Sequential modulations of poorer-strategy effects during strategy execution: An event-related potential study in arithmetic

When participants accomplish cognitive tasks, they obtain poorer performance if asked to execute a poorer strategy than a better strategy on a given problem. These poorer-strategy effects are smaller following execution of a poorer strategy relative to following a better strategy. To investigate ERP correlates of sequential modulations of poorer-strategy effects, we asked participants (n = 20) to accomplish a computational estimation task (i.e., provide approximate products to two-digit multiplication problems like 38 × 74). For each problem, they were cued to execute a better versus a poorer strategy. We found event-related potentials signatures of sequential modulations of poorer-strategy effects in two crucial windows (i.e., between 200 and 550 ms and between 850 and 1250 ms) associated with executive control mechanisms and allowing conflict monitoring between the better and the cued strategy. These results have important implications on theories of strategies as they suggest that sequential modulations of poorer-strategy effects involve earlier as well as later mechanisms of cognitive control during strategy execution.     

Operator and operand preview effects in simple addition and multiplication: A comparison of Canadian and Chinese adults

Using an arithmetic-based retrieval-induced forgetting (RIF) paradigm, researchers have found evidence that participants with very high arithmetic proficiency (Chinese adults), but not less-skilled participants (Canadian adults), solved some simple additions (e.g. 3 + 2) using fast procedural skills. Here we sought converging evidence for this using the operator-priming paradigm. Previous research testing simple addition and multiplication found that a 150-ms preview of the operator (+ or ×) facilitated only addition performance. This was taken as evidence that addition, but not multiplication, was solved by procedural algorithms that could be primed by presentation of the plus sign. In the present study, Chinese and Canadian adults (N = 144) were tested in the operator-priming paradigm but, in contrast to the RIF results, there was little evidence that operator-priming effects differed between the groups and robust operator priming was observed in both addition and multiplication. Thus, the operator preview results did not reinforce the results of previous research but the experiment revealed robust group differences in operand preview effects: For the Chinese, but not the Canadians, a preview of the numerical operands produced much greater facilitation for multiplication than addition. The fact that CN obtained a mean 103-ms gain for multiplication from the 150-ms preview of the operands strongly suggests that multiplication was their default operation in this paradigm. This result adds a potentially important new phenomenon to the behavioural distinctions between Chinese and North American adults' arithmetic skills.     

Effects of execution duration on within-item strategy switching in young and older adults

This study aimed at determining whether previously found age-related differences in within-item strategy switching is modulated by duration of engagement in initial strategy execution. In a computational estimation task, young and older adults had to find estimates to arithmetic problems like 37×64 while either rounding down (i.e., 30×60) or rounding up (i.e., 40×70) both operands to the closest decades. Participants were asked to execute a cued strategy for different durations (i.e., 1, 2, or 3 s), before deciding whether the cued strategy was the best strategy and to switch to the best strategy if the cued strategy was not the best. The main findings revealed that (1) young and older adults were able to switch strategies, especially when they started to execute poorer strategy on a given item; (2) older adults switched strategy less often than young adults, and (3) both young and older participants switched strategy less frequently for long than for short durations. These findings suggest that to be able to switch strategy within item, participants should not be too much engaged in execution of the initially selected strategy, and that duration of engagement in initial strategy execution does not modulate age-related differences in within-item strategy execution.     

Stability and change in children's division strategies

Age-related changes in children's performance on simple division problems (e.g., 6/2, 72/9) were investigated by asking children in Grades 4 through 7 to solve 32 simple division problems. Differences in performance were found across grade, with younger children performing more slowly and less accurately than older children. Problem size effects were also found in that children were faster and more accurate on small problems than on large problems. Two strategies changed across age, with children in Grade 4 relying heavily on the strategy of "addition" (adding the divisor until the dividend was reached) to solve the problems and children in Grades 5 through 7 relying primarily on the strategy of "multiplication" (recasting the division problem as a multiplication problem) to solve the problems. Surprisingly, the frequency of direct retrieval (retrieving the answer directly from memory) did not increase across grade and never became the dominant strategy of choice. Reasons for why retrieval use remains infrequent and age invariant are discussed. Overall, the results suggest that division is a unique operation and that the continued study of division may have implications for further understanding of how procedural and conceptual knowledge of arithmetic develops.     

Instruction and load effects on high-skill and low-skill individuals: A study in the domain of mental arithmetic

What happens when people are asked to respond as quickly or as accurately as possible? This study tested the effects of speed/accuracy instructions and working-memory load on people's strategy efficiency and strategy selection. Adult participants solved simple addition problems (Experiment 1) and simple multiplication problems (Experiment 2) under load and no-load conditions and provided trial-by-trial strategy reports. High-skill participants were more efficient than low-skill participants, but the underlying causes of these skill-related effects differed across experiments. In the addition experiment, high-skill participants responded adaptively to the changing situations by changing their strategy choices, which resulted in smaller effects on their actual performance. Low-skill participants in contrast, did not change their strategy choices as adaptively, which resulted in less efficient performance—and especially so under load conditions. In the multiplication experiment, high-skill and low-skill participants differed in strategy efficiencies rather than in strategy choices. In the discussion, the results are further interpreted and future adaptations for the adaptive strategy choice model (ASCM; Siegler & Jenkins, 1989) are suggested.     

