Inverse reference in adults-elementary arithmetic.

Mauro, LeFevre, and Morris (2003) and Campbell (2008) manipulated problem format to assess university students' simple division and subtraction. Large division problems (dividend > 25; e.g., 42 ÷ 6 = _) and large subtraction problems (minuend > 10; e.g., 13 ? 6 = _), but not small problems, were solved more quickly when presented in inverse operation format (e.g., 6 × _ = 42 for division; 6 + _ = 13 for subtraction). They concluded that adults often solve large simple division and subtraction problems by reference to the inverse operation but rely on direct memory retrieval for smaller problems. Their findings, however, might have resulted from unequal practice or mixing of the inverse operations. Here, in Experiment 1 (division) and Experiment 2 (subtraction) normal and inverse formats received equal practice and only one operation was practiced (i.e., division or subtraction). Large divisions and subtractions were solved substantially faster when presented in inverse format, but there was also evidence that subtraction ties (e.g., 12 ? 6 = 6) and small subtractions (minuend ≤10) benefited from inverse format. The results affirm that inverse reference is an important element in adult's performance of elementary subtraction and division. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Adults' Understanding of Inversion Concepts: How Does Performance on Addition and Subtraction Inversion Problems Compare to Performance on Multiplication and Division Inversion Problems?

Problems of the form a + b - b have been used to assess conceptual understanding of the relationship between addition and subtraction. No study has investigated the same relationship between multiplication and division on problems of the form d × e ÷ e. In both types of inversion problems, no calculation is required if the inverse relationship between the operations is understood. Adult participants solved addition/subtraction and multiplication/division inversion (e.g., 9 × 22 ÷ 22) and standard (e.g., 2 + 27 - 28) problems. Participants started to use the inversion strategy earlier and more frequently on addition/subtraction problems. Participants took longer to solve both types of multiplication/division problems. Overall, conceptual understanding of the relationship between multiplication and division was not as strong as that between addition and subtraction. One explanation for this difference in performance is that the operation of division is more weakly represented and understood than the other operations and that this weakness affects performance on problems of the form d × e ÷ e. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effects of problem format on division and manipulation performance: Division facts are mediated via multiplication-based representations.

In 2 experiments, participants solved division problems presented in multiplication-based formats (e.g., 8 × _ = 72) more quickly than division problems presented in division-based formats (e.g., 72 ÷ 8 = _). In contrast, participants solved multiplication problems presented in a division-based format (e.g., _ ÷ 8 = 9) slowly and made many errors. In both experiments, the advantage for multiplication-based formats on division problems was found only for large problems (i.e., those with products or dividends greater than 25). These findings provide support for the view that large single-digit division facts are mediated via multiplication-based representations and that multiplication is the primary mode of representation for both division and multiplication facts. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Selection of procedures in mental addition: Reassessing the problem size effect in adults.

Adults' solution times to simple addition problems typically increase with the sum of the problems (the problem size effect). Models of the solution process are based on the assumption that adults always directly retrieve answers to problems from an associative network. Accordingly, attempts to explain the problem size effect have focused either on structural explanations that relate latencies to numerical indices (e.g., the area of a tabular representation) or explanations that are based on frequency of presentation or amount of practice. In this study, the authors have shown that the problem size effect in simple addition is mainly due to participants' selection of nonretrieval procedures on larger problems (i.e., problems with sums greater than 10). The implications of these results for extant models of addition performance are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The relationship between adults’ conceptual understanding of inversion and associativity.

Children’s understanding of the mathematical concepts of inversion and associativity are positively related, as measured by the use of conceptually based shortcut strategies on 3-term inversion problems (i.e., a + b – b, d × e ÷ e) and associativity problems (i.e., a + b – c, d × e ÷ f; Robinson & Dubé, 2009; Robinson & Ninowski, 2003). Individuals who use the inversion shortcut (e.g., 3) are more likely to use the associativity strategy (e.g., 3 × 12 ÷ 4. 12 ÷ 4 = 3, 3 × 3 = 9), which is almost never used by an individual who does not also use the inversion shortcut (Robinson & Dubé, 2009). One possible reason for this relationship is that directing attention to the right-most operation during problem solving may be required to prime the conceptually based shortcut strategies for both problem types. This study investigated the relationship between adults’ understanding of inversion and associativity. Adults (N = 42) solved inversion and associativity problems in 1 of 2 conditions. The participants were either presented with the left-most operation and then the whole problem or presented with the right-most operation and then the whole problem. A positive relationship between the use of the conceptually based strategies was found, and it was strikingly similar to the relationship found in childhood. There was evidence that the presentation of the right-most operation first primed the inversion shortcut. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The organization of arithmetic facts in memory: evidence from a brain-damaged patient

