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

Testing the validity of the proposed ICD-11 PTSDand complex PTSD criteria using a sample fromNorthern Uganda

Background: The International Classification of Diseases (ICD-11) is currently under development with proposed changes recommended for the posttraumatic stress disorder (PTSD) diagnosis and the inclusion of a separate complex PTSD (CPTSD) disorder. Empirical studies support the distinction between PTSD and CPTSD; however, less research has focused on non-western populations. Objective: The aim of this study was to investigate whether distinct PTSD and CPTSD symptom classes emerged and to identify potential risk factors and the severity of impairment associated with resultant classes. Methods: A latent class analysis (LCA) and related analyses were conducted on 314 young adults from Northern Uganda. Fifty-one percent were female and participants were aged between 18 and 25 years. Forty percent of the participants were former child soldiers (n=124) while the remaining participants were civilians (n=190). Results: The LCA revealed three classes: a CPTSD class (40.2%), a PTSD class (43.8%), and a low symptom class (16%). Child soldier status was a significant predictor of both CPTSD and PTSD classes (OR=5.96 and 2.82, respectively). Classes differed significantly on measures of anxiety/depression, conduct problems, somatic complaints, and war experiences. Conclusions: To conclude, this study provides preliminary support for the proposed distinction between PTSD and CPTSD in a young adult sample from Northern Uganda. However, future studies are needed using larger samples to test alternative models before firm conclusions can be made

Which better predicts conduct problems? The relationship of trajectories of Conduct Problems, with ODD and ADHD Symptoms from childhood into adolescence

Background: To assess the co-occurrence in deviant trajectories of parent-rated symptoms of conduct disorder (CD), oppositional defiant disorder (ODD) and attention-deficit/hyperactivity disorder (ADHD) from age 4 to 18 years old in a general population sample of Dutch children. Methods: Developmental trajectories of CD, ODD, and ADHD were estimatedin a sample of 1,016 males and 1,060 females. Children's disruptive problem behaviors were rated at 5 time-points. The co-occurrence patterns between the deviant CD trajectory, and the high ODD and high ADHD trajectory were studied for males and females separately. Results: Four percent of males and 2% of females followed a deviant CD trajectory. Six percent of the sample followed a high ODD trajectory, and 5% a high ADHD trajectory. Engagement in the deviant CD trajectory was predicted by ODD and ADHD in females, but only by ODD in males. Conclusions: Although ADHD co-occurs with CD, the association between ADHD and CD is largely accounted for by accompanying ODD. Gender differences should be taken into account in understanding the onset of CD. © 2007 The Authors Journal compilation © 2007 Association for Child and Adolescent Mental Health

Which forms of child/adolescent externalizing behaviors account for late adolescent risky sexual behavior and substance use?

Background: Health risk behaviors like substance use (alcohol, tobacco, soft/hard drugs) and risky sexual behavior become more prevalent in adolescence. Children with behavior problems are thought to be prone to engage in health risk behaviors later in life. It is, however, unclear which problems within the externalizing spectrum account for these outcomes. Methods: Three hundred and nine children were followed from age 4/5 years to 18 years (14-year follow-up). Level and course of parent-rated opposition, physical aggression, status violations and property violations were used to predict adolescent-reported substance use and risky sexual behavior at age 18 years. Results: Both level and change in physical aggression were unique predictors of all forms of adolescent health risk behavior. Levels of status violations predicted smoking and soft drug use only, while change in property violations predicted each of the health risk behaviors. The links between opposition and health risk behaviors were accounted for by co-occurring problem behaviors. Conclusions: Of externalizing problems, physical aggression is the best predictor of adolescent substance use and risky sexual behavior from childhood onwards. Possible explanations and implications of these findings, and future research directions are discussed. © 2007 The Authors

Early risk indicators of internalizing problems in late childhood: A 9-year longitudinal study

Background: Longitudinal studies on risk indicators of internalizing problems in childhood are in short supply, but could be valuable to identify target groups for prevention. Methods: Standardized assessments of 294 children’s internalizing problems at the age of 2–3 years (parent report), 4–5 years (parent and teacher report) and 11 years (parent and teacher) were available in addition to risk indicators from the child, family and contextual domain. Results: Low socioeconomic status, family psychopathology at child age 2–3, parenting stress at child age 4–5 years, and parents’ reports of child internalizing problems at age 4–5 years were the strongest predictors of internalizing problems at the age of 11. If these early risk factors were effectively ameliorated through preventive interventions, up to 57% of internalizing cases at age 11 years could be avoided. Conclusions: Predictors from as early as 2–5 years of age are relevant for identifying children at risk of internalizing problems in late childhood. The methodological approach used in this study can help to identify children who are most in need of preventive interventions and help to assess the potential health gain and efficiency of such interventions. Keywords: Internalizing disorder, risk factors, prevention. Abbreviations: AF: attributable fraction; IRR: incidence rate ratio; LEQ: Life Events Questionnaire; NNT: numbers needed to be treated; RD: risk difference

Maturation, Peer Context, and Indigenous Girls\u27 Early-Onset Substance Use

This paper examines a biosocial model of the impact of puberty on Indigenous girls\u27 early-onset substance use by considering the potential mediating role of peer context (i.e. mixed-sex peer groups and substance use prototypes) on the puberty and substance use relationship. Data include responses from 360 girls of a common Indigenous cultural group residing on reservations/reserves in the upper Midwest and Canada. Results of structural equation modeling revealed that the statistically significant relationship between girls\u27 pubertal development and early-onset substance use was mediated by both mixed-sex/romantic peer groups and favorable social definitions of substance use. Implications for substance use prevention work include addressing the multiple and overlapping effects of peer influence from culturally-relevant perspectives

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