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Visual and Symbolic Representations as Components of Algebraic Reasoning
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- Author(s): Ünal, Zehra E.; Ala, Asli M.; Kartal, Gamze; Özel, Serkan; Geary, David C.
- Language:
English- Source:
Journal of Numerical Cognition. 2023 9(2):327-345.- Publication Date:
2023- Document Type:
Journal Articles
Reports - Research - Language:
- Additional Information
- Availability: Leibniz Institute for Psychology. Universitatsring 15, Trier, 54296, Germany. e-mail: [email protected]; Web site: https://jnc.psychopen.eu
- Peer Reviewed: Y
- Source: 19
- Sponsoring Agency: National Science Foundation (NSF), Division of Research on Learning in Formal and Informal Settings (DRL)
- Contract Number: 1659133
- Education Level: Grade 9
High Schools
Junior High Schools
Middle Schools
Secondary Education - Subject Terms:
- ISSN: 2363-8761
- Abstract: 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.
- Abstract: As Provided
- Publication Date: 2023
- Accession Number: EJ1400925
- Availability:
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