Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis

The tangent line is a central concept in many mathematics and science courses. In this paper we describe a model of students’ thinking – concept images as well as ability in symbolic manipulation – about the tangent line of a curve as it has developed through students’ experiences in Euclidean Geometry and Analysis courses. Data was collected through a questionnaire administered to 196 Year 12 students. Through Latent Class Analysis, the participants were classified in three hierarchical groups representing the transition from a Geometrical Global perspective on the tangent line to an Analytical Local perspective. In the light of this classification, and through qualitative explanations of the students’ responses, we describe students’ thinking about tangents in terms of seven factors. We confirm the model constituted by these seven factors through Confirmatory Factor Analysis

Measuring Metacognition in Cancer: Validation of the Metacognitions Questionnaire 30 (MCQ-30)

Objective The Metacognitions Questionnaire 30 assesses metacognitive beliefs and processes which are central to the metacognitive model of emotional disorder. As recent studies have begun to explore the utility of this model for understanding emotional distress after cancer diagnosis, it is important also to assess the validity of the Metacognitions Questionnaire 30 for use in cancer populations. Methods 229 patients with primary breast or prostate cancer completed the Metacognitions Questionnaire 30 and the Hospital Anxiety and Depression Scale pre-treatment and again 12 months later. The structure and validity of the Metacognitions Questionnaire 30 were assessed using factor analyses and structural equation modelling. Results Confirmatory and exploratory factor analyses provided evidence supporting the validity of the previously published 5-factor structure of the Metacognitions Questionnaire 30. Specifically, both pre-treatment and 12 months later, this solution provided the best fit to the data and all items loaded on their expected factors. Structural equation modelling indicated that two dimensions of metacognition (positive and negative beliefs about worry) were significantly associated with anxiety and depression as predicted, providing further evidence of validity. Conclusions These findings provide initial evidence that the Metacognitions Questionnaire 30 is a valid measure for use in cancer populations

Mix design considerations of foamed bitumen mixtures with reclaimed asphalt pavement material

In the present work, a mix design parametric study was carried out with the aim of proposing a practical and consistent mix design procedure for foamed bitumen mixtures (FBMs). The mix design parameters that were adopted in the study are mixing and compaction water content (MWC), compaction effort using a gyratory compactor and aggregate temperature. This parametric study was initially carried out on FBMs with virgin limestone aggregate without reclaimed asphalt pavement (RAP) material and a mix design procedure was proposed. This proposed methodology was also found to apply to FBMs with RAP. A detailed consideration was also given to characterising the RAP material so as to understand its contribution to the mechanical properties of FBMs. Optimum MWC was achieved by optimising mechanical properties such as indirect tensile stiffness modulus and indirect tensile strength (ITS-dry and ITS-wet). A rational range of 75–85% of optimum water content obtained by the modified Proctor test was found to be the optimum range of MWC that gives optimum mechanical properties for FBMs. It was also found that the presence of RAP influenced the design foamed bitumen content, which means that treating RAP as black rock in FBM mix design is not appropriate. To study the influence of bitumen and water during compaction, modified Proctor compaction and gyratory compaction were employed on mixes with varying amounts of water and bitumen. By this, the work also evaluated the validity of the total fluid (water + bitumen) concept that is widely used in bitumen–emulsion-treated mixes, and found it not to be applicable

Using latent class analysis to develop a model of the relationship between socioeconomic position and ethnicity: cross-sectional analyses from a multi-ethnic birth cohort study

