This paper contributes to understanding the work of teaching the university geometry courses that are taken by prospective secondary teachers. We ask what are the tensions that instructors need to manage as they plan and teach these courses. And we use these tensions to argue that mathematics instruction in geometry courses for secondary teachers…

In mathematics, students' abilities to make transformations between mathematical representations are fundamental. The recent implementation of digital technologies, such as Dynamic Geometry Environments (DGEs), have changed students' access to mathematical representations by providing a variety of different representations, available just by…

In this article, we consider certain minimization problems. If d[subscript 1], d[subscript 2] and d[subscript 3] are the distances of a boundary or inner point to the sides of a given triangle, find the point which minimizes d[subscript 1][superscript n] + d[subscript 2][superscript n] + d[subscript 3][superscript n] for positive integer n. These…

This study aims at elaborating a well-established theoretical framework that distinguishes three modes of thinking in linear algebra: the analytic-arithmetic, the synthetic-geometric, and the analytic-structural mode. It describes and analyzes the bundle of signs produced by an engineering student during an interview, where she was asked to recall…

This article presents a curricular reasoning model developed based on research conducted with middle grades teachers as they planned, taught, and reflected on a geometric transformations unit. Teachers can use the model to become aware of their own curricular reasoning to make key mathematical decisions as they plan and teach their lessons. While…

We investigate proving activities from a monistic embodied perspective, namely the functional dynamic systems (FDS) approach. Using proofs without words, we focus on proving activities that can be conceptualized as identifying and filling gaps. Using a microethnographic methodology enhanced by eye-tracking, we investigate sensory-motor processes…

Performing hand gestures such as pointing and tracing while learning is an area of increasing focus in educational research. Previous studies have demonstrated that learners who performed these gestures while engaging with static paper- or computer-based learning materials performed better on posttests in multiple learning areas, such as…

Creative thinking transforms existing information, either from long-term memory or external sources, into new representations and innovative ideas. Creative thinking is an activity that processes received information to produce new representations and innovative ideas. Developing this skill is essential for students; however, recent research has…

Mathematics textbooks are commonly considered to be tools for efficient teaching and implementing change in mathematics classrooms worldwide, helping teachers to teach and learners to learn. When the content as described in the curriculum is not faithfully and relevantly represented in textbooks, learners' opportunity is limited. Against this…

The aim of the present study is to explore strategies in enumerating units of three dimensional (3D) arrays. We analyse enumeration strategies of students in grade 3 (ages 8 to 9) in situations of cubical and spherical representations of units of 3D arrays. By exploring students' strategies in these two situations, we find that difficulties in…

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…

When justifying a mathematical statement, textbooks often interweave several instances of justification, creating, what we term, "paths of justification." This study aims to characterize the paths of justification of mathematical statements that are offered in eight 7th grade Israeli mathematics textbooks. The study attended to context…

The Great Mini-Golf Project requires students to use a ruler to identify measurements to the quarter-inch, with careful precision and accuracy, which supported the Standards for Mathematical Practice 5 and 6: using appropriate tools to solve mathematical problems with precision (NGA Center & CCSSO, 2010). This project also supported Standard…

Numerous countries, including Indonesia, have integrated their cultural heritage into various aspects of society, notably in the realm of traditional textiles. With its diverse cultural landscape, Indonesia showcases detailed and comprehensive characteristics in its traditional fabrics, particularly the South Sumatra Songket. Popular cultural…

Spatial ability is a multifaceted construct with demonstrated ties to success in mathematics and gesture production. Recent empirical work has also begun investigating whether targeted interventions for spatial ability can transfer to mathematics but are often limited to specific populations and specific math outcomes. Spatial anxiety has been…