We report a single case study of a brain-damaged patient with impaired arithmetic performance. Three principal findings are presented: First, in a task involving production of answers to simple arithmetic problems, the patient's performance was far better for subtraction than for addition or multiplication. Second, in all arithmetic operations performance was generally much better for problems potentially solvable by rule (e.g., 5 + 0) than for problems requiring retrieval of specific facts (e.g., 5 + 3). Third, the dissociation between subtraction and the other arithmetic operations obtained in the production task was not observed in a verification task. The implications of these findings for claims concerning the organization of stored arithmetic facts are discussed.     

Alcohol primes, expectancies, and the working self-concept.

Previous research has shown that alcohol consumption can lead to momentary changes in the self-concept (e.g., Steele & Josephs, 1990). In two studies (n = 150), we examined whether the implicit activation of alcohol expectancies (i.e., sociability-related expectancies) would also lead to changes in self-perception. To test this idea, participants first completed a measure of sociability-related alcohol expectancies. In a subsequent laboratory session, participants were exposed to either alcohol-related primes (i.e., pictures or words associated with alcohol) or neutral primes. After the priming task, participants completed an ostensibly unrelated self-concept survey that contained words related to sociability (e.g., “outgoing”) and nonsociability related words (e.g., “clever”). For both studies, results revealed that sociability-related alcohol expectancies were positively associated with sociability-related self-concept ratings for participants exposed to alcohol primes, but not for participants exposed to the neutral primes. Implications for the role implicit self-concept activation may have on drinking behaviors are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Psychologists as faculty developers.

Describes the methods, problems, and prospects of faculty development, beginning with a review of how the field has broadened to demand planned interventions and measureable results, and depicts psychologists from varied orientations (e.g., organizational psychology) as prepared to make strong contributions to the survival and success of their colleagues on campus. Gives advice for starting faculty development programs (e.g., visits to faculty members' offices), for coping with campus politics (e.g., territoriality), for recruiting the neediest faculty participants (e.g., as research subjects), and for evaluating program effectiveness (e.g., by conducting projects as simple experiments). Finishes with arguments about why psychologists are ideally suited for the role of faculty developer (e.g., assessment and intervention skills). (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The beginnings of orthographic knowledge: Children's knowledge of double letters in words.

Three experiments were carried out to examine the development of knowledge about double letters. Children and adults chose items they thought looked most word-like from pairs of nonwords. First graders chose nonwords with final doublets (e.g., baff) and allowable doublets (e.g., yill) as more word-like than nonwords with initial doublets (e.g., bbaf) or unallowable doublets (e.g., yihh). Children in late kindergarten chose final-doublet nonwords (e.g., pess) more often than initial-doublet nonwords (e.g., ppes), but performed at chance when choosing between items such as jull and jukk . The same children in 1st grade chose jull more often than jukk even though their own spellings were semiphonetic and phonetic according to stage theories of spelling development. Only participants in the 6th grade and above knew the correspondence between a medial doublet and a preceding short vowel (e.g., tebbif). The results suggest that even young writers know about simple orthographic patterns. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Individual differences in components of reaction time distributions and their relations to working memory and intelligence.

The authors bring together approaches from cognitive and individual differences psychology to model characteristics of reaction time distributions beyond measures of central tendency. Ex-Gaussian distributions and a diffusion model approach are used to describe individuals' reaction time data. The authors identified common latent factors for each of the 3 ex-Gaussian parameters and for 3 parameters central to the diffusion model using structural equation modeling for a battery of choice reaction tasks. These factors had differential relations to criterion constructs. Parameters reflecting the tail of the distribution (i.e., τ in the ex-Gaussian and drift rate in the diffusion model) were the strongest unique predictors of working memory, reasoning, and psychometric speed. Theories of controlled attention and binding are discussed as potential theoretical explanations. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Multiplication by eye and by ear for Chinese-speaking and English-speaking adults.

