Errors in children's subtraction

Many of the errors that occur in children' subtraction are due to the use of incorrect strategies rather than to the incorrect recall of number facts. A production system is presented for performing written subtraction which is consistent with an earlier analysis of the nature of such a cognitive skill. Most of the incorrect strategies used by schoolchildren can be accounted for in a principled way by simple changes in the production system, such as the omission of individual rules or the inclusion of rules appropriate to other arithmetical tasks. The production system model is evaluated against a corpus of over 1500 subtraction problems done by 10-year olds and is shown to account for about two-thirds of the (nonnumber fact) errors. It also provides an alternative, simpler interpretation of the subtraction errors analysed by Brown and Burton (1978). Some implications for teaching are discussed.     

The diamond ratio: A visual indicator of the extent of heterogeneity in meta-analysis

The result of a meta-analysis is conventionally pictured in the forest plot as a diamond, whose length is the 95% confidence interval (CI) for the summary measure of interest. The Diamond Ratio (DR) is the ratio of the length of the diamond given by a random effects meta-analysis to that given by a fixed effect meta-analysis. The DR is a simple visual indicator of the amount of change caused by moving from a fixed-effect to a random-effects meta-analysis. Increasing values of DR greater than 1.0 indicate increasing heterogeneity relative to the effect variances. We investigate the properties of the DR, and its relationship to four conventional but more complex measures of heterogeneity. We propose for the first time a CI on the DR, and show that it performs well in terms of coverage. We provide example code to calculate the DR and its CI, and to show these in a forest plot. We conclude that the DR is a useful indicator that can assist students and researchers to understand heterogeneity, and to appreciate its extent in particular cases.     

The Mental Vulnerability Questionnaire: A psychometric evaluation

Eplov, L.F., Petersen, J., Jørgensen, T., Johansen, C., Birket‐Smith, M., Lyngberg, A. C. & Mortensen, E. L. (2010). The Mental Vulnerability Questionnaire: A psychometric evaluation. Scandinavian Journal of Psychology 51, 548–554. The Mental Vulnerability Questionnaire was originally a 22 item scale, later reduced to a 12 item scale. In population studies the 12 item scale has been a significant predictor of health and illness. The scale has not been psychometrically evaluated for more than 30 years, and the aim of the present study was both to evaluate the psychometric properties of the 22 and 12 item scales and of three new scales. The main study sample was a community sample comprising more than 6,000 men and women. In this sample the coefficients of homogeneity were all over 0.30 for the three new scales, but below 0.30 for the 12 and the 22 item scales. All five Mental Vulnerability scales had positively skewed score distributions which were associated significantly with both SCL‐90‐R symptom scores and NEO‐PI‐R personality scales (primarily Neuroticism and Extraversion). Coefficient alpha was highest for the 22 and 12 item scales, and the two scales also showed the highest long‐term stability. The three new scales reflect relatively independent dimensions of Psychosomatic Symptoms, Mental Symptoms, and Interpersonal Problems, but because of reliability problems it remains an open question whether they will prove useful as predictors of health and morbidity.     

Triple Bottomline Many‐Objective‐Based Decision Making for a Land Use Management Problem

A land use many‐objective optimization problem for a 1500‐ha farm with 315 paddocks was formulated with 14 objectives (maximizing sawlog production, pulpwood production, milksolids, beef, sheep meat, wool, carbon sequestration, water production, income and Earnings Before Interest and Tax; and minimizing costs, nitrate leaching, phosphorus loss and sedimentation). This was solved using a modified Reference‐point‐based Non‐dominated Sorting Genetic Algorithm II augmented by simulated epigenetic operations. The search space had complex variable interactions and was based on economic data and several interoperating simulation models. The solution was an approximation of a Hyperspace Pareto Frontier (HPF), where each non‐dominated trade‐off point represented a set of land‐use management actions taken within a 10‐year period and their related management options, spanning a planning period of 50 years. A trade‐off analysis was achieved using Hyper‐Radial Visualization (HRV) by collapsing the HPF into a 2‐D visualization capability through an interactive virtual reality (VR)‐based method, thereby facilitating intuitive selection of a sound compromise solution dictated by the decision makers' preferences under uncertainty conditions. Four scenarios of the HRV were considered emphasizing economic, sedimentation and nitrate leaching aspects—giving rise to a triple bottomline (i.e. the economic, environmental and social complex, where the social aspect is represented by the preferences of the various stakeholders). Highlights of the proposed approach are the development of an innovative epigenetics‐based multi‐objective optimizer, uncertainty incorporation in the search space data and decision making on a multi‐dimensional space through a VR‐simulation‐based visual steering process controlled at its core by a multi‐criterion decision making‐based process. This approach has widespread applicability to many other ‘wicked’ societal problem‐solving tasks. Copyright © 2014 John Wiley & Sons, Ltd.     

A longitudinal assessment of the road to mental readiness training among municipal police

Police agencies increasingly implement training programs to protect mental health. The Road to Mental Readiness (R2MR) program was designed by the Canadian military to increase mental health resilience. A version of R2MR was adapted for municipal police by the Mental Health Commission of Canada (MHCC). The current research was designed to assess the R2MR program, as adapted and delivered by the MHCC, in a municipal police sample. Participants were 147 Canadian police agency employees (57% women) who received a single R2MR training session. Participants completed pre- and post-training self-report questionnaires, and follow-ups at 6 and 12 months. The questionnaires assessed mental health symptoms, work engagement, resiliency, mental health knowledge, and stigma. Multilevel modeling analyses assessed for within-participant changes over time. The results were consistent with other single session interventions; specifically, there were no significant changes in mental health symptoms, resilience, or work engagement (p > .05). There were small, but significant (p < .05), reductions in stigma at post-training that may facilitate help-seeking among police; relatedly, in open-ended response fields, participants commonly described the training as helpful for changing attitudes and improving communication. More engagement with the material may produce larger, sustained gains, but more published research is critically needed.