# Going through the Motions: Skill Differences in the Representation of Arithmetic Operations

- Marcie Penner-Wilger,
*Franklin & Marshall College*
- David H. Landy,
*University of Richmond*
- Xiaoyu Zhang,
*Franklin & Marshall College*
- Alison Weitzer,
*Franklin & Marshall College*

## Abstract

How do adults represent arithmetic operations? One proposal is
that addition is represented as rightward movement along a left-right mental
number-line, whereas subtraction is represented as leftward movement (Hubbard et
al., 2005). To test this proposal, 24 college students solved single-digit
arithmetic problems displayed on a computer screen along with rightward- or
leftward-moving dots. We hypothesized that that for addition, rightward motion
would facilitate problem solution (as it is congruent with the mental
representation of movement along a mental number-line) and that leftward movement
would interfere with problem solution (as it is incongruent). For subtraction,
the expectations of facilitation and interference were reversed. We found that
the response times of students with lower levels of mathematical skill, though
not with higher levels, showed the hypothesized operational momentum effect. This
research has implications for the development of math pedagogy, especially for
how operations are conceptually introduced.

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