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1.
From an educational point of view, mathematics is supposed to have a completely hierarchical structure in which all new concepts logically follow from prior ones. In this article we try to show that there are also concepts in mathematics which are difficult to learn because of problematic continuity from prior knowledge to new concepts. We focus on the problems of conceptual change connected with the learning of calculus and the shift from rational to real numbers. We demonstrate the difficulty of this conceptual change with the help of historical and psychological evidence. In the empirical study 65 students of higher secondary school were tested after a 40 hour calculus course. In addition, 11 students participated in individual interview. According to the results the conceptual change from a discrete to a continuous idea of numbers seems to be difficult for students. None of the subjects had developed an adequate understanding of real numbers although they had learned to carry out algorithmic procedures belonging to calculus. We discuss how appropriate recent theoretical ideas on conceptual change are for explaining learning problems in this domain. Also some educational implications are presented.  相似文献   
2.
This study explored parents' (N = 351) educational optimism in terms of their trust in the possibilities of school to develop children’s intelligence. It was found that educational optimism could be depicted as a bipolar factor with optimism and pessimism on the opposing ends of the same dimension. Optimistic parents indicated more satisfaction with their children’s school and had a relatively positive assessment of their children’s academic success, which they explained in accord with their dynamic notion of intelligence, i.e. the child’s effort and help from the teacher. Parental notions of intelligence seem to serve as an important interpretative source for educational hopefulness.  相似文献   
3.

Employability is an increasing concern for university students. Our survey set out to examine university students’ perceptions of their employability and the ways in which these perceptions relate to positions that subsequently connect students to working life: students’ self-representational position or “ability self”, and students’ life-historical positions such as chosen field of study, phase of degree and working life experience. The participants comprised a sample of students (N = 1819) from two Finnish universities, representing diverse fields of study. It was found that apart from the field of study, the perceived proximity to graduation and working life was associated with the perception of employability. Furthermore, a set of self-attributed capabilities was associated with students’ perceptions of employability, particularly extroversion, ambitious competitiveness, mental strength and the desired characteristics of a good employee; however, the attribution of academic skills showed opposing effects. It was concluded that both self-representational and live-historical positions are part of the construction of students’ optimism regarding their employability.

