To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…

Despite the growing popularity of both flipped classrooms and digital manipulatives, there is a need for empirical research to examine the impact of combining these instructional strategies in the context of an Algebra 1 course (Alsaeed, 2017; Brown et al., 2001). This study is grounded in Kolb's learning cycle, the Technological Pedagogical…

This paper introduces tools for converting circular-featured-waste into polygonal construction parts and then 3D polyhedra. The tools, including diagrams, 3D printable joiners and mathematical formulae are designed for mathematics-related play, re-use, learning, design and improvisation. Activities for students include making assemblies, gathering…

Museum-based mathematics exhibitions are increasingly prominent but under-theorized learning environments. In this study, we analyse the curriculum of United States mathematics exhibitions developed in the early 21st century in terms of their complex suggestions about the nature of mathematics and mathematical sense-making. We apply Rancière's…

Abstract Lego construction ability is associated with a variety of spatial skills and mathematical outcomes. However, it is unknown whether these relations are causal. We aimed to establish the causal impact of Lego construction training on: Lego construction ability; a broad range of spatial skills; and on mathematical outcomes in 7-9-year-olds.…

Mathematical inquiry involving hands-on activities has received increasing attention in mathematics education. Besides various customized physical teaching aids, subject-specific information technology, such as Dynamic Geometry System (DGS), finds extensive use in mathematical inquiry activities. However, effects of DGS and physical manipulatives…

There is a known association between LEGO® construction ability and mathematics achievement, yet the mechanisms which drive this association are largely unknown. This study investigated the spatial mechanisms underlying this association, and whether this differs for concrete versus digital construction. Between January 2020 and July 2021, children…

Physical manipulatives (PMs) are concrete objects used during hands-on learning activities (e.g., building blocks, fraction tiles, counters), and are widely used in primary-school teaching, especially during maths instruction. This scoping review collated studies that have examined the effectiveness of educational PM interventions with pre-primary…

All students, including students with learning disabilities, deserve a mathematics education that successfully prepares them for their future endeavors. This preparation includes effective instruction in algebra, which is known as the gatekeeper to post-secondary schooling, employment, and constructive citizenry. However, majority of students with…

Parents play a vital role in shaping the ways young children understand the world around them. This paper reports on how the Community Mathematics Project (CMP)--a mathematics tutoring program for parents of diverse young children--affected the ways parents engaged in mathematical sensemaking while using virtual manipulatives and questioning to…

This paper explores Grade R teacher expressions of themselves as teachers of numeracy, and as teachers working in the transition phase of schooling, after their participation in a research-informed numeracy-focused professional development (PD) intervention. The Early Number Fun (ENF) programme had 33 teachers from 17 Eastern Cape schools…

The purpose of this study was to examine the effects of an online multi-component intervention (video modeling, virtual manipulatives, digital games, self-monitoring and least to most prompting techniques) on the acquisition of several mathematical skills of two autistic elementary school students. We used a multiple probe design of a single-case…

Mathematics education for students with and at-risk for a disability is important and high-quality, research-supported practices should be used for online teaching--whether intentional or as a result of a global pandemic. This single-case design multiple probe replicated across participants study explored the online delivery of an intervention…

Although positive effects of lesson study on teachers learning are reported, only some studies have investigated teacher noticing as an analytical tool for supporting teachers with an explicit focus, as in LS, and more empirical evidence is needed. This qualitative interpretive case study design aims to investigate the noticing processes of a…

In this article, we question the prevalent assumption that teaching and learning mathematics should always entail movement from the concrete to the abstract. Such a view leads to reported difficulties in students moving from manipulatives and models to more symbolic work, moves that many students never make, with all the implications this has for…