Under two conditions, 32 English-speaking and 32 Chinese-speaking adults solved single-digit multiplication problems. In one condition, problems were presented as visual digits (e.g., 8×9). In the other condition, problems were presented as auditory number words in the participant's first language (e.g., /eit/ /taimz/ /nain/). Chinese-speaking adults made proportionately more operand-intrusion errors (e.g., 4×8=24) than English-speaking adults. Both groups made more operand-intrusion errors with auditory than with visual presentation. These findings are similar to those found when participants solve problems presented as visual number words (e.g., eight×nine), suggesting that in both cases the activation of phonological codes interferes with processing. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Help-seeking for alcohol-related problems in college students: Correlates and preferred resources.

Despite the development of a variety of efficacious alcohol intervention approaches for college students, few student drinkers seek help. The present study assessed students' history of help-seeking for alcohol problems, as well as their estimates of how likely they would be to use various help-seeking resources, should they wish to change their drinking. Participants were 197 college students who reported recent heavy drinking (46% male, 68.5% White, 27.4% African-American). Participants completed measures related to their drinking and their use (both past use and likelihood of future use) of 14 different alcohol help-seeking options. Repeated-measures analyses of variance revealed that students preferred informal help-seeking (e.g., talking to friends and family) over formal (e.g., talking with a counselor or medical provider) and anonymous resources (e.g., internet- or computer-based programs). Higher self-ideal discrepancy, greater depressive symptoms, and more alcohol-related consequences were positively associated with actual past help-seeking. Alcohol-related problems and normative discrepancy were negatively associated with hypothetical likelihood of utilizing all three help-seeking resources. These results suggest that heavy drinking college students prefer low-threshold intervention options including peer, family, computerized, and brief motivational interventions. Only 36 participants (18.3% of the sample) reported that they had utilized any of the help-seeking options queried, suggesting that campus prevention efforts should include both promoting low-threshold interventions and attempting to increase the salience of alcohol-related risk and the potential utility of changing drinking patterns. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Using conceptual models to teach BASIC computer programming.

Novices learned BASIC computer programming from a standard manual that emphasized the language's syntactic features or from a standard manual that included additional material emphasizing the underlying semantics (e.g., conceptual models). Although both kinds of training produced equivalent learning of the syntactic features of BASIC (i.e., syntactic knowledge), the semantically trained students developed fewer misconceptions (i.e., conceptual knowledge) and performed better on transfer tests of programming problem solving (i.e., strategic knowledge). In addition, problem-solving performance was strongly related to measures of conceptual knowledge. The results suggest that learning BASIC programming involves the growth of syntactic, conceptual, and strategic knowledge. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Interactive Effects of Numerical Surface Form and Operand Parity in Cognitive Arithmetic.

In Experiment 1, adults (n = 48) performed simple addition, multiplication, and parity (i.e., odd-even) comparisons on pairs of Arabic digits or English number words. For addition and comparison, but not multiplication, response time increased with the number of odd operands. For addition, but not comparison, this parity effect was greater for words than for digits. In Experiment 2, adults (n = 50) solved simple addition problems in digit and word format and reported their strategies (i.e., retrieval or procedures). Procedural strategies were used more for odd than even addends and much more for word than digit problems. The results indicate that problem encoding and answer retrieval processes for cognitive arithmetic are interactive rather than strictly additive stages. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Cognitive inhibition and working memory in attention-deficit/hyperactivity disorder.

Studies of cognitive control in attention-deficit/hyperactivity disorder (ADHD) have emphasized the ability to suppress motor responses (i.e., behavioral inhibition) rather than the ability to actively suppress prepotent mental representations (i.e., cognitive inhibition). Further, working memory deficits are suspected in ADHD, yet their distinction from cognitive inhibition is unclear. Two hundred and eighty-eight adolescent and adult participants, 115 of whom met criteria for ADHD and 173 of whom were for non-ADHD comparison, completed a sentence processing task that required the suppression of an incorrect interpretation and a working memory task. The results failed to support cognitive inhibition problems in ADHD. Moreover, the ability to reanalyze sentences with a temporary misinterpretation was at least partially related to working memory performance. The results challenge a unitary inhibition problem in ADHD and suggest inhibition problems do not extend to cognitive suppression in this age range. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Mental multiplication skill: Structure, process, and acquisition.

