Building activities can be used any time in the school year in mathematics classes to promote problem solving, perseverance, and to develop students' spatial thinking. Spatial visualization skills are the "ability to mentally manipulate, rotate, twist, or invert a pictorially presented stimulus object." The authors were guided by the…

While helping proofread a book during my doctoral studies, I came across a chapter that included (among other things) a discussion of a set of problems and tasks involving the building of towers using only two (or three) colours of cubes (Maher & Ahluwali, 2014). Later that year, as I started my tenure track position at the University of…

This article presents an original puzzle that supports students' development of visual thinking and geometry ideas based on the Van Hiele levels of geometric thought. The "Triangle Puzzle" is one of many tools teachers can use to guide students' learning of geometry. The Van Hiele's theory provides a way to assess and support this…

The duo of artefacts is a simplified model of the complex systems of various manipulatives (either tangible or virtual) that mathematics teachers and their students use in classrooms. It offers a means to study the complexity of the interweaving of the tangible and of the digital worlds in the teaching and learning processes. A duo of artefacts is…

In this article, we present an educational proposal designed to work on spatial geometry and three-dimensional thinking with students in the last years of Primary Education. The proposal is comprised of several activities that combine the use of a classroom videogame and working with manipulative materials to create a representation of the…

The purpose of this article is to introduce a lesson fondly referred to as the 'Lego Shop' lesson. It stands out as not only the most engaging lesson we've conducted but is also highly adaptable to accommodate a diverse range of learners. Successfully implemented across all year levels, from Foundation to Year 6, this lesson has proven to be…

The standby wooden blocks that are prevalent in most high-quality early childhood classrooms are missing from most primary and elementary grades. The goal for block play in early childhood is to support learning in mathematics, science, art, literacy and language arts, physical development, social studies, and social and emotional growth. This…

When thinking about digital equity, often what comes to mind are issues of access to digital technologies. Although that is a divide that must be conquered, once students have access to digital technologies, the next step is to ensure that they wield these technologies in such ways that they help to address the existing inequities in mathematics…

The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

This article presents some paper-folding activities for students to explore a different way to prove some of the angle properties in a circle.

Successful mathematical problem-solving relies on choices about how best to represent and solve problems. In this article, a range of methods and strategies are presented for solving a single mathematical problem, including novel methods posed by in-service teachers at one Australian university. The variety of problem-solving strategies rely on…

Wooden planks are a tool for developing youth skills through science, technology, engineering, and math exploration. These are small planks that can be stacked to create complex structures as youths explore math and physical relationships in an applied context. Building with wooden planks also cultivates planning, reasoning, and team skills as…

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…

Recognizing the challenges that students face when they may lack background and experiential knowledge with regard to coins is important so that teachers can address this during instruction. Exposure to coins is one of the basic necessities to learning about the coins, but that is just the initial part of the learning sequence. Unless students are…

Drawing on data from preschools in Australia and the United States, the authors highlight strategies to help teachers demystify the process of engaging young learners with tangible technologies and showcase how robotic manipulatives serve as catalysts for peer collaboration, socio-emotional development, and creative problem solving.