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…

This article describes the results of an investigation based on a Models and Modeling Perspective [MMP]. We present the evolution of the models built by university students when solving a model development sequence designed to promote their learning of the exponential function. As a result, we observed that students' thinking was modified,…

Background: When mathematical knowledge is expressed in general language, it is called verbalized mathematics. Previous studies on verbalized mathematics typically paid attention to mathematical vocabulary or educational practice. However, these studies did not exclude the role of symbolic mathematics ability, and almost no research has focused on…

Building proficiency with fraction arithmetic poses a consistent challenge for students with learning difficulties or disabilities in mathematics. This article illustrates how teachers can use the number line model to support struggling learners in making sense of fraction arithmetic. Number lines are a powerful tool that can be used to help…

This article proposes an in-depth mathematics analysis of simple and compound interest through an exploration of the mathematical structures underlying these concepts. Financial numeracy concepts (simple and compound interest, interest rates, interest period, present and future value, etc.) have been added to the mathematics curriculum of the…

Conceptual replications are part and parcel of education science. Methodologically rigorous conceptual replication studies permit researchers to test and strengthen the generalizability of a study's initial findings. The current conceptual replication sought to replicate the efficacy of a small-group, first-grade mathematics intervention with 240…

This study explores two Year 2 teachers' perceptions of the affordances of a novel mathematical manipulative, the Keyboard, based on their observations of its use in the classroom. Analysis of the semi-structured interviews indicated that the Keyboard's linear structure, design features, and hands-on nature promoted flexible number strategies,…

Evidence of positive associations between the frequency of home math activities and preschool children's math skills is mixed, and the operationalization of home math activities varies across studies. We test whether home math activities can be grouped by activity factors based on the math subdomain they target (i.e., counting and cardinality,…

A test method is described for determining the divisibility of non-negative integers by a prime number. The test uses an integer multiplying factor that is defined for each prime, designated as [beta], to reduce the non-negative integer that is being tested by an order of magnitude in each of a sequence of steps to obtain a series of new numbers.…

Much research has examined the reciprocal relations between a child's spontaneous focus on number (SFON) in the preschool years and later mathematical achievement. However, this literature relies on several different tasks to assess SFON with distinct task demands, making it unclear to what extent these tasks measure the same underlying construct.…

Taking a socio-cultural perspective, in this study we explored the challenges toddlers might face as they practice 1-1 correspondence in the playful context of setting a table, and how different individuals may participate in this playful activity. Findings indicated that toddlers' competence in carrying out one-to-one correspondence may be…

Mathematical cognition requires coordinated activity across multiple brain regions, leading to the emergence of resting-state functional connectivity as a method for studying the neural basis of differences in mathematical achievement. Hyper-connectivity of the intraparietal sulcus (IPS), a key locus of mathematical and numerical processing, has…

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…

This article presents a simple, fast, and equally accurate technique for measuring the area of a circle and of an ellipse without using geometric formulas. This therefore, together with the known radius of the circle and the semi-major and semi-minor axes of the ellipse, allows for the calculation of [pi]. The experiment is easy, thrilling, and…

Young children need to be taught using effective interventions. A good teaching method is one that will increase children's motivation to learn, keep them aware of their understanding and encourage them to reflect on what they learn, if this teaching is based on relevant and visible training. Otherwise, they may suffer from delays in mathematics.…