Loss aversion,diminishing sensitivity,and the effect of experience on repeated decisions

Three experiments are presented that explore the assertion that loss aversion and diminishing sensitivity drive the effect of experience on choice behavior. The experiments are focused on repeated choice tasks where decision makers choose repeatedly between alternatives and get feedback after each choice. Experiments 1a and 1b show that behavioral tendencies that were previously interpreted as indications of loss aversion in decisions from experience are better described as products of diminishing sensitivity to absolute payoffs. Experiment 2 highlights a nominal magnitude effect: A decrease in the magnitude of the nominal payoffs eliminates the evidence for diminishing sensitivity. These and related previous results can be captured with a model that assumes reliance on small samples of subjective experiences, and an increase in diminishing sensitivity with payoff variability. Copyright © 2008 John Wiley & Sons, Ltd.     

从效应量应有的性质看中介效应量的合理性

效应量的作用有两个方面, 一是弥补了统计检验的不足, 二是使得效应有可比性。结合统计显著性和效应量, 才能得出适当的统计结论。效应量应当具有一些基本性质, 包括与测量单位无关、单调性、不受样本容量的影响。国际上流行的中介效应量κ平方就是因为缺乏单调性而引发质疑和研究, 从而被彻底终结了其作为中介效应量的合法性。R平方型中介效应量同样有缺乏单调性的问题。文末讨论了如何报告中介效应量以及有待研究的问题。     

Understanding and using principles of arithmetic: operations involving negative numbers

Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers ( Dixon, Deets, & Bangert, 2001 ). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation. Participants ( N = 44) completed two tasks. In the Evaluation task, participants rated how well sets of equations were solved. Some sets violated principles of arithmetic and others did not. Participants rated non-violation sets higher than violation sets for two different principles for subtraction with a negative number. In the Word Problem task, participants read word problems and set up equations that could be used to solve them. Participants who displayed greater knowledge of principles of arithmetic with a negative number were more likely to set up equations that involved negative numbers. Thus, participants' knowledge of arithmetic principles was related to their problem representations.     

The cultural congruency effect: Culture, regulatory focus, and the effectiveness of gain- vs. loss-framed health messages

The present study contributes a cultural analysis to the literature on the persuasive effects of matching message frame to individuals’ motivational orientations. One experiment examines how members of cultural groups that are likely to differ in their regulatory focus respond to health messages focusing on either the benefits of flossing or the costs of not flossing. White British participants, who had a stronger promotion focus, were more persuaded by the gain-framed message, whereas East-Asian participants, who had a stronger prevention focus, were more persuaded by the loss-framed message. This cultural difference in persuasion was mediated by an interaction between individuals’ self-regulatory focus and type of health message. Thus health messages framed to be culturally congruent led participants to have more positive attitudes and stronger intentions to perform the health behaviors, and the interaction between self-regulatory focus and message frame emerged as the pathway through which the observed cultural difference occurs. Discussion focuses on the integration of individual difference, socio-cultural, and situational factors into models of health persuasion.     

Influence of the large–small split effect on strategy choice in complex subtraction

Two main theories have been used to explain the arithmetic split effect: decision‐making process theory and strategy choice theory. Using the inequality paradigm, previous studies have confirmed that individuals tend to adopt a plausibility‐checking strategy and a whole‐calculation strategy to solve large and small split problems in complex addition arithmetic, respectively. This supports strategy choice theory, but it is unknown whether this theory also explains performance in solving different split problems in complex subtraction arithmetic. This study used small, intermediate and large split sizes, with each split condition being further divided into problems requiring and not requiring borrowing. The reaction times (RTs) for large and intermediate splits were significantly shorter than those for small splits, while accuracy was significantly higher for large and middle splits than for small splits, reflecting no speed–accuracy trade‐off. Further, RTs and accuracy differed significantly between the borrow and no‐borrow conditions only for small splits. This study indicates that strategy choice theory is suitable to explain the split effect in complex subtraction arithmetic. That is, individuals tend to choose the plausibility‐checking strategy or the whole‐calculation strategy according to the split size.     

