Despite convincing research and strong public support, education budget cuts have forced schools and districts to limit or even eliminate arts instruction. Author Robin Ward argues that educators need to address the critical need to preserve and, in those cases, re-integrate the arts back into the school curriculum--mostly because the arts are…

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 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…

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…

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 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…

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 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.

This article reports a study of educators differentiating aspects of mathematical knowledge for teaching in preschool as part of a further-education programme. Eight Swedish preschool educators participated in focus group discussions about documentations from their own practice during a school year, to enhance their awareness of their mathematics…

This paper reports on results of a targeted and extended (two school terms) program for building Grade 3 and Grade 4 students' facility with number facts and application for mental computation. As part of a larger project, this paper reports results from two schools. Results indicated strong gains in number fact recall and mental computation for…

Although students and adults alike are constantly exposed to visuals both online and offline, merely being exposed to visuals does not guarantee visual literacy (Kedra & Zakeviciute, 2019). This study explored K12 teachers' perceptions regarding their personal and instructional use of online images as well as the influence of a visual literacy…

This article shows how to modify classroom evaluation items to avoid four potential difficulties that limit a teacher's insight into students' mathematical understanding by addressing these issues: (1) poor choice of numbers; (2) implausible or inappropriate contexts; (3) inclusion of graphics that do not help make learning visible; and…

This research paper reports on phase one of an investigation of video recorded intensive one-to-one teaching interactions with 6-7-year-old students who were in their second year of schooling in Australia and identified by the their teacher as low attaining in early number. The two-phased study from which this paper emerges was originally…

In 1859, on the occasion of being elected as a corresponding member of the Berlin Academy, Bernard Riemann (1826-66), a student of Carl Friedrich Gauss (1777-1855), presenteda lecture in which he presented a mathematics formula, derived from complex integration, which gave a precise count of the primes on the understanding that one of the terms in…