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Fig. 1 | Cognitive Research: Principles and Implications

Fig. 1

From: Mastering algebra retrains the visual system to perceive hierarchical structure in equations

Fig. 1

Object-based attention for perceptual and algebraic objects. a Visual property verification (e.g., same or different color?) is facilitated when visual elements appear to belong to the same (top) rather than different (bottom) objects. b The syntax of algebra produces hierarchically organized sub-expressions (illustrated by dotted rectangles). c Trials began with the presentation of an expression (left). On Color Verification trials (top right), two adjacent variables were changed to either red or blue; participants decided whether the colors were the same or different. If the hierarchical structure of algebra elicits object-based attention, verification should be facilitated within algebraic sub-expressions (e.g., c and f) rather than between them (e.g., c and a). On Algebraic Equivalence trials, a second expression—created by permuting the original expression—appeared to the right, and participants decided whether the expressions were algebraically equivalent. Half the permutations produced expressions that were equivalent—for instance, swapping variables separated by multiplication (middle right), which is both commutative and the higher-precedence operation. The other permutations produced expressions that were not equivalent—for instance, swapping variables separated by addition (bottom right), the lower-precedence operation

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