Ensuring students correctly understand the notion of equality is a fundamental problem in teaching mathematics. Is it possible to teach arithmetic in such a way that students do not misinterpret the equal sign "=" as indicating the result of an arithmetic operation and, consequently, viewing the arithmetic operation symbols (+, -, or x)…

The goal of this paper is to present a succinct consolidation of the why, what and how of the 'Model' method as there is a lack of such documentation for researchers, practitioners and policy makers thus far. The 'Model' method is a tool for representing and visualising relationships when solving whole number arithmetic (WNA) word problems. The…

The history of the number zero is an interesting one. In early times, zero was not used as a number at all, but instead was used as a place holder to indicate the position of hundreds and tens. This article briefly discusses the history of zero and challenges the thinking where divisions using zero are used.

In Peru, national assessments repeatedly rank Indigenous mathematics students as the lowest performing across the entirety of Latin America and South America. Whereas lack of financial resources often predicts low measures, the history of educational practice teaches us that students' poverty need not predict their educational outcomes -- creative…

This study's purpose was to investigate effects of 3 intervention approaches for building working memory (WM) and improving word-problem solving (WPS). Children with mathematics difficulties (n = 240; 7.51 years [SD = 0.33]) were randomized to 4 conditions: a control group, general WM training with contiguous math practice, WPS intervention…

The present study is the first to examine the computation estimation skills of dyscalculics versus controls using the estimation comparison task. In this task, participants judged whether an estimated answer to a multidigit multiplication problem was larger or smaller than a given reference number. While dyscalculics were less accurate than…

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

Mangarevan traditionally contained two numeration systems: a general one, which was highly regular, decimal, and extraordinarily extensive; and a specific one, which was restricted to specific objects, based on diverging counting units, and interspersed with binary steps. While most of these characteristics are shared by numeration systems in…

The related literature emphasizes that mathematics content knowledge (MCK) itself is not sufficient for effective teaching; teachers also need to have deep and wide mathematics pedagogical content knowledge (MPCK). In this study, we worked with 12 pre-service primary teachers through Teaching Practice course in order to examine how their MCK…

In Norway, children are encouraged to pose a problem that they can solve using an arithmetical calculation. This is known as 'regnefortelling'. During a larger project, we became interested in a small group of "regnefortelling" which used unusual contexts, contexts that made us uneasy and invoked a feeling of uncertainty about how we…

Instruction geared toward priming the underlying problem structures was suggested as an evidence-based practice for students with a learning disability. Schema-based instruction is one intervention aligned with this principle. We extended prior work by: (1) using a teacher as the implementer; (2) providing teacher flexibility in intervention…

The purpose of this study was to examine the effectiveness of video-based mathematics instruction for seven middle school students with specific learning disability (SLD), using an augmented reality-based training package. The dependent variable was the percentage of steps students performed correctly to solve each type of mathematics problem. The…

Intuitive conceptions in mathematics guide the interpretation of mathematical concepts. We investigated if they bias teachers' conceptions of student arithmetic word problem solving strategies, which should be part of their pedagogical content knowledge (PCK). In individual interviews, teachers and non-teaching adults were asked to describe…

Pedagogical content knowledge forms the core of teachers' professional knowledge; it refers to knowledge about making subject matter accessible to students. Thus, the formation of pedagogical content knowledge constitutes a crucial issue for educational research and practice. We investigated the contributions of content knowledge and pedagogical…

Background: Several studies have shown the influence of mathematical knowledge on both individual opportunities and chances for a self-determined and prosperous life as well as the welfare of nations. Against this background, the contents of maths education in the foundation phase as well as the way in which it is conveyed gain importance. While…