Background: Almost all studies in health research control or investigate socioeconomic position (SEP) as exposure or confounder. Different measures of SEP capture different aspects of the underlying construct, so efficient methodologies to combine them are needed. SEP and ethnicity are strongly associated, however not all measures of SEP may be appropriate for all ethnic groups. Methods: We used latent class analysis (LCA) to define subgroups of women with similar SEP profiles using 19 measures of SEP. Data from 11,326 women were used, from eight different ethnic groups but with the majority from White British (40%) or Pakistani (45%) backgrounds, who were recruited during pregnancy to the Born in Bradford birth cohort study. Results: Five distinct SEP subclasses were identified in the LCA: (i) "Least socioeconomically deprived and most educated" (20%); (ii) "Employed and not materially deprived" (19%); (iii) "Employed and no access to money" (16%); (iv) "Benefits and not materially deprived" (29%) and (v) "Most economically deprived" (16%). Based on the magnitude of the point estimates, the strongest associations were that compared to White British women, Pakistani and Bangladeshi women were more likely to belong to groups: (iv) "benefits and not materially deprived" (relative risk ratio (95% CI): 5.24 (4.44, 6.19) and 3.44 (2.37, 5.00), respectively) or (v) most deprived group (2.36 (1.96, 2.84) and 3.35 (2.21, 5.06) respectively) compared to the least deprived class. White Other women were more than twice as likely to be in the (iv) "benefits and not materially deprived group" compared to White British women and all ethnic groups, other than the Mixed group, were less likely to be in the (iii) "employed and not materially deprived" group than White British women. Conclusions: LCA allows different aspects of an individual’s SEP to be considered in one multidimensional indicator, which can then be integrated in epidemiological analyses. Ethnicity is strongly associated with these identified subgroups. Findings from this study suggest a careful use of SEP measures in health research, especially when looking at different ethnic groups. Further replication of these findings is needed in other populations

Gender differences in developmental links between antisocial behavior, friends' antisocial behavior and peer rejection in childhood: Results in two cultures

This study addressed gender differences in the developmental links among antisocial behavior, friends' anti-social behavior, and peer rejection. High and increasing, moderate, and low antisocial developmental trajectories were identified among 289 Dutch children, ages 7 to 10, and 445 French-Canadian children, ages 9 to 12. Only boys followed the high trajectory. These boys had more deviant friends and were more often rejected than other children. A minority of girls followed the moderate antisocial behavior trajectory. These girls had fewer deviant friends than moderate antisocial boys, but moderate antisocial boys and girls were equally likely to be rejected. The influence of friends and poor peer relations plays a crucial but different role in the development of antisocial behavior among boys and girls. © 2005 by the Society for Research in Child Development, Inc. All rights reserved

Fatigue Intervention by Nurses Evaluation - The FINE Trial. A randomised controlled trial of nurse led self-help treatment for patients in primary care with chronic fatigue syndrome: study protocol. [ISRCTN74156610]

Background: Chronic fatigue syndrome, also known as ME (CFS/ME), is a condition characterised primarily by severe, disabling fatigue, of unknown origin, which has a poor prognosis and serious personal and economic consequences. Evidence for the effectiveness of any treatment for CFS/ME in primary care, where most patients are seen, is sparse. Recently, a brief, pragmatic treatment for CFS/ME, based on a physiological dysregulation model of the condition, was shown to be successful in improving fatigue and physical functioning in patients in secondary care. The treatment involves providing patients with a readily understandable explanation of their symptoms, from which flows the rationale for a graded rehabilitative plan, developed collaboratively with the therapist. The present trial will test the effectiveness and cost-effectiveness of pragmatic rehabilitation when delivered by specially trained general nurses in primary care. We selected a client-centred counselling intervention, called supportive listening, as a comparison treatment. Counselling has been shown to be as effective as cognitive behaviour therapy for treating fatigue in primary care, is more readily available, and controls for supportive therapist contact time. Our control condition is treatment as usual by the general practitioner (GP). Methods and design: This study protocol describes the design of an ongoing, single-blind, pragmatic randomized controlled trial of a brief (18 week) self-help treatment, pragmatic rehabilitation, delivered by specially trained nurse-therapists in patients' homes, compared with nurse-therapist delivered supportive listening and treatment as usual by the GP. An economic evaluation, taking a societal viewpoint, is being carried out alongside the clinical trial. Three adult general nurses were trained over a six month period to deliver the two interventions. Patients aged over 18 and fulfilling the Oxford criteria for CFS are assessed at baseline, after the intervention, and again one year later. Primary outcomes are self-reported physical functioning and fatigue at one year, and will be analysed on an intention-to-treat basis. A qualitative study will examine the interventions' mechanisms of change, and also GPs' drivers and barriers towards referral

