Any quadratic function has a line of symmetry going through its vertex; any cubic function has 1800 rotational symmetry around its point of inflection. However, polynomial functions of degree greater than three can be both symmetrical and asymmetrical (Goehle & Kobayashi, 2013). This work considers algebraic conversions of symmetrical quartic…

Is the natural number 7 rational? Is it complex? We argue that the answers to these questions relate to the ways numbers are taught. Commonly, a new kind of numbers is presented as an expansion of a previously familiar kind of numbers, which results in a nested image of the relations between number sets. In this article, we introduce an…

This research examines the relationships between mathematics intervention for basic facts automaticity in the upper middle grades, corrective peer feedback as a component of remediation, and mathematics academic self-concept. The goal of basic facts intervention is to aid students in achieving automatic recall of single-digit addition,…

This secondary analysis of data from a randomized control trial of an early mathematics intervention, ROOTS, explored whether patterns of intervention response were best categorized by the typical response/non-response binary or a more complex framework with additional response profiles. Participants included kindergarten students at risk for…

Leading by doing takes an unwavering and visible commitment to an intentional, continuous improvement process. Teams at every system level distribute leadership to support effective practice so outcomes improve. Using a practice-based approach to improving mathematics outcomes, the Kentucky Department of Education (KDE) facilitated a continuous…

Mathematics support, the provision of additional learning opportunities to, primarily, non-mathematics specialist undergraduates has grown significantly since the early 1990s, particularly in the UK, Ireland and Australia. Alongside the growth in volume of provision, there has been a marked increase in the amount of research and scholarship…

Providing students with rich tasks that are both engaging and mathematically important is a vital aspect of teaching primary mathematics effectively. One means of supporting the development of rich tasks that meet these criteria is to embed them in a narrative. Narratives can aid in the development of mathematical understanding through a number of…

Multiplication and division are complex constructs for young children to understand. In this article, the authors explore young children's ability to visualise and make groups of objects before they had formally been introduced to multiplication and division. The results provide some valuable insights into students' early understandings of…

This classroom study immersed high school geometry students in the creative and intellectually challenging design task of developing unique logos using mathematics and technology. The students applied and deepened their knowledge of transformations while using dynamic geometry software. One of the main aims of the task was to elevate student…

The introduction of paramedical science into universities has led to unprecedented enrolment numbers in Australian undergraduate paramedical science programs. At the same time however, there has been an associated increase in complexity of student learning expectations and requirements. One area of paramedical education that is proving challenging…

In this article, we report from a group (N=98) of students from two campuses of one Finnish university, on their study habits, and to what extent they use different kinds of learning materials in university mathematics courses. Our results show that the older students are more communicative with their teachers, whereas the younger students ask for…

Cognitive diagnosis models (CDMs) are restricted latent class models that can be used to analyze response data from educational or psychological tests. The Deterministic Input Noisy Output "AND" gate (DINA) model and the Deterministic Input Noisy Output "OR" gate (DINO) model there are two popular cognitive diagnosis models…

Improving STEM retention is a major focus of universities and studies have shown calculus to be a barrier for STEM intending students. Prior to this study, local data indicated students did not pursue STEM fields because they were not passing calculus. The goal of this study is to report on factors related to student success in first-semester…

Background: Research has indicated that young learners are capable of learning mathematics because they are born with an innate core of mathematics knowledge. Teachers of young learners are, therefore, expected to offer mathematical curriculum that exposes learners to a deep and explicit knowledge of high mathematics. Aim: The study aimed at Grade…

We examine the relationship between how teachers talk about teaching and their actual teaching practices. Analyses of their talk were based on extensive transcripts and writings and focused on metaphors and images invoked when discussing knowledge, learning, and teaching. Three distinct and coherent webs of association were identified, which we…