Academic journal article Canadian Journal of Experimental Psychology

Operand-Operator Compatibility in Cognitive Arithmetic

Academic journal article Canadian Journal of Experimental Psychology

Operand-Operator Compatibility in Cognitive Arithmetic

Article excerpt

Adults' simple addition performance (e.g., 3 + 4 = ?) is faster, more accurate, and more often based on direct memory retrieval (rather than a procedural method, such as counting) when problems are presented in digit format (3 + 4) than written-word format (three + four). A possible explanation is that the mathematical symbol + is more compatible to memory retrieval with Arabic numerals than word numerals. To investigate this, two groups of 42 participants received eight blocks of 72 simple addition problems. For one group, operand format (digits or words) switched across trials within each block and operator (the symbol + or the word plus) alternated between blocks. For the other group, operator switched across trials, whereas operand format alternated between blocks. In the switch-format condition, compatible formats (e.g., 3 + 4, three plus four) were solved by direct memory retrieval more often than were incompatible formats (3 plus 4, three + four). There was no compatibility effect on use of direct memory retrieval when operand format was fixed within blocks and operator format switched across trials. There was also a reaction time (RT) advantage only for digit operands with + relative to plus when format switched, but + facilitated only word problems when operand format was blocked. The results indicate that operand- operator compatibility and format switching had previously unsuspected effects that qualify previous research examining format effects in arithmetic.

Keywords: simple arithmetic, strategy choice, operand format

This experiment investigated effects of numeral format (e.g., 3 + 4 vs. three + four) on adults' simple addition performance. Much research has demonstrated that adults' simple arithmetic with writtenword operands is substantially slower, more error prone, and relies more on procedural strategies (e.g., counting) than digit-format problems (see Campbell & Epp, 2005, for a review). Furthermore, these effects are often exaggerated for larger, more-difficult problems (e.g., 7 + 9) relative to small problems (3 + 2; e.g., Campbell & Alberts, 2009). The source of these effects has been the focus of considerable debate. Some researchers argue that format effects in arithmetic arise only during problem encoding or response stages (e.g., McCloskey & Macaruso, 1995; Noël, Fias, 8c Brysbaert, 1997; Sokol, McCloskey, Cohen & Aliminosa, 1991), whereas others propose format can directly affect retrieval or calculation processes (e.g., Bernardo, 2001; Blankenberger & Vorberg, 1997; Campbell, 1994; Campbell & Alberts, 2009; Campbell, Parker, & Doetzel, 2004).

The majority of experiments that have compared simple arithmetic performance with digit and written-word operands have used a mathematical symbol (+, -, X, +) to identify arithmetic operation. As a result, the difficulty of the word-format condition might owe to the fact that it mixes two formats: The operands are in written-verbal format whereas the operator is a pictorial symbol (e.g., four + five). In contrast, the constituents of Arabic problems are all pictorial symbols (4 + 5). The performance advantage typically observed for the digit format might occur because the operands and operator are compatible and cohere as a compound retrieval cue, whereas a combination of written-words and symbol may be difficult to encode. Indeed, using compatible stimuli (e.g., 4X6, four times six), Sokol et al. (1991) found no difference between digit and word formats in the simple multiplication performance of two acalculic subjects. Another reason to suspect that operand- operator compatibility is potentially important is that solving simple arithmetic problems in spoken-word format is no more difficult than digit format when digits are presented sequentially to match spoken format (LeFevre, Lei, Smith-Chant, & Mullins, 2001; Metcalfe & Campbell, 2008). With spoken-word problems, the operands and operator are encoded phonologically and therefore do not involve inconsistent formats. …

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