Developmental trajectories of externalizing behaviors in childhood and adolescence [IF: 3.3]

This article describes the average and group-based developmental trajectories of aggression, opposition, property violations, and status violations using parent reports of externalizing behaviors on a longitudinal multiple birth cohort study of 2,076 children aged 4 to 18 years. Trajectories were estimated from multilevel growth curve analyses and semiparametric mixture models. Overall, males showed higher levels of externalizing behavior than did females. Aggression, opposition, and property violations decreased on average, whereas status violations increased over time. Group-based trajectories followed the shape of the average curves at different levels and were similar for males and females. The trajectories found in this study provide a basis against which deviations from the expected developmental course can be identified and classified as deviant or nondeviant

Sex Differences in Sum Scores May Be Hard to Interpret: The Importance of Measurement Invariance

In most assessment instruments, distinct items are designed to measure a trait, and the sum score of these items serves as an approximation of an individual’s trait score. In interpreting group differences with respect to sum scores, the instrument should measure the same underlying trait across groups (e.g., male/female, young/old). Differences with respect to the sum score should accurately reflect differences in the latent trait of interest. A necessary condition for this is that the instrument is measurement invariant. In the current study, the authors illustrate a stepwise approach for testing measurement invariance with respect to sex in a four-item instrument designed to assess disordered eating behavior in a large epidemiological sample (1,195 men and 1,507 women). This approach can be applied to other phenotypes for which group differences are expected. Any analysis of such variables may be subject to measurement bias if a lack of measurement invariance between grouping variables goes undetected

Advances in Behavioral Genetics Modeling Using Mplus: Applications of Factor Mixture Modeling to Twin Data

This article discusses new latent variable techniques developed by the authors. As an illustration, a new factor mixture model is applied to the monozygotic-dizygotic twin analysis of binary items measuring alcohol-use disorder. In this model, heritability is simultaneously studied with respect to latent class membership and within-class severity dimensions. Different latent classes of individuals are allowed to have different heritability for the severity dimensions. The factor mixture approach appears to have great potential for the genetic analyses of heterogeneous populations. Generalizations for longitudinal data are also outlined

Development and Validation of the Behavioral Tendencies Questionnaire

At a fundamental level, taxonomy of behavior and behavioral tendencies can be described in terms of approach, avoid, or equivocate (i.e., neither approach nor avoid). While there are numerous theories of personality, temperament, and character, few seem to take advantage of parsimonious taxonomy. The present study sought to implement this taxonomy by creating a questionnaire based on a categorization of behavioral temperaments/tendencies first identified in Buddhist accounts over fifteen hundred years ago. Items were developed using historical and contemporary texts of the behavioral temperaments, described as “Greedy/Faithful”, “Aversive/Discerning”, and “Deluded/Speculative”. To both maintain this categorical typology and benefit from the advantageous properties of forced-choice response format (e.g., reduction of response biases), binary pairwise preferences for items were modeled using Latent Class Analysis (LCA). One sample (n1 = 394) was used to estimate the item parameters, and the second sample (n2 = 504) was used to classify the participants using the established parameters and cross-validate the classification against multiple other measures. The cross-validated measure exhibited good nomothetic span (construct-consistent relationships with related measures) that seemed to corroborate the ideas present in the original Buddhist source documents. The final 13-block questionnaire created from the best performing items (the Behavioral Tendencies Questionnaire or BTQ) is a psychometrically valid questionnaire that is historically consistent, based in behavioral tendencies, and promises practical and clinical utility particularly in settings that teach and study meditation practices such as Mindfulness Based Stress Reduction (MBSR)