Manipulating Algebra: Comparing Concrete and Virtual Algebra Tiles for Students with Intellectual and Developmental Disabilities

Long, Holly; Bouck, Emily C.; Domka, Anna

doi:10.1080/09362835.2020.1850454

Cited by 6 publications

(4 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Intervention studies have shown that using manipulatives and pictorial representations of quantities and variables, with a gradual transition to the conventional algebraic form, can be effective in teaching algebra (Long et al, 2021;Satsangi et al, 2016Satsangi et al, , 2018). An innovative approach to this method would be to prompt students to construct self-gener ated visuals after becoming familiar with provided manipulatives and pictorial representations.…”

Section: Educational Implicationsmentioning

confidence: 99%

“…One of the recurring themes in intervention studies is the use of manipulatives and object pictures to represent quantity and variables, followed by a gradual transition to standard algebraic form (e.g., Long et al, 2021;Satsangi et al, 2016Satsangi et al, , 2018. However, these studies often overlook assessments of students' preexisting mental models of algebraic problems.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Visual and symbolic representations as components of algebraic reasoning

Ünal,

Ala,

Kartal

et al. 2023

J. Numer. Cogn.

View full text Add to dashboard Cite

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 values of variables, and algebraic-visual, which involved formal representations like the number line and the coordinate plane. Symbolic representations, on the other hand, encompassed the use of standard algorithms to solve equations, such as changing the place of terms in an equation. The results reveal that the use of algebraic visuals, as opposed to arithmetic visuals, was associated with enhanced algebraic reasoning. Further, although the students initially relied on standard algorithms to explain equations and inequalities, they could produce accurate algebraic-visual representations when prompted. These findings suggest that students have multiple representations of equations and inequalities but only express visual representations when asked to do so. In keeping with the general relationship between visuospatial abilities and mathematics, self-generated algebraic-visual representations partially mediated the relation between overall mathematics achievement and algebraic reasoning.

show abstract

Section: Educational Implicationsmentioning

confidence: 99%

mentioning

confidence: 99%

Visual and symbolic representations as components of algebraic reasoning

Ünal,

Ala,

Kartal

et al. 2023

J. Numer. Cogn.

View full text Add to dashboard Cite

show abstract

“…Similar to the literature on concrete manipulatives, researchers have examined the use of virtual manipulatives on their own (e.g., Bouck, Park, Levy, et al, 2019), as part of a manipulative-based instructional sequence (e.g., VRA; Park et al, 2020; Root et al, 2021) and as compared with concrete manipulatives (e.g., Bassette et al, 2019; Long et al, 2020). In a synthesis of single-case research on virtual manipulatives for students with LD, Park et al (2022) identified 19 studies involving virtual manipulatives.…”

Section: Manipulative-based Instructional Sequencesmentioning

confidence: 99%

An Evidence-Based Practice Synthesis of Virtual Manipulatives for Students With ASD and IDD

Long

Bouck

Kelly

2022

Focus Autism Other Dev Disabl

Self Cite

View full text Add to dashboard Cite

Virtual manipulatives are increasingly being used to support students with autism spectrum disorder and intellectual and developmental disability (ASD/IDD), in mathematics. However, to date, virtual manipulatives have not been examined or classified as an evidence-based practice for students with ASD/IDD, despite classifications of virtual manipulatives as evidence-based for students with learning disabilities (LD; Park, Bouck, & Fisher, 2021) and concrete manipulatives as evidence-based for students with ASD/IDD (Spooner et al., 2019). The purpose of this review was to assess the current state of the literature on virtual manipulatives and determine whether virtual manipulatives are an evidence-based practice for students with ASD/IDD. Eighteen of the 24 articles located for the review met quality indicators according to Cook et al. (2014) and presented positive results for the 42 students. The authors of this synthesis concluded virtual manipulatives broadly and virtual manipulative-based instructional sequences disaggregated are evidence-based practices in mathematics for students with ASD/IDD.

show abstract

“…The studies conducted by Bouck E.C. mainly related to the effectiveness of using concrete and virtual manipulatives in teaching various mathematics topics to students with learning disabilities (i.e., Bassette et al, 2019;Bouck & Park, 2020, Bouck et al, 2017b, 2018b, 2018dLong et al, 2021;Satsangi & Bouck, 2015;Satsangi et al, 2016). Thusly, the studies are highly relevant in the research domain with 'mathematics' and 'learning disabilities' as the top keywords.…”

Section: What Are the Contributions Of The Most Relevant Author In Ea...mentioning

confidence: 99%

Mathematics Learning from Concrete to Abstract (1968-2021): A Bibliometric Analysis

Chin

Meng

SUSEELAN

2022

Participatory Educational Research

View full text Add to dashboard Cite

Mathematics learning is illustrated as a developmental progression in the direction of concrete-to-abstract by educational theorists. Various studies rooted in this notion were conducted in the past. This study aimed to profile the landscape of research rooted in this notion which was published from 1968 to 2021. The bibliographic data of 425 related publications were retrieved from the Scopus database for bibliometric analysis. Descriptive analysis and regression analysis were performed to profile the publication trend. Then, author bibliographic coupling analysis was carried out to identify the domains of research related to mathematics learning from concrete to abstract. The findings show an increasing trend of publication following the exponential model. The research was clustered into five research domains: (i) 'manipulatives and arithmetic learning'; (ii) 'mathematics learning of students with learning disabilities'; (iii) 'Concrete-Representational-Abstract sequence in elementary mathematics teaching'; (iv) 'Ideal mathematics teaching'; and (v) 'mathematics problem-solving and mathematics learning of students with autism spectrum disorder'. The two emergent research domains in this research area are (i) 'mathematics learning of students with learning disabilities'; and (ii) 'mathematics problem-solving and mathematics learning of students with autism spectrum disorder', which have the highest proportion of publications since 2015. The findings of this study can help researchers to understand the current landscape of research with the notion of mathematics learning from concrete to abstract, and hence propose pathways for future research.

show abstract

Manipulating Algebra: Comparing Concrete and Virtual Algebra Tiles for Students with Intellectual and Developmental Disabilities

Cited by 6 publications

References 31 publications

Visual and symbolic representations as components of algebraic reasoning

Visual and symbolic representations as components of algebraic reasoning

An Evidence-Based Practice Synthesis of Virtual Manipulatives for Students With ASD and IDD

Mathematics Learning from Concrete to Abstract (1968-2021): A Bibliometric Analysis

Contact Info

Product

Resources

About