The authors of this study conducted an exploratory study of the teaching and learning processes of a tutor and a student with a mild intellectual disability (MID) while working on two-step equations. The researchers focused on situations in which the participant was likely to struggle with memory and processing as well as the challenges of the…

Current reforms in geometry seek to challenge prevailing ideas about "what it means to do mathematics" (p. 139) by engaging learners in "the grasping of space" (p. 241). This study takes up this challenge by investigating problematizing activity as an embodied phenomenon among 21 eighth-grade learners who engaged with spatial…

The aim of this study is to determine the non-routine problem solving performances of mathematics teacher candidates. A descriptive survey model was used for this work and it was conducted with 50 teacher candidates studying elementary mathematics teaching in a medium-sized university in Turkey. To determine the non-routine problem solving…

Central in the frameworks that describe algebra from K-12 is the idea that algebraic thinking is not a single construct, but consists of several algebraic thinking strands. Validation studies exploring this idea are relatively scarce. This study used structural equation modeling techniques to analyze data of middle school students' performance on…

Mathematical learning is an integral part of early childhood education (ECE). In Aotearoa New Zealand there is a range of valuable curriculum resources including "Te Kakano," a "living, evolving" framework of purposeful activities, to assist teachers to notice and respond to mathematics learning. This article aims to contribute…

Visualising positive and negative numbers on a number line is helpful for exploring problems involving operations with positive and negative numbers. This is because number lines lend themselves to exploring problems involving continuous linear contexts such as travelling distances and temperature. Teachers in a professional development program…

The purpose of these notes is to generalize and extend a challenging geometry problem from a mathematics competition. The notes also contain solution sketches pertaining to the problems discussed.

We present a validation study of fifteen new math anxiety scale items designed to augment the widely-used Revised Mathematics Anxiety Scale (RMARS). While the RMARS and other standard instruments measure students' anxiety in response to computation, test situations, and math course activities such as buying a textbook or watching a lecture, the…

This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety…

A typical mathematics assignment consists of one or two dozen practice problems relating to the same skill or concept, yet empirical evidence suggests that there is little or no long-term benefit from working more than a few problems of the same kind in immediate succession. Alternatively, randomized experiments in the laboratory and classroom…

This paper reports on an exploratory study designed to determine and enhance the conceptual understanding of a group of pre-service mathematics teachers at one Irish university utilizing an established framework for understanding mathematics. 23 students on a one year Professional Diploma in Mathematics Education participated in the study, which…

The aim of this study is to investigate the misanalogical construction of undergraduate students in their cognitive conflict in doing a non-routine mathematical task. Qualitative methods were used in this research. Data were collected from 68 seventh semester undergraduate students of Mathematics Education Study Program, Universitas Negeri Malang…

Reform-based discourses in mathematics education have fabricated different subjectivities for teachers such as the "traditional" and the "new" teacher. Professional development programs are proposed as effective mechanisms to fabricate the "new" teacher. However, this teacher has proved hard to produce. Thus, the…

This study explored the mental constructions displayed by pre-service mathematics teachers (PMTs) when applying Cramer's rule. The aim was to reveal the character of mental constructions made around the nature of the solution set of equations and the role of parameters in the solution of equations with parametric coefficients. These mental…

The purpose of these notes is to provide examples of large-scale geometry problems that have the potential to promote "constructive struggling" in high-school geometry classrooms. These problems are suitable for being explored in a dynamic geometry environment. The notes also contain brief sketches of solutions to the two problems.