An integrated theory of whole number and fractions development

This article proposes an integrated theory of acquisition of knowledge about whole numbers and fractions. Although whole numbers and fractions differ in many ways that influence their development, an important commonality is the centrality of knowledge of numerical magnitudes in overall understanding. The present findings with 11- and 13-year-olds indicate that, as with whole numbers, accuracy of fraction magnitude representations is closely related to both fractions arithmetic proficiency and overall mathematics achievement test scores, that fraction magnitude representations account for substantial variance in mathematics achievement test scores beyond that explained by fraction arithmetic proficiency, and that developing effective strategies plays a key role in improved knowledge of fractions. Theoretical and instructional implications are discussed.     

Age-related changes in children's executive functions and strategy selection: A study in computational estimation

Third, fifth, and seventh graders selected the best strategy (rounding up or rounding down) for estimating answers to two-digit addition problems. Executive function measures were collected for each individual. Data showed that (a) children's skill at both strategy selection and execution improved with age and (b) increased efficiency in executive functions contributed significantly to age-related improvement in children's strategy selection skill. These findings have implications for understanding of age-related differences in computational estimation, strategy selection processes, and mechanisms of strategic development in children.     

Adolescent suicide, gender, and culture: A rate and risk factor analysis

The current paper provides a comprehensive research review of gender differences in rates of and risk factors for adolescent suicidal behavior in four main U.S cultural subgroups: African Americans, Native Americans, Asian Americans, and Latino Americans. The paper highlights substantial findings from the most recent literature and provides direction for future research and clinical work. The data presented suggest that clinicians and interventionists relying on nonfatal expressions of suicide will continue to fail to identify adolescent males at risk for suicide, as females are more likely to report suicide ideation and attempts across all cultural groups reviewed. We conclude that researchers and clinicians should utilize indirect, broad measures of suicide proneness, as opposed to the traditional direct self-report tools. Although past research has examined cultural and gender differences in risk factors for suicidal behavior, these investigations have been primarily isolated from each other. Therefore, we sought to examine adolescent suicidal behavior and how it operates as a function of both gender and culture.     

The culture of perceptual expertise and the other-race effect

In our commentary, we propose that the ORE can be viewed as a form of perceptual expertise. Like experts, we recognize own-race faces at the subordinate level as individuals and novices when recognize other-race faces at the basic level of race. Applying a perceptual expertise account, we explain the ORE in terms of its cognitive, neural, and motivational factors. We suggest that by creating a culture of “other-race” expertise, improvements in other-race face recognition can be achieved.     

Use of the mathematical principle of inversion in young children

An important issue in the development of mathematical cognition is the extent to which children use and understand fundamental mathematical concepts. We examined whether young children successfully use the principle of inversion and, if so, whether they do so based on qualitative identity, length, or quantity. Twenty-four preschool children and 24 children in Grade 1 were presented with three-term inversion problems (e.g., 3+2-2) and standard problems of similar magnitude (e.g., 2+4-3). Problems were presented in three conditions to determine whether children used inversion at all and, if so, whether their decisions were based on quantitative or nonquantitative features of the problems. Both preschool and Grade 1 children showed evidence of using inversion in a fully quantitative manner, indicating that this principle is available in some form prior to extensive formal instruction in arithmetic.     

Common language effect size for correlations

The Pearson correlation coefficient can be translated to a common language effect size, which shows the probability of obtaining a certain value on one variable, given the value on the other variable. This common language effect size makes the size of a correlation coefficient understandable to laypeople. Three examples are provided to demonstrate the application of the common language effect size in interpreting Pearson correlation coefficients and multiple correlation coefficients.     

Spatial and visual working memory ability in children with difficulties in arithmetic word problem solving

Although various studies support the multicomponent nature of visuospatial working memory, to date there is no general consensus on the distinction of its components. A difference is usually proposed between visual and spatial components of working memory, but the individual roles of these components in mathematical learning disabilities remains unclear. The present study aimed to examine the involvement of visual and spatial working memory in poor problem-solvers compared with children with normal level of achievement. Fourth-grade participants were presented with tasks measuring phonological loop, central executive, and visual versus spatial memory. In two separate experiments, both designed to distinguish visual and spatial component involvement, poor problem-solvers specifically failed on spatial—but not visual or phonological—working memory tasks. Results are discussed in the light of possible working memory models, and specifically demonstrate that problem-solving ability can benefit from analysis of spatial processes, which involves ability to manipulate and transform relevant information; instead, no benefit is gained from the analysis of visual pictorial detail.     

DSM-5: The intersectionality of spirituality,culture, and aging

Counselors practice with older adults whose religion and spirituality may be factors in assessment and treatment. The DSM-5 includes religion and spirituality as part of pathology or culture. This approach is supported in counselor education. Religion as a cultural derivative only reflects the human aspect of religion, not including a client’s perception of divine actions possibly beyond the human experience, i.e., a miracle. How does the clinician discern if a client’s experience reflects pathology or the possibility of some sort of miracle? This article includes strengths and limitations of a cultural definition of religious and spiritual experience with case applications.