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.     

Genetics Education for Health Professionals: Strategies and Outcomes from a National Initiative in the United Kingdom

The National Health Service (NHS) National Genetics Education and Development Centre was established by the Department of Health in 2004 to help drive and co-ordinate genetics education for health professionals working outside specialist genetic services. This paper reviews the experiences and lessons learned to date. At the outset, it was clear that understanding the learning ethos, preferred delivery methods and attitudes towards genetics of different NHS healthcare groups was vital. We collected evidence by undertaking needs assessments with educators, practitioners and patients. We have determined the genetics knowledge, skills and attitudes which they said were needed and translated these into learning outcomes and workforce competences in a continuum of education. Beginning with core concepts introduced (and examined) pre-registration, the continuum continues with development of concepts post-registration as appropriate for role, leading to practical application and assessment of competences in the workplace. These are supported by a portfolio of resources which draw heavily on patient based scenarios to demonstrate to staff that genetics is relevant to their work, and to convince educators and policy makers that genetic education is likely to result in real clinical benefit. A long term educational policy, inclusive of learners, educationalists and their institutions must be evidence based, flexible and responsive to changes in workforce structure, provision of clinical services and conceptual and financial commitments to education. The engagement of national policy, regulatory and professional bodies is vital ().     

An algebra of human concept learning

An important element of learning from examples is the extraction of patterns and regularities from data. This paper investigates the structure of patterns in data defined over discrete features, i.e. features with two or more qualitatively distinct values. Any such pattern can be algebraically decomposed into a spectrum of component patterns, each of which is a simpler or more atomic “regularity.” Each component regularity involves a certain number of features, referred to as its degree. Regularities of lower degree represent simpler or more coarse patterns in the original pattern, while regularities of higher degree represent finer or more idiosyncratic patterns. The full spectral breakdown of a pattern into component regularities of minimal degree, referred to as its power series, expresses the original pattern in terms of the regular rules or patterns it obeys, amounting to a kind of “theory” of the pattern. The number of regularities at various degrees necessary to represent the pattern is tabulated in its power spectrum, which expresses how much of a pattern's structure can be explained by regularities of various levels of complexity. A weighted mean of the pattern's spectral power gives a useful numeric summary of its overall complexity, called its algebraic complexity. The basic theory of algebraic decomposition is extended in several ways, including algebraic accounts of the typicality of individual objects within concepts, and estimation of the power series from noisy data. Finally some relations between these algebraic quantities and empirical data are discussed.     

Individual differences in information order effects: The importance of right-hemisphere access in belief updating

The order in which information is received alters the evaluation of causal hypotheses. Specifically, research suggests that the last piece of information oftentimes has the greatest impact on the evaluation and that the difference in subjective value between two pieces of information is an important factor influencing the magnitude of this recency effect. The present paper extends this line of work by exploring individual differences in this phenomenon via one's degree of handedness. Two hundred and five participants were given two hypothetical scenarios and related causal hypotheses accompanied by two pieces of additional information and asked to revise their belief in each hypothesis as information accumulated. Results confirmed predictions that 1) inconsistent/mixed-handers (those who use their non-dominant hand for at least some activities) show a larger effect with two pieces of inconsistent weak or strong information, and 2) neither mixed-handers nor consistent/strong-handers (those who use their dominant hand for almost all activities) show an effect with strong and weak pieces of consistent information. Mixed-handers' susceptibility to persuasive arguments and Ramachandran’s (1995; Ramachandran and Blakeslee, 1998) belief-updating theory centered around communication between the two halves of the brain and functional access to the right hemisphere are used to account for these data.     

Association between individual differences in non-symbolic number acuity and math performance: A meta-analysis

Many recent studies have examined the association between number acuity, which is the ability to rapidly and non-symbolically estimate the quantity of items appearing in a scene, and symbolic math performance. However, various contradictory results have been reported. To comprehensively evaluate the association between number acuity and symbolic math performance, we conduct a meta-analysis to synthesize the results observed in previous studies. First, a meta-analysis of cross-sectional studies (36 samples, N = 4705) revealed a significant positive correlation between these skills (r = 0.20, 95% CI = [0.14, 0.26]); the association remained after considering other potential moderators (e.g., whether general cognitive abilities were controlled). Moreover, a meta-analysis of longitudinal studies revealed 1) that number acuity may prospectively predict later math performance (r = 0.24, 95% CI = [0.11, 0.37]; 6 samples) and 2) that number acuity is retrospectively correlated to early math performance as well (r = 0.17, 95% CI = [0.07, 0.26]; 5 samples). In summary, these pieces of evidence demonstrate a moderate but statistically significant association between number acuity and math performance. Based on the estimated effect sizes, power analyses were conducted, which suggested that many previous studies were underpowered due to small sample sizes. This may account for the disparity between findings in the literature, at least in part. Finally, the theoretical and practical implications of our meta-analytic findings are presented, and future research questions are discussed.     