Collected response time (RT) and error data on multiplication problems up to 9?×?9 from 86 Ss in Grades 2–5 and from 60 undergraduate and graduate students. Results show that most errors involved correct products to other problems and that a developmental trend emerged in which the specific errors made by children mirrored adult errors by Grade 5. The error patterns indicate that an associative network evolves in which problem operands become linked to specific sets of candidate answers. Retrieval is governed by a process that activates candidates, and accessibility of correct answers is impeded by competing associations: At all skill levels, both problem-error rates and product-error rates (i.e., how often a problem's correct product occurs as an incorrect response to other problems) contributed to predicting correct problem RT in multiple regression analyses. These interference variables yielded higher correlations than did structural variables (e.g., the numerical size of problem operands), the latter having provided the basis for previous models of arithmetic memory. A network-interference account is proposed that explains the slow course of acquisition and differential problem difficulty in terms of interference by false associations. (French abstract) (37 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effects of practice and learner control on short- and long-term gain and efficiency

This study investigated the effects of practice opportunities and learner control on short- and long-term learning from a computer-based introductory statistics curriculum. In all, 380 participants were assigned to one of five conditions. The first four conditions differed in terms of the number of problems to solve per problem set. The fifth condition allowed learners to choose the amount of practice. A subset (n = 120) of the original participants returned for testing following a six-month interval. Overall, the fixed-practice conditions showed learning gains that varied in relation to the amount of practice (i.e., more was better). The data from the learner-control condition was unexpected, showing learning gains comparable with the most extended practice condition yet the fastest tutor-completion times. We discuss implications of these findings in relation to the design of efficacious instruction. Actual or potential applications of this research include the modification of computer-based instruction that can enhance individuals' learning efficiency and outcome scores.     

Multiple routes to solution of single-digit multiplication problems.

Researchers have assumed that adults solve simple arithmetic problems by retrieving answers from a network of stored facts. In 2 studies, undergraduates described their solutions of single-digit multiplication problems. They reported direct retrieval on approximately 80% of trials but also reported rules (e.g., anything times 0 is 0), repeated addition (e.g., 2?×?4?=?4?+?4), number series (e.g., 3?×?5?=?5, 10, 15), and derived facts (e.g., 6?×?7?=?[6?×?6]?+?6). Participants were slower to retrieve problems that were most likely to be solved by nonretrieval procedures and faster to retrieve problems that were usually solved by retrieval. These results indicate that direct-retrieval models are incomplete accounts of adults' performance and support a continuing influence of learning and experience on the mental representation of simple multiplication problems. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On the recollection of specific- and partial-source information

Memory judgments can be based on information that is more or less specific with respect to the source of an item. The authors introduce a procedure and multinomial model for measuring specific- and partial-source information. In 2 experiments, participants heard words spoken by 4 different voices: 2 male voices and 2 female voices. During the test, participants were required to remember who spoke the test items (e.g., Male 1, Male 2, Female 1, Female 2, or new word). Participants often remembered information about the gender of the source (i.e., partial-source information) when they did not remember information that identified the source itself (i.e., specific-source information). Dividing attention during retrieval impaired participants' memory for specific-source information (i.e., voice information) but did not affect memory for partial-source information (i.e., gender information).     

I fear your envy, I rejoice in your coveting: On the ambivalent experience of being envied by others.

We present 2 studies on being envied. Study 1 used an emotional narrative methodology. We asked 44 Spanish (23 women, 21 men) and 48 European American (36 women, 12 men) participants to tell us about a recent experience in which others envied them. We classified the antecedents, relationship context, markers of envy, coping strategies, and positive and negative implications of being envied. In Study 2, 174 Spanish (88 women, 86 men) and 205 European American (106 women, 99 men) participants responded to a situation in which they had something someone else wanted. We manipulated the object of desire (academic achievement or having “a better life”). We measured individual differences in orientation to achievement (i.e., vertical individualism), cooperation and interpersonal harmony (i.e., horizontal collectivism), a zero-sum view of success, beliefs that success begets hostile coveting, fear of success, and dispositional envy. We also measured participants' appraisals, positive and negative emotions, and coping strategies. The findings from both studies indicate that being envied has both positive (e.g., increased self-confidence) and negative consequences (e.g., fear of ill will from others). Being envied had more positive and more negative psychological and relational consequences among those participants who were achievement oriented (European Americans) than among participants who were oriented to cooperation and interpersonal harmony (Spanish). (PsycINFO Database Record (c) 2010 APA, all rights reserved)