The purpose of this study was to conduct a replication study of a kindergarten mathematics intervention, ROOTS, delivered within the context of a research base core program. In the study, sixty two classrooms were randomly assigned to treatment (ROOTS) or a business as usual control. All classrooms implemented a research based core program (Early…

Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: "Every real root of a monic polynomial with integer coefficients is either an integer or irrational." The paper offers a new perspective in understanding the meaning of 'irrational numbers' from a deeper…

Partially automated assessment is implemented via the 'Printable worksheet' mode in the Numbas e-assessment system to create a mathematical modelling worksheet which is individualised with random parameters but completed and marked as if it were a non-automated piece of coursework, preserving validity while reducing the risk of academic misconduct…

In this article, we analyse a lesson on Thales's theorem in a Chilean secondary school classroom through the combination of two theories: Mathematics Teachers' Specialised Knowledge (ThMTSK) and Mathematical Working Spaces (ThMWS). Both theories, first separately and then in relation to one another, are used to analyse two tasks proposed by the…

A common exercise given to students early in a molecular biology course is the creation of a restriction map of a plasmid "digested" by two restriction enzymes (RE). Meanwhile, students have learned from an early age about the properties and analyses of circles in their mathematics courses. But it is rare for students to learn using…

In this article we present topics that can be considered when developing a landscape of investigation that reflects on the issues of the LGBTQ+ community. We outline the landscape "LGBTQ+ Life Conditions," having prospective teachers in mind. The outlining takes place in four steps: (1) We indicate the relevance of this topic and bring…

This study aims to reveal the possible benefits of incorporating the Broadwell-Burch four-stage model of competence development into mathematics teacher training. First, a historical overview is given about the appearance of the four-stage model starting from the original sources by Broadwell and Burch arriving at today's widespread use in the…

We present a method to compute the power series expansions of e[superscript x] ln (1 + x), sin x, and cos x without relying on mathematical analysis. Using the properties of elementary functions, we determine the coefficients of each series through the method of undetermined coefficients. We have validated our formulae through the use of…

The tutoring market has expanded dramatically over the past decade particularly in mathematics. In this paper, we problematise the growth of mathematics tutoring given its societal impacts and the current lack of evidence for its effectiveness. In addition to gaps in research on its effectiveness, there exist no comprehensive frameworks for…

This study aims to address the teaching of integrals in multivariable calculus concerning the role taken by geometry, specifically, geometrical content dealing with boundaries in integrals that appear as curves and surfaces in R[superscript 2] and R[superscript 3]. Adopting the framework of the Anthropological Theory of the Didactic, we approached…

This paper presents an alternative approach of teaching systems of two linear equations to the students in Tanzanian ordinary secondary schools. I conducted a desk-based research on methods that have been used by in-service mathematics teachers for teaching systems of two linear equations in ordinary secondary schools. It was found that five…

Research on young children's development of executive function (EF) and early mathematics has established relationships between the two, but studies have not investigated whether these relations differ for children with different outcomes in mathematics and EF, especially in the context of interventions. To examine the homogeneity of those…

The concepts of commitment and anxiety are essential components of the teaching process, and these concepts come across as the commitment to and concern of mathematics in the field of mathematics learning. This study aims to explore the effect of secondary school students' mathematics class commitment and anxiety on mathematics success. Another…

Links between mathematical attainment and economic performance, coupled with England's poor showing in international comparisons of skills, have focussed attention on post-16 mathematics education, for example, in the UK Government's 2017 Industrial Strategy. Whilst high-stakes academic qualifications at 16 (GCSE) and 18 (A-level) have stood the…

The purpose of this study was to examine relationships between students' semiotic representational transformations and students' mathematics performance outcomes in digital math games. The study employed a convergent parallel mixed methods design. Students in Grades 4, 5, and 6 (ages 9-12) played nine digital math games. Researchers administered…