Analyse des discours non strictement mathematiques accompagnant des cours de mathematiques

Resume Dans cet article, nous travaillons sur le discours non strictement mathématique qu'un enseignant peut tenir en classe de mathématiques; nous nous sommes restreintes à des élèves de plus de 15 ans, et aux moments d'exposition des connaissances. Nous présentons d'abord trois grandes fonctions que l'enseignant peut donner à ce discours (communication, structuration et étiquetage, réflexion), en illustrant notre propos par des exemples empruntés à un même cours de niveau universitaire. Nous cherchons diverses caractéristiques de ces trois fonctions, en dégageant notamment leur lien avec le déroulement même du cours, leur portée éventuelle pour les étudiants, leur lien avec les contenus exposés... Nous en déduisons des pistes de recherches ultérieures, notamment en ce qui concerne la troisiéme fonction, qui nous semble la plus susceptible d'être l'objet d'un travail spécifique de préparation de l'enseignant.

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Analysis of not strictly mathematical discourse in mathematics classes

In this article we examine the discourse which is not strictly mathematical that a teacher might adopt in a mathematics class. We have confined our discussion to students over 15 and to periods of teacher exposition. First we present three major functions of such discourse:communication, structuring and labelling, and reflection. We examine various characteristics of these three functions, primarily to make clear their relevance to the unfolding of the lesson itself, their influence on the students, and their bearing on the material taught, from this we develop lines for future enquiry, notably on the third function, which seems to us to be the most likely focus for specific preparation by the teacher.

     

21 Ideas: A 42-Year Search to Understand the Nature of Giftedness

In this article, I describe the 21 ideas underlying a 42-year search to understand giftedness. I present the ideas roughly chronologically, in the order in which they arose, and discuss how in a career as in science, progress means supplementing or even superseding one idea with the next. In terms of the 21 ideas, I start with a discussion of how I thought IQ tests could account for giftedness and end with a discussion of the ACCEL (Active Concerned Citizenship and Ethical Leadership) model. But I frame the article in terms of a paradox—that despite the fact that IQs rose 30 points during the 20th century, people often seem to be operating at an intellectual level that is not notably higher and may even be lower in some respects than in previous times.     

Developmental change in proactive interference

The aim of the present research was to examine age-related change in proactive interference, which refers to impaired recall due to interference from material presented previously. Study 1 was a meta-analysis based on 26 studies that included 82 data sets. The results indicated that proactive interference decreased between 4 and 13 years of age. In Study 2, children from grades 3 through 6 and college students (N = 125) were administered a short-term memory task in which they briefly remembered sets of three words. For all ages, recall was accurate on Trial 1. However, recall became less accurate over Trials 2 through 4, particularly for the younger children in the sample. In addition, structural equation modeling revealed that age-related change in interference was linked to age-related change in speed of information processing. Results are discussed in terms of the nature of age-related change in interference.     

Competition in individualized CAI

Designers of computer-based practice systems give primary attention to aspects of cognitive learning. However, observations of students practicing arithmetic, with two CAI systems widely used in Israel, revealed factors in the computer learning environment that substantially affected students' social behavior, particularly with respect to competition and cooperation in the course of learning. A questionnaire was designed on the basis of the observations to examine the effects of these factors in CAI work. It was administered to 457 fourth graders in 16 classes (two CAI systems x two SES categories x two schools x two classes). While neither CAI system was intended to foster competition, the observations and questionnaire data suggested that one encourages social comparison and competition whereas the other discourages these features and encourages cooperation and peer help. Boys appear to be significantly more competitive than girls. One system, compared with the other, significantly increases competitive behavior of high achievers (but not of low achievers); results in teachers' greater encouragement of social comparison and competition among students; and, as used in the schools we studied, causes disadvantaged students rather than advantaged students to develop negative feelings because of low CAI performance. The other system discourages competitive behavior and encourages cooperation. All these findings bear important implications for the instructional design of computer-based learning environments.     

Reintegrating Janus: Eclectics and dialectics in counselling and psychotherapy

The history of science reveals a number of significant shifts in the conception of the universe. Recently, 20th century physics with its new discoveries has broken away from the traditional view of the universe to seeing it as interrelated, holistic, and emergent. This version of reality is complementary with the concept of dialectics. Dialectics is defined accordingly and its flexibility is suited to guide the present eclectic stance in counselling psychology and psychotherapy. Counselling psychology and psychotherapy are discussed within Kuhn's (1970) framework of normal science, crisis, and revolution. The normal science phase demonstrates variations of the subject/object dichotomy, and active/passive therapeutic orientations. Eclecticism reflects the crisis stage. Eclecticism is a multiple perspective that does not usually guide metatheory. The revolution and resolution phase for therapeutic psychology is manifested in a new paradigm based on dialectics. Dialectics makes eclecticism legitimate and comments towards that end are presented.     

The role of signaled periods of nonreinforcement in responding on a random schedule in autoshaping

Little responding develops to a conditioned stimulus (CS) that is placed in a random relation to an unconditioned stimulus (US). However, if the USs not preceded by that CS are themselves signaled by another stimulus, then the CS does come to elicit responding. This result has been attributed (e.g., by Durlach, 1983) to the signal’s blocking of conditioning to background cues that otherwise would prevent conditioning of the CS. However, Goddard and Jenkins (1987) have suggested the alternative that signaling the USs promotes responding due to the adventitious creation of periods of signaled nonreinforcement. Two experiments were conducted to assess this alternative, involving an autoshaping preparation in pigeons. In Experiment 1, little responding to a keylight CS presented in a random relation to a food US occurred, despite the explicit presentation of a discrete noise signaling periods of no food in the intertrial interval (ITI). Experiment 2 was designed to replicate the procedure of Goddard and Jenkins, in which an auditory stimulus extended throughout the ITI of a random schedule, terminating only prior to extra USs and during the CS. Contrary to their findings, little responding developed to the target CS. However, responding did develop when the sound-free period occurred only prior to the extra USs. These results offer little support for the hypothesis that signaled periods of nonreinforcement promote responding on random schedules. However, they are consistent with the view that signaling of ITI USs acts by preventing conditioning of potentially competitive background cues.     

The effects of age of viewer and gender of the narrator on children's visual attention and recall of story ideas

The purpose of this study was to investigate the effects of the age of viewers and the gender of the narrator in a film, and to examine the interaction between these two variables. Subjects in second and fifth grades were randomly assigned to two treatment groups. One group watched a film narrated by a female and the other watched the same film narrated by a male. As subjects watched the film, the experimenters measured their visual attention to the program. Recall of story ideas was also measured, using a multiple-choice test. The results indicated that the gender of the narrator influenced the recall of second-graders, but did not influence the recall of fifth-graders. Results suggest that older children pay greater visual attention to a program than younger children. Implications for developing audio-visual materials for children are discussed.