The New Zealand Curriculum is comprised of eight compulsory learning areas: English, the arts, health and physical education, learning languages, mathematics and statistics, science, social sciences, and technology. Collectively, these learning areas are intended to provide children with a broad and balanced education. Despite this, the…

Even when using mixed-ability grouping--grouping students so that students with a range of mathematical thinking work together--there is potential to position some students as more capable than others. In this article, the authors describe two approaches to mixed-ability grouping, providing examples of how teachers using those approaches describe…

Mathematical writing (MW) can support students' mathematical learning and is common in mathematics assessment. However, MW is known to be particularly challenging for students with learning disabilities. While the use of model compositions of both high- and low-quality writing and the act of revision are evidence-based practices in writing…

There are both educational and cultural benefits to first language (L1) instruction, particularly in the early years of school, but in Australia, few Indigenous language-speaking students are taught in their own languages. Teaching mathematics in Indigenous languages requires both linguistically capable Indigenous educators and the identification…

In this paper, we explore how the typical second year undergraduate topic of matrix diagonalisation can be applied to solve a geometric problem which arises frequently in Vector Calculus: to find the curve of intersection of a plane and a surface. We use GeoGebra, which offers a cost-free and dynamic interface, to explore a specific variant of…

This paper reports on a novel corequisite design and implementation for College Algebra at Florida International University. The corequisite course uses online, just-in-time, prerequisite assignments delivered on an open-educational platform. Students get help from near-peer learning assistants inside a math emporium environment. The course…

In this article, we present a framework of culturally relevant science and mathematics pedagogy (CRSMP), which is grounded in the tenets of culturally relevant pedagogy. It delineates practices ranging from the most accessible and easy-to-implement, to the most challenging and often contentious ways to teach mathematics and science. We provide…

This article provides teachers with a toolkit for assessing students in the context of data-based individualization (DBI) in mathematics. Assessing students is a critical component of DBI because it provides teachers with information about what they may need to modify in their instructional programs. In this article, we provide teachers with…

Three one-dimensional maps are presented. The maps are analysed with a combination of Feigenbaum diagrams, the calculation of global Lyapunov exponents, and the evaluation of fixed points. It is shown that in certain cases period two orbits can be evaluated by careful observation of the form of the related pairs of equations. A range of classroom…

I explore some facts about the area, position, etc. of the Steiner ellipse using GeoGebra and numerical analysis. Students can use these for mathematical inquiry.

Higher education increasingly relies on remedial coursework to bridge knowledge gaps among incoming students (Chen, 2016). Students assessed as below college level enroll in remediation to review secondary concepts, especially in mathematics (Kane et al., 2020). However, pressures over funding, student persistence, and completion rates exacerbate…

Fractions are an important concept used throughout advanced mathematical ideas and everyday life. Students need a solid understanding of fraction concepts, such as magnitude, equivalence, and operations. However, many students, including students with learning disabilities (LD) in mathematics, struggle with fractions. In this article, the use of…

We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

We automate and randomize the building of linear systems with a parameter, appropriate for assigning to students. When the parameter takes on a specific value, the system has no solutions. When the parameter takes on a different value, the system has an infinite number of solutions.

Over three decades ago, National Council of Teachers of Mathematics (NCTM, 1991) proposed that "for students to develop the ability to formulate problems, to explore, conjecture, and reason logically, to evaluate whether something makes sense, classroom discourse must be founded on mathematical evidence" (p. 34). As math interventionists…