It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use in…

The main goal of this paper is to show how Vasily Davydov's powerful ideas about the nature of mathematical thinking and learning can transform the teaching and learning of additive word problem solving. The name Vasily Davydov is well known in the field of mathematics education in Russia. However, the transformative value of Davydov's theoretical…

Multiplicative thinking has been widely accepted as a critically important "big idea" of mathematics and one which underpins much mathematical understanding beyond the primary years of schooling. It is therefore of importance to consider the capacity of children to think multiplicatively but also to consider the capacity of their…

This paper explores how a young child (56 m) builds an understanding of the cardinality principle through communicative, touchscreen-based activities involving talk, gesture and body engagement working via multimodal, touchscreen interface using contemporary mobile technology. Drawing upon Nemirovsky's perceptuomotor integration theoretical lens…

In contrast to previous studies on Spontaneous Focusing on Quantitative Relations (SFOR), the present study investigated not only the "extent" to which children focus on (multiplicative) quantitative relations, but also the "nature" of children's quantitative focus (i.e., the types of quantitative relations that children focus…

This paper describes and analyses the implementation of a "flipped classroom" approach, in an undergraduate mathematics course on numerical methods. The approach replaced all the lecture contents by instructor-made videos and was implemented in the consecutive years 2014 and 2015. The sequential case study presented here begins with an…

This research explores the interplay between students' understandings of proportional and functional relationships. Approximately 90 students participated in an early algebra intervention in Grades 3- 5. Before the intervention and after each year of the intervention, we evaluated their understandings of proportional and functional relationships.…

In this study, I use a systemic functional linguistics approach to examine mathematics classroom discourse with the aim of providing a plausible explanation of how students could actively participate in productive classroom discussions without adopting ways of reasoning that were accepted in the classroom community. In this way, I work in the…

In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…

The main aim of this article was to investigate the educational potential of a game-based math game competition to engage students in training rational numbers. Finnish fourth (n = 59; M[subscript age] = 10.36) and sixth graders (n = 105; M[subscript age] = 12.34) participated in a math game competition relying on intra-classroom cooperation and…

This paper addresses the issue of integrating students with special needs into foreign language programs in the early childhood years. A partnership between a university and a charter school in central Florida began as a result of parent and teacher interest in providing a foreign language program for its prekindergarten students. Since 2014,…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…

The use of enabling and extending prompts allows tasks to be both accessible and challenging within a classroom. This article provides an example of how to use enabling and extending prompts effectively when employing a challenging task in Year 2.

Research Findings: Young children develop numeracy competencies during interactions with more knowledgeable others. Such interactions typically occur in the home numeracy environment (HNE). In this study a nonintensive intervention procedure was developed to improve both the HNE and numerical competencies. All parents of 113 Australian children…

The purpose of this quantitative study was to examine the ability of standardized test scores to predict the performance of students in first-year mathematics courses, and the extent to which these tests displayed differential validity among various subgroups. Using discriminant analysis, it was established that the following percentages of…