We make a "prima facie" case for identifying a single pathway in the learning of Hindu-Arabic numerical symbols and discuss why this ability may be a critical gateway concept in developing mathematical competencies. A representative sample of English and Scottish children was assessed using a number symbol identification paradigm in the…

In this paper, dialogue among a group of adult women with basic adult education is examined. Women read books of mathematics in the context of a "dialogic mathematics gathering" (DMG). There is limited evidence in research on how adults develop their 'numerical understanding'. The objective of this study is to analyze how adults engage…

"Fraction Face-Off!" is a supplemental math program designed to support fourth-grade students who need assistance solving fraction problems. Teachers use program materials with individual students or small groups to promote understanding of the magnitude of fractions, to compare two fractions, to put three fractions in order, and to…

"Fraction Face-Off!" is a supplemental math program designed to support fourth-grade students who need assistance solving fraction problems. Teachers use program materials with individual students or small groups to promote understanding of the magnitude of fractions, to compare two fractions, to put three fractions in order, and to…

"Fraction Face-Off!" is a supplemental math program designed to support fourth-grade students who need assistance solving fraction problems. Teachers use program materials with individual students or small groups to promote understanding of the magnitude of fractions, to compare two fractions, to put three fractions in order, and to…

This study revealed how students' understanding of negative numbers and identified their difficulties related with the concept of integer and its counting operation as part of identifying epistemological obstacles about negative numbers. Even though teachers have explained counting operation procedure of integer, but there was concept…

This paper is based on the analysis of the relationship between early education, mathematical skills, and student achievement in Bosnia & Herzegovina, using data from the trends in international mathematics and science study (TIMSS) 2019. The study involves 5,628 fourth-grade students whose average age was 10.1 years. The research specifically…

Dyscalculia is a learning difficulty that negatively affects individuals' abilities to understand, apply, and learn mathematical operations. This study aims to explore the wide-ranging impacts of dyscalculia on individuals' lives. The experiences of Nur, an English teacher, are used to examine the effects of dyscalculia on personal, social,…

We present the basic theory of denesting nested square roots, from an elementary point of view, suitable for lower level coursework. Necessary and sufficient conditions are given for direct denesting, where the nested expression is rewritten as a sum of square roots of rational numbers, and for indirect denesting, where the nested expression is…

This paper presents an interesting deduction of the Golden Spiral equation in a suitable polar coordinate system. For this purpose, the concepts of Golden Ratio and Golden Rectangle, and a significant result for the calculation of powers of the Golden Ratio ? using terms of the Fibonacci sequence are mentioned. Finally, various geometrical…

Let R be a ring with identity. Then {0} and R are the only additive subgroups of R if and only if R is isomorphic (as a ring with identity) to (exactly) one of {0}, Z/pZ for a prime number p. Also, each additive subgroup of R is a one-sided ideal of R if and only if R is isomorphic to (exactly) one of {0}, Z, Z/nZ for an integer n = 2. This note…

In this short thought-piece, I attempt to capture the type of freewheeling discussions I had with our late colleague, Mika Seppälä, a research mathematician from Helsinki. Mika, not being a psychometrician or learning scientist, was blissfully free from the design constraints that experts sometimes ingest, unwittingly. I also draw on delightful…

The intent of this commentary is to identify elements of fraction sense and note how the research studies provided in this special issue, in related but somewhat different ways, validate the importance of such understandings. Proficiency with fractions serves as a prerequisite for student success in higher level mathematics, as well as serving as…

How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We…

The purpose of the present study was to understand how number writing in a class of low-income, pre-kindergarten children (N = 15) developed over the course of a school year, and to see what role that development played in their overall math readiness. The study used a mixed-methods approach. The target class was explicitly taught number writing…