Explaining color term typology with an evolutionary model

An expression-induction model was used to simulate the evolution of basic color terms to test Berlin and Kay's (1969) hypothesis that the typological patterns observed in basic color term systems are produced by a process of cultural evolution under the influence of biases resulting from the special properties of universal focal colors. Ten agents were simulated, each of which could learn color term denotations by generalizing from examples using Bayesian inference, and for which universal focal red, yellow, green, and blue were especially salient, but unevenly spaced in the perceptual color space. Conversations between these agents, in which agents would learn from one another, were simulated over several generations, and the languages emerging at the end of each simulation were investigated. The proportion of color terms of each type correlated closely with the equivalent frequencies found in the World Color Survey, and most of the emergent languages could be placed on one of the evolutionary trajectories proposed by Kay and Maffi (1999). The simulation therefore demonstrates how typological patterns can emerge as a result of learning biases acting over a period of time.     

Memories affect mood: evidence from covert experimental assignment to positive, neutral, and negative memory recall

Memory recall has been proposed as a common and effective mood regulation strategy. Although several studies have presented results suggesting that recalling valenced memories affects subsequent mood, their designs allow for alternative interpretations of the observed effects. Two such alternatives include the reverse effect (mood effects on memory due to non-experimental assignment to memory recall condition) and demand characteristics of the experiment. We used covert experimental assignment to memory condition, asking subjects (N=314; 56% female) to recall memories that were primarily positive, neutral, or negative. Results showed the expected effect on mood (p<.002), with reported mood worst in the negative memory condition, better in the neutral condition, and best in the positive condition. These results suggest that valenced memory recall does indeed exert an effect on mood, and may do so even without the individual's awareness.     

Interoceptive fear conditioning as a learning model of panic disorder: an experimental evaluation using 20% CO(2)-enriched air in a non-clinical sample

Despite the role afforded interoceptive fear conditioning in etiologic accounts of panic disorder, there are no good experimental demonstrations of such learning in humans. The aim of the present study was to evaluate the interoceptive conditioning account using 20% carbon dioxide (CO(2))-enriched air as an interoceptive conditioned stimulus (CS) (i.e., physiologically inert 5-s exposures) and unconditioned stimulus (US) (i.e., physiologically prepotent 15-s exposures). Healthy participants (N=42) were randomly assigned to one of three conditions: a CS-only, contingent CS-US pairings, or unpaired/non-contingent CS and US presentations. Electrodermal and self-report (e.g., distress, fear) served as indices of conditioned emotional responding. Results showed greater magnitude electrodermal and evaluative fear conditioning in the paired relative to the CS-only condition. The explicitly unpaired condition showed even greater electrodermal and evaluative responding during acquisition, and marked resistance to extinction. The latter results are consistent with the possibility that the unpaired procedure constituted a partial reinforcement procedure in which CO(2) onset was paired with more extended CO(2) exposure on 50% of the trials. Overall, the findings are consistent with contemporary learning theory accounts of panic.     

Paired-associate learning, phoneme awareness, and learning to read

We report two studies examining the relations among three paired-associate learning (PAL) tasks (visual-visual, verbal-verbal, and visual-verbal), phoneme deletion, and single-word and nonword reading ability. Correlations between the PAL tasks and reading were strongest for the visual-verbal task. Path analyses showed that both phoneme deletion and visual-verbal PAL were unique predictors of a composite measure of single-word reading and of irregular word reading. However, for nonword reading, phoneme deletion was the only unique predictor (and visual-verbal PAL was not a significant predictor). These results are consistent with the view that learning visual (orthography) to phonological mappings is an important skill for developing word recognition skills in reading and that individual differences in this ability can be tapped experimentally by a PAL task.     

A model of working memory capacity in the radial-arm maze task

The radial arm maze is one of the most commonly used tests for assessing working memory in laboratory animals. However, to date, there exists no quantitative method of estimating working memory capacity from performance on this task. Here, we present a mathematical model of performance on the radial arm maze from which we can derive estimates of capacity. We derive explicit results for the two most commonly used measures of performance as functions of number of arms in the maze and memory capacity, assuming a uniform random search. We simulate random non-uniform search strategies. Comparing our model to previous experiments, we show that our model predicts a working memory capacity in the range of 3-9 at the level of performance observed in these experiments. This estimate is within the typical estimate of human working memory capacity. Performance of rats on large mazes (e.g. 48 arms) has been used as evidence that the working memory capacity of rats may be significantly larger than that of humans. We report that memory capacity in the range 3-9 is sufficient to explain the performance of rats in very large radial mazes. Furthermore, when we simulate non-uniform random search strategies observed in the experiments, the resulting estimates do not differ significantly from those assuming a uniform random search. We conclude that a list-based model of working memory with modest capacity is more powerful than previously expected.