On the surface, the number line may seem like a basic tool with obvious applications. However, using a number line is not always intuitive for students. Students may not recognize significant features such as the size of the unit, how units are represented by iterated equal lengths, or that the accumulation of iterated units is a magnitude of…

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…

In a pre-service mathematics methods class I taught, in which we mathematized political districting (first horizontally, then vertically), student questions led to engaging mathematics, in particular, the development of a new number sequence.

This study explored the utilisation of GeoGebra as a modelling tool to develop undergraduate engineering mathematics students' conceptual and procedural knowledge of complex numbers. This mission was accomplished by implementing GeoGebra-enriched activities, which provided carefully designed representational support to mediate between students'…

This paper reports on the design, implementation, and evaluation processes of an activity that focused on the comparison meaning of the subtraction of integers and included the number line model as the primary representation. Finding the answer and determining the sign of the answer in the subtraction questions were targeted as the learning…

The algebraic group Spin[subscript 3 × 3] arises from spinning collections of the numbers 1-9 on a 3×3 game board. The authors have been using this group, as well as a corresponding online application, to introduce undergraduate students to core concepts in group theory. We discuss the benefits of using this deceptively simple, toy-like puzzle in…

The role of executive function training in supporting child development has been increasingly studied. Executive function is largely related to the prefrontal cortex. The anterior portion of the prefrontal cortex, which is area 10 on the Brodmann map, is essential for the emergence of higher-order executive functions. Accumulating evidence…

This theoretical reflection implies the main proposal that the activities of planning and teaching are linked; it is the main ingredient to cognition and metacognition. Two main parts make up this article: a theoretical discussion of the linkage, detailing a descriptive letter and content to be taught in the classroom. Within this part, a…

Number naming, or knowledge of math numerals, has been described as a gatekeeper skill in preschool math development because it is necessary for later math tasks such as calculation. This article describes a small group intervention piloted with 10 preschoolers found to be at risk for delays in early numeracy development during universal…

This research aimed to determine the difficulties that the students experience in inequality solutions that contain inequality in general and rational (proportional) expressions, and to solve these difficulties with an activity. Totally 108 students, who were enrolled in the Department of Mathematics and Science Education, consisted respectively…

We report here on an intervention implementing a structural approach to arithmetic problem-solving in relation to learning outcomes among preschoolers. Using the fundamental principles of the variation theory of learning for developing the intervention and as an analytical framework, we discuss teaching and learning in commensurable terms. The…

This article aims to interrogate the Cartesian rationality determining current early childhood mathematics by highlighting the irrational aspect of mathematics learning, which is usually underemphasized and even devalued by the dominant discourse. Using Deleuze and Guattari's concept of refrain as the method, the article explores the unfolding…

It is important for students to connect with real life in mathematics courses. The aim of this study is to investigate the activities which are written by prospective primary school teachers in the context of Realistic Mathematics Education. This research is a case study of which data were collected by qualitative methods. The participants of the…

Research indicates that mathematical understanding before formal schooling influences later attainment. This study investigated the mathematical activities of preschool-aged children in Japan, a neglected topic despite the high mathematical attainment of Japanese children. Preschool activities were investigated using surveys, observations, and…

This article presents an analysis of contextual tasks to support the development of counting in Foundation Year classrooms. The tasks allowed the students to engage in authentic and realistic number experiences on which to build their understandings of early number.