The Development of Internal Representations of Magnitude
and Their Association with Arabic Numerals
Orly Rubinsten, Avishai Henik, Andrea Berger, and Sharon Shahar-Shalev
Ben-Gurion University of the Negev, Beer-Sheva, Israel
Developmental aspects of number concepts were evaluated using participants from the
beginning and end of first grade (6–7 years old), third and fifth grades (7–11 years old),
and university (22 years old). Participants evaluated the numerical value or physical size
of stimuli varying along both dimensions. The numerical distance effect appeared in all
groups. In contrast, the size congruity effect started to appear only at the end of first grade.
Based on our results, a model of internal representation of magnitude claiming that there
are two different representations was propose. At the beginning of first grade children can
automatically access only one of these representations and only from the end of first grade
can they access both of these representations. © 2002 Elsevier Science
Key Words: Arabic numeral; quantity; automaticity; development.
Moyer and Landauer (1967) were the first to find that the larger the numerical
difference between two digits, the shorter the time required to decide which is
larger. For example, it takes longer to decide that “8” is larger than “6” than to
decide that “8” is larger than “1.” This distance effect has since been reported in
numerous studies (e.g., Banks, Mermelstein, & Yu, 1982; Dehaene, 1989;
Dehaene, Dupoux, & Mehler, 1990; Duncan & McFarland, 1980; Henik &
Tzelgov, 1982; Link, 1990; Moyer, 1973; Moyer & Bayer, 1976; Parkman, 1971;
Schwarz & Heinze, 1998; Tzelgov, Meyer, & Henik, 1992). Dehaene (1997)
trained university students to avoid the distance effect and found that even after
1600 training trials, participants were still slower with close digits than with more
distant ones. Moyer and Landauer (1967) suggested that people convert written
or auditory numbers into analog magnitudes. The comparison between these
magnitudes is made in much the same way that comparisons are made between
physical stimuli such as lengths of lines. It has been postulated that the source of
the distance effect is the overlap between representations of numbers. That is, the
74
Journal of Experimental Child Psychology 81, 74–92 (2002)
doi:10.1006/jecp.2001.2645, available online at http://www.idealibrary.com on
0022-0965/02 $35.00
© 2002 Elsevier Science
All rights reserved.
This work was supported by a grant to A. Henik from the Israel Science Foundation founded by
the Israel Academy of Sciences and Humanities. We thank Mrs. Kineret Hadad, principal of Oriyan
Elementary School in Beer-Sheva, Israel, for allowing us to conduct our research in the school. We
also thank the teachers and students in Oriyan Elementary School for helping and participating in the
experiment.
Address correspondence and reprint requests to Avishai Henik, Department of Behavioral
Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel. Fax: 972-8-6472932. E-mail:
henik@bgumail.bgu.ac.il.