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Abstracts 2005 - The Psychonomic Society

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Saturday Noon Posters 4121–4122<br />

specific lesson that requires them to apply a variety of math concepts.<br />

<strong>The</strong>n, after some delay, they are asked to summarize what they have<br />

learned and understood by doing a guided recall task. Lesson plans<br />

and data from five groups of fifth through eighth graders from a region<br />

in the southwestern United States are shown, and methods of<br />

their evaluation, together with conclusions, are presented.<br />

(4121)<br />

<strong>The</strong> Whole or the Sum of the Parts: Strategies for Multidigit Addition.<br />

TINA SHANAHAN & JO-ANNE LEFEVRE, Carleton University<br />

(sponsored by Jo-Anne LeFevre)—Adults and children use a variety<br />

of procedures to solve simple mental arithmetic problems (e.g., 2 + 3,<br />

7 + 9), and these procedures are differentially effective. For example,<br />

in mental addition, direct retrieval of stored number facts is faster and<br />

more accurate than counting up. Strategy choice in simple arithmetic<br />

varies with characteristics of the individual, such as age and math ability,<br />

and with problem characteristics, such as complexity. In the present<br />

research, we examined the range of strategies that were reported<br />

by young adults (N = 30) in mental calculation of multidigit sums (e.g.,<br />

37 + 28) and determined the extent to which these choices were influenced<br />

by individual differences (e.g., math ability) and by problem<br />

characteristics (e.g., complexity, orientation). <strong>The</strong> results have impli-<br />

123<br />

cations for understanding how adults select strategies for complex<br />

mental calculations.<br />

(4122)<br />

<strong>The</strong> Perceptual Constituents of Algebraic Knowledge. DAVID<br />

LANDY & ROBERT L. GOLDSTONE, Indiana University (sponsored<br />

by Robert L. Goldstone)—In addition to being a cognitive activity<br />

of great practical significance, algebraic reasoning is a default<br />

example of symbolic processing. Unlike purely internal processes, algebraic<br />

symbol manipulation requires complicated acts of perception.<br />

This poster presents the results of two experiments that demonstrate<br />

a significant interaction between the application of the order of precedence<br />

laws and nonmathematical grouping effects. In both experiments,<br />

subjects judged whether an equation containing both additions<br />

and multiplications was valid. In the first, the spacing between terms<br />

was manipulated to either support or violate the order of operations.<br />

In the second experiment, the symbols were chosen so that letters on<br />

the sides of an operation were either nearby or distant in the alphabet.<br />

In both experiments, grouping pressures inconsistent with the order<br />

or precedence rule impeded correct judgment only when the correct<br />

answer depended on the grouping. This indicates that algebraic reasoning<br />

interacts with nonmathematical grouping pressures.

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