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.

     

The evolution of an approach for using analogies in teaching and learning science

An important contribution to effective teaching and learning can be made by teachers' understanding of the central topics in each subject area and knowing how to transform their content knowledge into knowledge for teaching. One aspect of this knowledge is the use of analogies which can effectively communicate concepts to students of particular backgrounds and prerequisite knowledge. Indeed, analogies are considered to be an important component in the repertoire of effective teachers. However, research about teachers' use of analogies in science lessons provides little guidance about the optimum approaches that may be taken by preservice teachers, novice teachers, experienced teachers or reluctant analogy users. This paper describes the evolution of an approach for using analogies in science teaching that addresses both findings from the research literature and recognises the needs of practising teachers. Specializations: learning and teaching science concepts, technology education.     

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.     

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.     

Grandparent learning and cultural differences

People are living longer so expectations of grandparents should be redefined. Learning for them should focus on fulfilling family and community roles to retain a sense of purpose. Grandparent education requires a willingness to learn from the observations of younger family members. The intergenerational perceptions of American grandparents were examined to identify conditions for success in a technological environment. The 2,535 non-consanguineous participants were three generations of African-Americans (n = 777), Caucasian-Americans (n = 1,086), and Mexican-Americans (n = 672). Perceptions of the grandparents (n = 1,117), parents (n = 624), and grandchildren (n = 794) were compared within and between the cultures. Each generation completed a separate version of the Grandparent Strengths and Needs Inventory. The six subscales of this instrument assess grandparent Satisfaction, Success, Teaching, Difficulty, Frustration, and Information Needs. All generations and cultures identified favorable aspects of grandparent behavior as well as contexts for further learning. Significant differences were found in observations of grandparent attitudes and behavior across cultures and between generations within cultures. The most significant demographic variable was amount of time a grandparent spent with a grandchild. Lesson themes that represent the uniqueness of cultures and the observations of three generations are recommended as a framework for a differentiated curriculum in grandparent education.     

How to use preconceptions? The contact strategy dismantled

The effects of the contact strategy (a computer-assisted instructional strategy aimed at conceptual change in text processing) were investigated by dismantling the strategy. An experiment with 86 Ss (5th/6th-graders) was conducted in which the number of instructional steps was cumulatively varied from 0 steps (no activation) over 1 step (search for old idea) and 3 steps (1. search for old idea; 2. compare and contrast with new information; 3. formulate new idea) to all 5 contact steps (1. search for old idea; 2. compare and contrast with new information; 3. formulate new idea; 4. apply new idea; 5. evaluate new idea). A design with 2 between-subjects factors (instructional strategy and students familiarity with the central concepts from the 7 instructional texts used) and 2 within-subjects factors (type of learning performance test item and time of testing) was used. Dependent variables concerned quality of final conceptions and learning performance. Results indicated that the complete contact strategy was the most effective variant. It seemed to be the case, however, that students mainly focused their attention on the central concepts from the texts. In our view, instructional strategies to foster conceptual change should both support knowledge restructuring processes and offer a solution for this problem of selective attention.