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 ability to reason about how things were made is a pervasive aspect of how humans make sense of physical objects. Such reasoning is useful for a range of everyday tasks, from assembling a piece of furniture to making a sandwich and knitting a sweater. What enables people to reason in this way even about novel objects, and how do people draw…

There is a growing perception that computational thinking can be developed in unplugged environments. A recent trend among these unplugged approaches is the use of tabletop games. While there are many commercial tabletop games on the market that are promoted as teaching computer science and/or computational skills, little is known about how these…

When teaching fractions, teachers make instructional decisions about if, when, and how to use the many different types of fraction models and manipulatives. In this study, we sought insights into their pedagogical reasoning with fraction representations via their preferences, both for solving tasks themselves and for teaching (in general and for…

An alternating treatments design was used to analyze the effects of concrete and virtual manipulatives on the duration and number of correctly solved linear equations by three middle school students with cognitive disabilities. Participants physically manipulated algebra tiles to solve an equation during the concrete manipulative condition. During…

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…

Technology is transforming children's lived experience with spatial play. In particular, parents may interact with children differently depending on whether they play together with tangible or digital materials. The present research examined whether the medium for play (tangible or digital) affected kindergarten-aged children's language experience…

Teachers cannot escape being learners if they are to be proficient practitioners. This study interrogates the effects of a professional development programme on mathematics teachers' pedagogical practices in South African primary schools. Using critical theory as the illuminating lens, this qualitative study, which is cast within the participatory…

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…

This work seeks to understand the emergent nature of mathematical activity mediated by learners' engagement with multiple artifacts. We explored the problem solving of two learners as they aimed to make sense of fraction division by coordinating meanings across two artifacts, one being a physical manipulative and the other a written expression of…

In kindergarten, children are usually engaged with both verbal activities and non-verbal activities, often requiring the manipulation of physical objects. During technical tasks (e.g., problem solving), children can use argumentation as one of the languages of science that mediates how they interact with the surrounding world. In this paper, we…