Retrieval savings with nonidentical elements: The case of simple addition and subtraction

The identical elements (IE) theory of fact representation (Rickard, 2005) proposes that memorized facts that are composed of identical elements (e.g., 6 × 8 = 48 and 8 × 6 = 48) share a common representation in memory, whereas facts with nonidentical elements (e.g., 6 × 8 = 48 and 48 ÷ 8 = 6) are represented separately in memory. The IE model has been successfully applied to the transfer of practice in simple multiplication and division, in transition from procedure-based to retrieval-based performance, and in cued episodic recall. In the present article, we examined the effects of practicing simple addition problems (e.g., 3 + 6 = 9) on the performance of corresponding subtraction problems (9 − 6 = 3), and vice versa. According to IE theory, there should be no transfer of retrieval savings between addition and subtraction facts if performance is based on discrete IE fact representations. Cross-operation response time savings were observed, however, for both small, well-memorized problems (e.g., practice 3 + 2, test 5 − 2) and larger problems (6 + 8, 14 − 6), and they were statistically robust when trials that were self-reported as direct retrieval were analyzed. The transfer of retrieval practice savings between facts with nonidentical elements challenges IE theory as a comprehensive model of transfer in memory retrieval.     

Target strength and retrieval-induced forgetting in semantic recall

Retrieval-induced forgetting (RIF) occurs when practice of a memory item impairs retrieval of related, unpracticed items. Here, we demonstrated that RIF in semantic memory is retrieval dependent. University students either studied (7 × 8 = 56) or retrieved (7 × 8 = ?) the answers to a set of multiplication problems for 40 blocks and then were tested on their addition counterparts (7 + 8 = ?). For the retrieval practice group, but not the study practice group, response time for the multiplication-practiced addition facts was about 100 msec slower, relative to control addition problems, in the first of five postpractice addition blocks. Subsequent blocks of addition were interleaved with retrieval blocks of all the multiplication counterparts, which permitted measurement of RIF for the control addition problems after only a single retrieval of their multiplication counterparts. The control problems presented RIF in excess of 200 msec, much larger than the RIF observed after massive practice. This is consistent with the hypothesis that inhibition of competitors should be weaker when target strength is high than when target strength is only moderate (Anderson, 2003; Norman, Newman, &; Detre, 2007). The evidence that RIF in semantic retrieval is both retrieval dependent and weaker following massive target practice than following moderate target practice provides strong support for inhibition-based theories of RIF.     

Cultural differences in gender role attitudes between Chinese and American students

A total of 665 Chinese college students in Taiwan and Caucasian college students in eastern North Carolina were administered several sex role attitude scales developed by Spence et al. (1978, 1980). The scales were translated into Chinese for Chinese subjects. Results indicated cultural differences in attitudes toward Marital Roles, Expressivity, Social Interaction, and Preference for males. In both cultures, females were found to be significantly more liberal, as shown in Attitudes Toward Women, Marital Roles, and Social Interaction. These results are consistent with previous research. Cultural differences were also as expected, with Chinese holding more conservative views.An earlier version of this paper was presented in part at the 63rd Annual Convention of the Eastern Psychological Association, Boston, Massachusetts, April 3, 1992.     

Conditions of error priming in number-fact retrieval

Analysis of errors in simple multiplication has shown that answers retrieved on previous trials are initially inhibited (negative error priming) but later are promoted as errors to subsequent problems (positive error priming). Two experiments investigated whether error priming is associated either with problem-specific retrieval processes or with representations of answers that can be manipulated independently of problems. In Experiment 1, answers were primed by visually presenting products for 200 msec prior to problems. Correct-answer primes facilitated retrieval, related-incorrect primes interfered with retrieval more than unrelated primes, and both effects were greater for more difficult problems. Primes affected only the trial on which they were presented, however, whereas both negative and positive error priming from previous problems were observed across trials. In Experiment 2, subjects named and retrieved multiplication products on alternating trials. Just-named products were inhibited as errors to the following multiplication problem (i.e., negative error priming), but, compared to positive priming from previous retrieved products, positive error priming from previously named numbers was weak. The results indicate that positive error priming is due mainly to an encoding or retrieval bias produced by previous problems, whereas negative error priming entails suppression, or de-selection, of answer representations.     

Calculation latency: The μ of memory and the τ of transformation

Does numeral format (e.g., 4 + 8 vs. four + eight) affect calculation per se? University students (N=47) solved single-digit addition problems presented as Arabic digits or English words and reported their strategies (memory retrieval or procedures such as counting or transformation). Decomposition of the response time (RT) distributions into μ (reflecting shift) and t (reflecting skew) confirmed that retrieval trials contributed predominantly to μ, whereas procedure trials contributed predominantly to τ. The format × problem size RT interaction (i.e., greater word-format RT costs for large problems than for small problems) was associated entirely with μ and not with τ. Reported use of procedures presented a corresponding format × size interaction. Together, these results indicate that, relative to the well-practiced digit format, the unfamiliar word format disrupts number-fact retrieval and promotes use of procedural strategies.     

Identical elements model of arithmetic memory: Extension to addition and subtraction

The identical elements (IE) model of arithmetic fact representation (Rickard, 2005; Rickard & Bourne, 1996) was developed and tested with multiplication and division. In Experiment 1, we demonstrated that the model also applies to addition and subtraction by examining transfer of response time (RT) savings between prime and probe problems tested in the same block of trials. As is predicted by the IE model, there were equivalent probe RT savings for addition with identical repetition (prime 6 + 9 --> probe 6 + 9) or an order change (9 + 6 --> 6 + 9), but much greater savings for subtraction with identical repetition (15 - 6 --> 15 - 6) than with an order change (15 - 9 --> 15 - 6), and no savings with an operation change (15 - 9 --> 6 + 9 or 6 + 9 --> 4 15 - 6). In Experiment 2, we examined transfer in simple multiplication and division and demonstrated symmetrical transfer between operations. Cross-operation RT savings were eliminated, however, when the RT analysis included only trials on which both the prime and the probe problems were reportedly solved by direct retrieval. An IE model extended to accommodate savings associated with procedural strategies provides a coherent account of facilitative transfer effects in simple arithmetic.     

Illuminating the dark side of creative expression: assimilation needs and the consequences of creative action following mortality salience

Previous research indicates that mortality salience and creative behavior combine to increase feelings of guilt, presumably over the disruption to social connection elicited by the call for innovative expression. The present studies examined whether satiating assimilation motives by highlighting conformity to others reduces this effect (Study 1) and facilitates positive psychological engagement (Study 2). Study 1 used a 2 (conformity vs. neutral feedback)x2 (mortality salience vs. control)x2 (creative task vs. noncreative task) design and had participants complete a self-report measure of guilt. Study 2 used a 2 (mortality salience vs. control)x2 (other goal task vs. self-goal task) design, and after a creativity exercise, had participants complete measures of positive mood, vitality, and creative problem solving. Results indicated attending to assimilation needs reduced the elevated guilt that follows the juxtaposition of mortality salience and creative behavior and also increased a sense of positive engagement. Implications are briefly discussed.