Who can escape the natural number bias in rational number tasks? A study involving students and experts

Many learners have difficulties with rational number tasks because they persistently rely on their natural number knowledge, which is not always applicable. Studies show that such a natural number bias can mislead not only children but also educated adults. It is still unclear whether and under what conditions mathematical expertise enables people to be completely unaffected by such a bias on tasks in which people with less expertise are clearly biased. We compared the performance of eighth‐grade students and expert mathematicians on the same set of algebraic expression problems that addressed the effect of arithmetic operations (multiplication and division). Using accuracy and response time measures, we found clear evidence for a natural number bias in students but no traces of a bias in experts. The data suggested that whereas students based their answers on their intuitions about natural numbers, expert mathematicians relied on their skilled intuitions about algebraic expressions. We conclude that it is possible for experts to be unaffected by the natural number bias on rational number tasks when they use strategies that do not involve natural numbers.     

Are Collective Efficacy,Disorder and Social Support Associated with One’s Quality of Life? Evidence from the Multilevel SWING Study in Belgium

The current study assesses the evidence for the association between several neighborhood social processes (collective efficacy and social disorder) and two important individual-level quality of life indicators, which are avoidance behaviour and mental health. In addition to these neighborhood characteristics, the study also assesses the impact of an individual’s social support network on these two outcomes. Hypotheses are derived from a theoretical framework that integrates insights from social capital theory, collective efficacy theory and broken windows theory. Hypotheses about both neighborhood- and individual-level effects are tested by applying multilevel analyses to data from the ‘Social capital and Well-being In Neighborhoods in Ghent’ (SWING) survey of 2011, which consists of face-to-face interviews among the adult population in the second largest municipality of Belgium. Results suggest that individuals living in neighborhoods with lower levels of social trust and higher levels of disorder report more avoidance behaviour. Neighborhood effects on mental health are rather negligible. Individuals who experience more social support report both a better mental health and fewer avoidance behaviour.     

Post‐merger identification as a function of pre‐merger identification,relative representation,and pre‐merger status

This experiment examined the impact of pre‐merger identification (low, high), pre‐merger group status (low, high) and relative representation (low, high) upon identification with a new merger group. In the first phase of the study, 156 university students were assigned to a pre‐merger team of ‘inductive’ thinkers. Pre‐merger identification was manipulated by giving the participants feedback about the extent to which they used the inductionist style. Pre‐merger status was manipulated by informing participants that their team had performed worse or better than a deductionist team on a decision‐making task. In the second phase, the two pre‐merger teams were combined into a merger team of analyst thinkers. Relative representation was manipulated by maintaining most or none of the features of the pre‐merger team in this new merger team. The results revealed that high pre‐merger identifiers identified more strongly with the merger group than did low pre‐merger identifiers, but only when the relative representation was high. Pre‐merger status did not influence post‐merger identification. Copyright © 2006 John Wiley & Sons, Ltd.     

Alzheimer's disease patients' cognitive status and course years prior to symptom recognition

This is a prospective examination of the cognitive performance and cognitive course of persons in an asymptomatic "preclinical" phase who eventually developed Alzheimer's disease (AD). We compared performances on the Mayo Cognitive Factor Scales (MCFS) of 20 persons in a neurologically normal cohort who subsequently developed AD to the performances of 60 persons who remained free of dementia symptoms. For the AD patients, exams occurred prior to the appearance of dementia symptoms (an average of 4.2 and 1.5 years prior to symptom onset). Results reveal strong group differences on learning and retention, with eventual AD patients scoring lower than controls years prior to reporting symptoms of the disease. There was no significant interaction effect (group x testing session) for memory retention, suggesting that memory decline in this preclinical period may be too slow to be a useful indicator of future AD. A significant interaction (but no group effect) was seen for verbal comprehension.     

Does switching between strategies within the same task involve a cost?

In two experiments, participants had to switch regularly between two cognitive strategies of a different complexity in the context of a numerosity judgement task. Expt 1 comprised bivalent stimuli (i.e. allowing the application of the two strategies), whereas Expt 2 involved univalent stimuli (i.e. allowing the application of only one strategy). Both experiments revealed that switching between strategies entailed a cognitive cost that was reflected in longer response times on switch compared to non‐switch trials but not in reduced accuracy. The size of this switch cost did not differ as a function of strategy complexity but tended to diminish as a strategy became more appropriate for solving a particular problem. We discuss the extent to which current theories of task switching can account for these findings.     

