an important swathe of school mathematics. In so doing, we review two interrelated conversations within multiplication research. The first has to do with identifying and classifying situations that can be modeled by…

This report delineates the outcomes of an intervention conducted with in-service high school educators, focusing on elucidating three distinct scenarios within geometric and arithmetic domains: the infinitely large, infinitely numerous, and infinitesimally close. Grounded in the theoretical framework of conceptual change, it is posited that when…

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,…

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…

In mathematics, three integer numbers or triples have been shown to govern a specific geometrical balance between triangles and squares. The first to study triples were probably the Babylonians, followed by Pythagoras some 1500 years later (Friberg, 1981). This geometrical balance relates parent triples to child triples via the central square…

Background: The role of gender in both spatial and mathematics performance has been extensively studied separately, with a male advantage often found in spatial tasks and mathematics from adolescence. Spatial reasoning is consistently linked to mathematics proficiency, yet despite this, little research has investigated the role of spatial…

In many countries, teachers often have to set their own questions for tests and examinations: some of them even set their own questions for assignments for students. These teachers do not usually select questions from textbooks used by the students because the latter would have seen the questions. If the teachers take the questions from other…