Visual and Symbolic Representations as Components of Algebraic Reasoning

Autor/inn/en	Ünal, Zehra E.; Ala, Asli M.; Kartal, Gamze; Özel, Serkan; Geary, David C.
Titel	Visual and Symbolic Representations as Components of Algebraic Reasoning
Quelle	In: Journal of Numerical Cognition, 9 (2023) 2, S.327-345 (19 Seiten) PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
Schlagwörter	Grade 9; Algebra; Mathematics Instruction; Algorithms; Equations (Mathematics); Problem Solving; Visual Aids; Symbols (Mathematics); Thinking Skills; Cues; Spatial Ability; Teaching Methods; Mathematics Achievement + Suchen Sie Ihr Suchwort? School year 09; 9. Schuljahr; Schuljahr 09; Mathematics lessons; Mathematikunterricht; Algorithm; Algorithmus; Equations; Mathematics; Gleichungslehre; Problemlösen; Anschauungsmaterial; Denkfähigkeit; Stichwort; Räumliches Vorstellungsvermögen; Teaching method; Lehrmethode; Unterrichtsmethode; Mathmatics sikills; Mathmatics achievement; Mathematical ability; Mathematische Kompetenz
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. (As Provided).
Anmerkungen	Leibniz Institute for Psychology. Universitatsring 15, Trier, 54296, Germany. e-mail: support@psychopen.eu; Web site: https://jnc.psychopen.eu
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01