Disentangling the Mechanisms of Symbolic Number Processing in Adults’ Mathematics and Arithmetic Achievement

A growing body of research has shown that symbolic number processing relates to individual differences in mathematics. However, it remains unclear which mechanisms of symbolic number processing are crucial—accessing underlying magnitude representation of symbols (i.e., symbol‐magnitude associations), processing relative order of symbols (i.e., symbol‐symbol associations), or processing of symbols per se. To address this question, in this study adult participants performed a dots‐number word matching task—thought to be a measure of symbol‐magnitude associations (numerical magnitude processing)—a numeral‐ordering task that focuses on symbol‐symbol associations (numerical order processing), and a digit‐number word matching task targeting symbolic processing per se. Results showed that both numerical magnitude and order processing were uniquely related to arithmetic achievement, beyond the effects of domain‐general factors (intellectual ability, working memory, inhibitory control, and non‐numerical ordering). Importantly, results were different when a general measure of mathematics achievement was considered. Those mechanisms of symbolic number processing did not contribute to math achievement. Furthermore, a path analysis revealed that numerical magnitude and order processing might draw on a common mechanism. Each process explained a portion of the relation of the other with arithmetic (but not with a general measure of math achievement). These findings are consistent with the notion that adults’ arithmetic skills build upon symbol‐magnitude associations, and they highlight the effects that different math measures have in the study of numerical cognition.     

Player Identification in Online Games: Validation of a Scale for Measuring Identification in MMOGs

This article proposes a scale for measuring player identification in massively multiplayer online games (MMOGs). Three dimensions have been derived from the literature, avatar identification, group identification, and game identification, whereby avatar identification is a second-order factor consisting of similarity identification, wishful identification, and embodied presence. Based on the results of a cross-sectional survey of 544 World of Warcraft players, the measurement instrument's proposed factorial structure was confirmed and the constructs were successfully tested for convergent validity. Subsequently, support for nomological validity was gathered by testing nine theoretically rooted hypotheses linking the identification constructs to motivations for playing MMOGs. The results show that avatar identification is positively associated with roleplay, customization, and escapism; group identification with socializing and relationship; and game identification with escapism, discovery, advancement, and mechanics. These findings indicate that the Player Identification Scale provides a reliable measure of identification in online games ready to be used and further validated in subsequent research.     

Teenage uploaders on YouTube: networked public expectancies, online feedback preference, and received on-platform feedback

This article focuses on teenage YouTube uploaders' networked public expectancies when posting a video. These expectancies allow uploaders to cope temporarily with the uncertainty of who exactly will view their video. The results indicate that teenage uploaders strongly expect viewers that are situated close to them in both geographic and socio-demographic terms. Furthermore, we discuss the uncertainty-reducing properties of online feedback. We propose that different types of online feedback are preferred to verify the prior networked public expectancies. An effect of the identified online public expectancy (viewers with a similar interest/activity) is found for the importance of feedback both on the platform (e.g., views, comments) and off the platform (e.g., interaction on a social-network site). The identified offline public expectancy (friends/family) affects the importance attributed to off-platform feedback. Surprisingly, no effect of the unidentified online public expectancy (the general public) was found on on-platform feedback. This finding, in conjunction with the low expectancy of this group, raises the question of whether teenagers either cannot conceive this ambiguous mass public, or, if their expectancies are accurate, whether they are aware of the fact that only a small fraction of the videos on YouTube reach notable popularity. Therefore, in a second study, we test the accuracy of the online networked public expectancies by testing their effects on the longitudinal growth of actual feedback (views, comments, and rates). The results provide modest evidence that teenage uploaders have accurate online public expectancies.     

Quine's Weak and Strong Indispensability Argument

Quine's views on indispensability arguments in mathematics are scrutinised. A weak indispensability argument is distinguished from a strong indispensability thesis. The weak argument is the combination of the criterion of ontological commitment, holism and a mild naturalism. It is used to refute nominalism. Quine's strong indispensability thesis claims that one should consider all and only the mathematical entities that are really indispensable. Quine has little support for this thesis. This is even clearer if one takes into account Maddy's critique of Quine's strong indispensability thesis. Maddy's critique does not refute Quine's weak indispensability argument. We are left with a weak and almost unassailable indispensability argument. This revised version was published online in August 2006 with corrections to the Cover Date.     

WordGen: A tool for word selection and nonword generation in Dutch,English, German,and French

WordGen is an easy-to-use program that uses the CELEX and Lexique lexical databases for word selection and nonword generation in Dutch, English, German, and French. Items can be generated in these four languages, specifying any combination of seven linguistic constraints: number of letters, neighborhood size, frequency, summated position-nonspecific bigram frequency, minimum position-nonspecific bigram frequency, position-specific frequency of the initial and final bigram, and orthographic relatedness. The program also has a module to calculate the respective values of these variables for items that have already been constructed, either with the program or taken from earlier studies. Stimulus queries can be entered through WordGen’s graphical user interface or by means of batch files. WordGen is especially useful for (1) Dutch and German item generation, because no such stimulus-selection tool exists for these languages, (2) the generation of nonwords for all four languages, because our program has some important advantages over previous nonword generation approaches, and (3) psycholinguistic experiments on bilingualism, because the possibility of using the same tool for different languages increases the cross-linguistic comparability of the generated item lists. WordGen is free and available athttp://expsy.ugent.be/wordgen.htm.