Beyond Conceptual Change: Using Representations to Integrate Domain-Specific Structural Models in Learning Mathematics

ABSTRACT— Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for promoting representational change across cognitive development. I provide an example of an integrated structural model that highlights the underlying cognitive structures that connect numbers, mathematical operations, and functions. The model emphasizes dynamic multiple representations that students can internalize within the number line and which lead to developing a dynamic mental structure. In teaching practice, the model focuses on a counting task format, which integrates a variety of activities, specifically addressing motor, visual, and verbal skills, as well as various types of learning transfer.     

The relationship between sexual abuse and substance abuse among psychiatrically hospitalized adolescents

A comparative study using matched samples was conducted to investigate the relationship between sexual abuse and substance abuse. The sample included 48 adolescent psychiatric inpatients who had been sexually abused (abuse group) and 48 psychiatric inpatients without a known history of such abuse (control group) matched by age, race, sex, and primary psychiatric diagnosis. Statistically significant differences emerged between the groups in several areas. Abuse group subjects indicated more regular use of cocaine and stimulants, greater frequencies of alcohol and drug use, and more reported drunkenness and times high on drugs than their control counterparts. Explanations of the association between substance abuse and sexual victimization are explored. Discussion suggests the possibility of earlier coping strategies being related to later chemical use patterns. Implications for service delivery are offered.     

Young Children's Language of Togetherness Le Langage de e Togetherness f des Jeunes Enfants El Idioma del Sentimiento de Unio´n de Los Menores

In this article we discuss verbal strategies used by children to express and construct a sense of togetherness. In a case study the language of one child was audiotaped over 2 years (at the start he was 3 years old) in his interactions with other children and teachers. Brown and Levinson's theoretical model for analysing the politeness strategies of adults is used to analyse the verbal strategies of these children. Three general mechanisms for expressing togetherness are distinguished: expression of common ground, of cooperation and of care. The expression of common ground seems a specific domain for 2- and 3-year-olds at the day care centre. Young children use imitation and repetition of (nonsense) words and the explicit reference to sameness as a favourite mode of expressing common ground. Dans cet article, nous examinons les stratégies verbales utilisées par les enfants pour exprimer et construire un sens de e togetherness f . Dans une étude de cas, le langage d'un enfant a été enregistrésur deux ans (à partir de l'âge de trois ans) dans ses interactions avec d'autres enfants et ses enseignants. Le modèle théorique d'analyse des stratégies de politesse des adultes de Brown et Levinson est utilisé pour analyser les stratégies verbales de ces enfants. On distingue trois mécanismes généraux d'expression de la e togetherness f : expression de points communs, de coopération et d'affection. L'expression de points communs semble être un domaine spécifique pour les enfants de deux et trois ans de l'école maternelle. Les jeunes enfants emploient l'imitation et la répétition de mots (dépourvus de sens) et la référence explicite à la similitude comme mode préféré d'expression de points communs. En este artículo hablamos de las estrategias verbales usadas por los niños para expresar y elaborar un sentido de unión. En un estudio de caso, se grabó el lenguaje de un niño durante dos años (al inicio tenía tres años) en sus interacciones con otros niños y professores. Su usa el modelo teórico de Brown and Levinson para analizar las estrategias de buena educación de adultos a fin de analizar las estrategias verbales de estos niños. Se distinguen tres mecanismos generales para expresar unión: expresión de puntos en común, de cooperación y de atención. La expresión de puntos en común parece un dominio específico para los niños de dos y tres años en la guardería. Los menores usan imitaciones y repeticiones de palabras (sin sentido) y la referencia explícita a identidad como un modo favorito de expresión del punto común.     

