Diagrams are succinct, visual representations of real-world or mathematical objects that serve to communicate properties of the objects and facilitate problem solving. This study explored perceptions of mathematics teachers in Singapore, who are heads of mathematics departments in their respective schools, related to diagrams and their use in the…

This article illustrates one of several learning sequences from the Interdisciplinary Mathematics and Science (IMS) Learning project, connecting science and mathematics learning in the primary school. Investigating Body Height involved a series of investigations conducted in Years 5 and 6 across six classes in one school. The project teachers…

This article aims to outline the important role of the summary phase within a mathematics instructional model and provide six strategies to support teachers to move beyond "share time." By drawing upon good teaching strategies during the summary phase, teachers can enhance the learning experience for themselves and for their students.…

The purpose of the study is to enumerate the representations in high school geometry, to narrow the focus to the most common ones, and to describe how the common representations are coordinated. To achieve this purpose, I analyzed several sections of a popular geometry textbook using thematic analysis, semiotics, and a pragmatic approach to…

Algebra I encompasses several topics that serve as a basis for students' subsequent mathematics courses as they progress in school. Some of the key topics that students struggle with is solving linear equations and algebraic word problems. There are several factors that may contribute to this ongoing struggle for students such as the structure of…

This study continues an investigation of how spherical units, compared to cubical units, can facilitate students' units-locating and organizing units in composites. We analyze how Norwegian grade 3 students enumerate 3D arrays with cubical and spherical units. Our results show how spherical units can act as perceptual clues that facilitate…

Eleven high school students participated in a one-week STEM summer camp focused on designing and building parachutes to deliver fragile objects safely. Using the Engineering Design Process (EDP) as a framework, students explored how canopy size affects performance. They applied physics concepts such as terminal velocity, forces, and acceleration,…

We developed an Authentic GeometryGo (AGG) app to help students application of geometry in authentic contexts through authentic measurements and peer assessments. The study included an experimental group (EG) using an AGG app and a control group (CG) using paper-based methods. The results showed that the EG outperformed the CG in terms of…

For years, educators have been using "foldables" as a visual and/or kinesthetic approach to note taking within elementary school classrooms. The purpose of the study is to determine to what extent these foldables have on students' self-efficacy of grade level math concepts. We previously found that there were learning gaps in students'…

Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities. The study grouped visual representations into two categories: arithmetic-visual, which entailed the use of real-world objects to represent specific…

This study investigates geometry teachers' evaluations of problems that use visual arts contexts. We ask, "how do teachers' evaluations relate to the four arguments justifying the geometry course?" and "How do teachers draw on the APPRAISAL system to evaluate sample geometry problems from textbooks?" Nine high school teachers…

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K--8. Readers are provided with a strong mathematical background, downloadable copies…

Background/purpose: Although mathematical representation ability is a significant ability and an interesting topic to study, quite a few researchers have studied this ability, and even fewer have examined it through the implementation of epistemic learning patterns based on problem-solving. In fact, this learning pattern is epistemic and makes…

In this article, we examine spatial inscriptions marked in real or rendered spaces, rather than on two-dimensional surfaces, conceptualize spatial inscriptions from an inclusive materialist perspective and consider realizations of spatial inscriptions that are possible with emerging technologies (e.g. 3D pens, immersive virtual reality). We then…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…