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4.
The study set out to explore the bases on which the school assesses pupils’ educability and which show up as pupil categorizations manifested in seating order. The research was carried out with ethnographic methods and focused on the classroom situations of one first-grade class during one autumn term. The points of interest were those changes and episodes in which the seating order organized the action. Four stages was the spontaneous order created by the pupils themselves on their first day of school; the seating order of the other three stages was set up by the teacher on the basis of mixing boys and girls, of reading skills, of settledness, of capability for pair-work, and of “interpersonal chemistry”. It was found that the teacher made an active use of seating order as a pedagogical instrument. The pupils seemed to adopt the classification criteria and used them in their talk, but the application of these criteria, especially gender and interpersonal relations, was a constant source of dispute between the pupils and the teacher. It was concluded that seating order manifests, implements, and conveys to the pupils important symbolic elements of the representation of educability endorsed by the school.  相似文献   
5.
Finland has been celebrated as a country where everyone has the possibility to educate themselves and to get ahead in life through education. However, social differences of educability continue to persist and social differences of employability are further construed in the neo-liberal market economy. In this article we will examine 2 adult graduates’ educational and working life histories based on an 8-year qualitative follow-up study. Lisa with a working-class background and Henri from a middle-class family have both graduated from general upper-secondary school for adults and also accomplished higher education degrees in adulthood. Lisa and Henri's cases show how class and gender, as well as age, intertwine in the construction of educability and employability in different narrative environments. Based on our analysis, academic education may turn out as a broken promise instead of a great salvation with good occupational prospects for individuals like Lisa with a working-class background.  相似文献   
6.
The mothers and fathers (n?=?43) of third- and sixth-grade children were asked to assess their child’s academic potential in comparison with the child’s earlier competence and with that of her/his peers. In the interpersonal domain, the mothers’ and fathers’ perceptions of their child’s academic potential were related to each other, especially in mathematics, already when the child was in the third grade. Conversely, in the intrapersonal domain, the mothers’ and fathers’ perceptions were more consistent when assessing the sixth-grade than the third-grade children’s academic potential. These findings suggest that the normative feedback received from school tends to unify parental perceptions of their child’s academic potential as the child proceeds through school, even when the parents assess their child’s individual advancement.  相似文献   
7.
By comparing the reasons given for the peer assessments of children at different grade levels, the study set out to examine how children acquire the criteria of the conception of ability represented by the school. A sample of pre-school children, pupils (ages 6-10) of the first, second, third, and fourth grade (N = 112), were presented two tasks. In the free classification task, the children were asked to group their classmates on the basis of similarity; in the team selection task, they were requested to name those classmates whom they would like to have on their team for different academic contests and as playmates. In both tasks, the children were asked to give reasons for their responses. The findings from the team selection task indicated that, by the fourth grade, children have acquired the elements of the school's conception of ability in a fairly clear form. They begin to use comparative criteria and the correctness and speed of performance in the assessment of theoretical skills in particular. In the free classification task, references to academic skills made a clear appearance only as late as the fourth grade, suggesting that the influence of the school extends to the domain of non-academic peer assessment as well. En comparant les justifications fournies par des élèves de différents degrés d'études qui ont essayé d'évaluer leurs camarades de classe, cette étude a voulu mettre au clair de quelle facon les enfants s'attribuent-ils des critères de la conception de la capacité représentée par l'école. Deux tâches ont été donnés aux élèves préscolaires ainsi qu'aux élèves de première, seconde, troisième et quatrième année scolaire (N = 112). Dans un premier exercice de libre classification, on a demandé aux enfants de grouper leurs camarades selon la ressemblance de ceux-ci; dans un deuxième exercice de sélection d'équipes, les enfants ont dû choisir ceux de leurs camarades qu'ils voudraient avoir dans leur équipe pour participer à des concours scolaires les plus divers et ceux qu'ils voudraient avoir comme compagnons de jeux. Dans ces deux tâches les enfants ont dû également justifier leurs choix. Les résultats de l'exercice de sélection d'équipes ont prouvé que, avant de commencer la quatrième année scolaire, les enfants se sont attribués clairement des éléments des conceptions quant à la capacité qui sont celles de l'école même. Les enfants commencent à employer des critères comparatifs, ainsi que la correction et la rapidité de l'acte, pour évaluer surtout des capacités théoriques. Dans l'exercice de libre classification, les allusions aux capacités scolaires ne se sont présentées de facon nette qu'au cours de la quatrième année scolaire. Ce résultat semble indiquer que l'influence de l'école s'étend aussi dans le domaine de l'évaluation non-scolaire de camarades. Comparando las justificaciones dadas por alumnos de diferentes niveles escolares que han tratado de evaluar sus compañeros de clase, este estudio ha querido aclarar de qué manera los niños adoptan criterios del concepto de capacidad representado por la escuela. Se dieron dos tareas a alumnos preescolares y a alumnos del primer, segundo, tercer y cuarto año escolar (N = 112). En un primer ejercicio de libre clasificación, los alumnos tuvieron que agrupar sus compañeros según la semejanza de éstos; en un segundo ejercicio de selección de equipos, los alumnos tuvieron que elegir aquellos de sus compañeros que querían tener en su equipo para participar en diversos concursos escolares y aquellos que querían tener como compañeros de juego. En ambos ejercicios los alumnos también tuvieron que justificar sus preferencias. Los resultados en cuanto al ejercicio de selección de equipos mostraron que, antes de comenzar el cuarto año escolar, los niños han adoptado claramente elementos de los conceptos de la escuela sobre la capacidad. Los alumnos empiezan a servirse de criterios comparativos, de la corrección y la rapidez del acto para evaluar sobre todo capacidades teóricas. En el ejercicio de libre clasificación, las alusiones a las capacidades escolares aparecieron con claridad sólo durante el cuarto año escolar. Este resultado parece indicar que la influencia de la escuela se extiende también al campo de la evaluación no-escolar de compañeros.  相似文献   
8.
This longitudinal study set out to examine, in the light of the parents’ education and gender and the child’s gender, the changes that occurred in the course of five years in parents’ satisfaction with the functioning of their child’s school. Academically and vocationally educated mothers and fathers (N = 391) were asked to indicate their satisfaction with different aspects of their child’s school at the end of the first, third and fifth school year. It was found that the level of parental satisfaction was fairly high at the start, and despite a decreasing trend, it remained high; parental satisfaction was widely shared, and the number of dissatisfied parents remained small and stable. The academic parents displayed more satisfaction with their child’s school success and the fairness of the treatment than the vocational parents did. The results are discussed in terms of educational policy.  相似文献   
9.
Purpose:?This study set out to investigate pupils' evaluations of their academic abilities in different school subjects and their ratings of their potential for improving their performance in those school subjects.

Sample:?Twenty-eight pupils from the third grade (approximately age nine) and 30 pupils from the sixth grade (approximately age 12) in a primary school in Finland were interviewed.

Design and method:?The interview included tasks where the pupils were asked to rate and explain their potential for improvement in mathematics, the foreign language and the mother tongue. The explanations given were content-analysed and coding categories were formulated on that basis.

Results:?In all the three school subjects, the third-graders had a more positive view of their ability and its potential for improvement than the sixth-graders, and they based their view on a perspective of development and learning new things. The sixth-graders were more moderate and more uncertain in assessing their future performance.

Conclusions:?This study provided support to the earlier findings to the effect that pupils' faith in their abilities decreases in the course of their school years. We seek to explain this phenomenon in terms of the early stabilisation of the pupils' school performance, which is conveyed and constructed in the school's evaluative practices, especially in normative assessment. These practices clearly convey a differential conception of ability, which the pupils adopt as part of their self-assessments as shown e.g. by their use of school-like explanations in assessing their performance.  相似文献   
10.
This study examined parental views of their child’s educability through the parents’ perceptions of their child’s resilience. The purposes of the study were: (1) to examine psychometric properties of the rating scale created to measure parental views of their child’s educational and psychological resilience, (2) to explore whether the parents’ views of the child’s resilience were related to their notions of the child’s competencies and (3) to examine how parents’ perceptions of their child’s resilience were related to the parent’s social position and the child’s gender. Data were collected by questionnaire from the parents of fifth-grade children (N=391). The parental rating scale consisted of three dimensions of resilience, all with satisfactory reliability. Parents’ views of their child’s resilience were related to their perceptions of child’s abilities and school success, suggesting that the parental rating scale had concurrent validity. The results also indicated that parents’ views of their child’s resilience were related to their gender and education and to the child’s gender. Furthermore, parents’ views of their child’s educational resilience, based on parents’ trust in their child’s internal capacities, were related to the parental definition of their child’s cognitive-verbal competencies, in particular.  相似文献   
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