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'…

Studies show that spatial interventions lead to improvements in mathematics. However, outcomes vary based on whether physical manipulatives (embodied action) are used during training. This study compares the effects of embodied and non-embodied spatial interventions on spatial and mathematics outcomes. The study has a randomized, controlled,…

Teachers and teacher educators have been sharing strategies and resources for implementing mathematics routines in National Council of Teachers of Mathematics (NCTM) journals for years. A less commonly shared mathematics routine, especially with young learners, is "Clothesline Math" (Shore, 2017, 2018). In this routine, teachers create…

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…

This article addresses the nature of student-generated representations that support students' early algebraic reasoning in the realm of generalized arithmetic. We analyzed representations created by students for the following qualities: representations that distinguish the behavior of one operation from another, that support an explanation of a…

The hearing impairment can result in students having difficulty accepting learning. Obstacles Students in special schools when observing the understanding the numeracy skills. Students have problems sorting numbers and adding numbers from 1 to 10. Numeracy skills are an introductory lesson in learning mathematics. Several studies have shown that…

The goals of the current study were: 1) to modify and expand an existing spatial mathematical language coding system to include quantitative mathematical language terms and 2) to examine the extent to which preschool-aged children used spatial and quantitative mathematical language during a block play intervention. Participants included 24…

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 study examined how colored educational tools improve children's numerosity ("number sense") and/or mathematics. We tested children 6-10 years (n = 3,236) who had been exposed to colored numbers from the educational tools "Numicon" (Oxford University Press, 2018) or "Numberjacks" (Ellis, 2006), which map colors to…

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…

Poor numeracy skills among remedial pupils remained a critical issue for Malaysia to achieve educational goals. This systematic literature review identified research trends and evidence-based practices on teaching aids to enhance remedial mathematics instruction. The review followed PRISMA model through four phases, searching WoS and Scopus…

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…

The purpose of this mixed-methods study was to measure the impact of a sequential use of manipulatives and visual models on third-grade students' multiplication fluency, math attitudes, and fact retention. According to results of this study, there was significant evidence that the students who gained a conceptual understanding of multiplication…

A child's home environment has been shown to be related to the development of early numeracy skills in some countries. However, significant relationships between home learning environment and math achievement have not consistently been found, and likely vary across different cultural and socio-political contexts. Here we explored the home…

We investigated the effect of conceptual transparency in the physical structure of manipulatives on place-value understanding in typically developing children and those at risk for mathematics learning disabilities. Second graders were randomly assigned to one of three manipulatives conditions: (a) attachable beads that did not make the…