Definitions of bullying: a comparison of terms used,and age and gender differences,in a fourteen-country international comparison

The study of school bullying has recently assumed an international dimension, but is faced with difficulties in finding terms in different languages to correspond to the English word bullying. To investigate the meanings given to various terms, a set of 25 stick-figure cartoons was devised, covering a range of social situations between peers. These cartoons were shown to samples of 8- and 14-year-old pupils (N = 1,245; n = 604 at 8 years, n = 641 at 14 years) in schools in 14 different countries, who judged whether various native terms cognate to bullying, applied to them. Terms from 10 Indo-European languages and three Asian languages were sampled. Multidimensional scaling showed that 8-year-olds primarily discriminated nonaggressive and aggressive cartoon situations; however, 14-year-olds discriminated fighting from physical bullying, and also discriminated verbal bullying and social exclusion. Gender differences were less appreciable than age differences. Based on the 14-year-old data, profiles of 67 words were then constructed across the five major cartoon clusters. The main types of terms used fell into six groups: bullying (of all kinds), verbal plus physical bullying, solely verbal bullying, social exclusion, solely physical aggression, and mainly physical aggression. The findings are discussed in relation to developmental trends in how children understand bullying, the inferences that can be made from cross-national studies, and the design of such studies.     

Preschoolers' Attributions of Mental States in Pretense

When young children appear to recognize that someone else is engaging in make-believe play, do they infer what the pretender is thinking? Are they aware that the pretender is thinking about a pretend scenario yet knows what the real situation is? Preschoolers ages 3–5 ( N = 45) viewed scenes from the Barney & Friends television series depicting either make-believe or realistic actions. Children were questioned concerning the presence of pretense and the thoughts and beliefs of the TV characters. The children where also presented with false belief and appearance/reality theory of mind tasks. Children who identified when TV characters were engaging in pretend play did not necessarily infer the pretenders thoughts and beliefs. Inferring pretenders' thoughts was related to performance on false belief and appearance/reality tasks, but simply recognizing pretense was not. These data support the view that children initially learn to recognize pretense from contextual cues and are able to infer pretenders' beliefs only with further development of metarepresentational ability.     

Behavioral intervention strategies with child abusive parents: A home intervention program

This article describes a therapeutic program for child abusive parents that is psychoeducationally based and is conducted through home visits by trained behavioral interventionists. The immediate goals of the intervention are to teach abusive parents effective child management procedures based on social learning therapy and to modify faulty or excessive expectations these parents have toward the behavior of their children. The general model is discussed as well as criteria for selection of parents for home intervention services, the differences between home intervention with abusive and non-abusive parents and the procedures used in home intervention services. A general discussion is also provided of the various goals and stages through which parents progress.     

Why schools should make condoms available to teenagers

The controversy surrounding sex education and condom availability programs in schools in New York City and throughout the US continues because parents worry that such programs encourage teenagers to engage in sexual behavior. But the reality is that more and more teenagers are engaging in sexual behavior anyway. The Carnegie Council on Adolescent Development found the 17% of girls and 29% of boys engaged in sexual intercourse by the time they were 16 years old. Many parents are ready to blame sex education and condom availability programs for these figures; these parents issue calls for "chastity education." Opponents of sex education also believe that these programs violate the rights of parents to education their children about moral behavior and religious values. But the truth is that these programs do not preclude the right of a parents to teach a child anything. They simply prevent the use of the public schools to impose religious beliefs on students. Those who argue that the mandate of schools is only to teach academic subjects forget that public high schools are the best place for sex education and condom availability programs because the schools are full of teenagers and of adults who are trained and willing to counsel them. Few educators would argue that schools should not teach values, and sex education and condom availability programs provide an excellent way to help teenagers understand not only human sexuality, reproduction, and the spread of disease but also social relationships, the development of cultural norms, and the role of responsible citizens. At the same time that we encourage sexual abstinence among young people, we must also teach about sexual responsibility. Sexual responsibility today means using a condom to prevent pregnancy and disease. If teenagers are embarrassed in their efforts to acquire condoms, pregnancy and diseases will be the result, not abstinence.