A memory-based account of automatic numerosity processing

Abstract

We investigated the mechanisms responsible for the automatic processing of the numerosities represented by digits in the size congruity effect (Henik & Tzelgov, 1982). The algorithmic model assumes that relational comparisons of digit magnitudes (e.g., larger than {8,2}) create this effect. If so, congruity effects ought to require two digits. Memory-based models assume that associations between individual digits and the attributes "small" and "large" create this effect. If so, congruity effects ought only to require one digit. Contrary to the algorithmic model and consistent with memory-based models, congruity effects were just as large when subjects judged the relative physical sizes of small digits paired with letters as when they judged the relative physical sizes of two digits. This finding suggests that size congruity effects can be produced without comparison algorithms.

The role of parity, physical size, and magnitude in numerical cognition: The SNARC effect revisited

“…The results of a recent study probing the SCE (Choplin & Logan, 2005) reinforce the idea that numerals are associated instinctively with the left or right side of space. These authors found that people selected the physically larger member of the pair 4 2 faster than they did that of the pair 4 2 (the SCE).…”

“…The numerals 1-4 are small in virtually all natural and experimental contexts, regardless of the overall range. Choplin and Logan (2005) suggested that "the smallest digits are most strongly associated with the attribute 'small' and most weakly associated with the attribute 'large'"(p. 27). Choplin and Logan's data suggest that people retrieve instances of number-space and number-magnitude associations from past experience, commensurate with a learning account of stimulus-response mapping.…”

“…When the relative physical sizes of numerals in a pair are compared, people respond faster for congruent pairs (e.g., 8 2) than for incongruent pairs (e.g., 8 2; Fitousi & Algom, 2006). For singly presented numerals, people react to the large physical format of 8 faster than they do to that of 2, but the reverse holds true for 8 versus 2 (Algom, Dekel, & Pansky, 1996;Choplin & Logan, 2005). The task in studies of the SCE entails a nonsemantic attribute of digits, yet irrelevant numerical value cannot be ignored and affects task performance.…”

The cognitive architecture for chaining of two mental operations

“…We should insist here that we need not, and do not, assume that these two operations are arithmetical in the sense of relying on the same psychological mechanisms as in more standard arithmetical paradigms. Clearly, the limited number of stimuli and the repetition of many trials with them encourages a simple memory retrieval strategy (see the work of G. Logan and colleagues on automatization as memory retrieval, notably in the case of arithmetic: Choplin & Logan (2005); Klapp, Boches, Trabert, & Logan (1991);Logan (2002);Logan (1992Logan ( , 1988; ; Reder & Ritter (1992)). However, none of our predictions depend on this first operation being ''truly" arithmetical in any sense of the term.…”

Distinguishing Reconfiguration and Compound-cue Retrieval in Task Switching

“…We assumed that associations between the digits and the category High were strong for the higher digits and became weaker for lower digits. For simplicity, we assumed that association strength varied linearly Schneider and Logan (2005) with the value of the digits, with association strengths decreasing from 1-9 for the category Low and increasing from 1-9 for the category High (Choplin & Logan, 2005;Miller & Gelman, 1983;Shepard, Kilpatric, & Cunningham, 1975). We assumed a common slope, m, for both linear functions (formally, -m and m).…”