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E. Fischbein 《Educational Studies in Mathematics》1969,2(2-3):290-306
Sans résumé 相似文献
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The intuition of infinity 总被引：2，自引：0，他引：2
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The main purpose of the present research was to check the possibility of measuring the feeling of “intuitive acceptance”, experienced by a subject when he offers an intuitive solution to a problem. It was postulated that two dimensions have to be considered and combined: The level of confidence and the degree of obviousness. Almost all the questions asked referred to the notion of infinity. The subjects were pupils belonging to grades 8 and 9. Three main categories of problematic situations have been identified:
- Problems which got high percentages of correct solutions and high levels of intuitive acceptance.
- Problems which got two types of contradictory solutions, each of them being accepted with moderate intuitiveness.
- Problems which got low frequencies of correct solutions and high frequencies of typical incorrect solutions, the second category presenting higher levels of intuitive acceptance than the first (counter-intuitive problematic situations).
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Efraim Fischbein Maria Sainati Nello Maria Sciolis Marino 《Educational Studies in Mathematics》1991,22(6):523-549
Six hundred and eighteen pupils, enrolled in elementary and junior-high-school classes (Pisa, Italy) were asked to solve a number of probability problems. The main aim of the investigation has been to obtain a better understanding of the origins and nature of some probabilistic intuitive obstacles. A linguistic factor has been identified: It appears that for many children, the concept of certain events is more difficult to comprehend than that of possible events. It has been found that even adolescents have difficulties in detaching the mathematical structure from the practical embodiment of the stochastic situation. In problems where numbers intervene, the magnitude of the numbers considered has an effect on their probability: bigger numbers are more likely to be obtained than smaller ones. Many children seem to be unable to solve probability questions, because of their inability to consider the rational structure of a hazard situation: chance is, by itself, an equalizing factor of probabilities. Positive intuitive capacities have also been identified: some problems referring to compound events are better solved when addressed in a general form than when addressed in a particular way. 相似文献
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Two baboons were trained on oddity problems with sets of stimuli involving parallel lines. When stable discrimination performance had been established, occasional test trials were run with Zöllner illusion figures. Both animals appeared to have been deceived by the illusion. 相似文献
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A three-year programme in upper secondary school is compulsory in Sweden. In reality, some youngsters refrain from applying to the upper secondary school (8 per cent) or drop out in advance (9 per cent). In Stockholm the Youth Centre has been assigned to arrange individual programmes for these pupils. The aim of this study is to investigate their reading and writing ability and to relate this retrospectively to their school experience. Instruments measuring reading comprehension, vocabulary and dictation were carried out on 286 respondents; in addition, background information concerning school attainment was collected. Ten respondents were selected, five high and five low achievers. An unstructured interview was used to investigate their home background, school and reading experiences. Students attending individual programmes at the Youth Centre had lower than average reading and writing abilities in comparison to students at the vocational programmes in upper secondary school. The whole group is characterized by low marks, immigrant background and partial school attendance. The analyses of interview statements reveal a common category - powerlessness - for those with and without reading disabilities. Separate categories were for high achievers - boredom - and for low achievers - lack of opportunity. 相似文献
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Intuitions and Schemata in Mathematical Reasoning 总被引：3，自引：0，他引：3
Efraim Fischbein† 《Educational Studies in Mathematics》1999,38(1-3):11-50
The present paper is an attampt to analyze the relationship between intuitions and structural schemata. Intuitions are defined as cognitions which appear subjectively to be self-evident, immediate, certain, global, coercive. Structural schemata are behavioral-mental devices which make possible the assimilation and interpretation of information and the adequate reactions to various stimuli. Structural schemata are characterized by their general relevance for the adaptive behavior. The main thesis of the paper is that intuitions are generally based on structural schemata. The transition from schemata to intuitions is achieved by a particular process of compression described in the paper.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
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The paper analyzes the effects of a teaching programme in probability devised for junior high school pupils (grades 5, 6 and 7). It was found that most of the notions were too difficult for the fifth grade pupils. In contrast, about 60–70% of the sixth graders and about 80–90% of the seventh graders were able to understand and use correctly most of the concepts contained in the programme. It was also found that, as an indirect effect the course on probability had a beneficial effect on some intuitively based misconceptions of the subjects, like: the representiveness effect; the positive recency effect; the notion of a lucky choice; the superstitious belief in the possibility of influencing the course of events by some particular behaviour. 相似文献
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The problem that inspired the present research refers to the relationships between schemata and intuitions. These two mental categories share a number of common properties: ontogenetic stability, adaptive flexibility, internal consistency, coerciveness and generality. Schemata are defined following the Piagetian line of thought, either as programs for processing and interpreting information or as programs for designing and performing adaptive reactions. Intuitions are defined in the present article as global, immediate cognitions. On the basis of previous findings (Fischbein et al., 1996; Siegler, 1979; Wilkening, 1980; Wilkening & Anderson, 1982), our main hypothesis was that intuitions are always based on certain structural schemata. In the present research this hypothesis was checked with regard to combinatorial problems (permutations, arrangements with and without replacement, combinations). It was found that intuitions, even when expressed as instantaneous guesses, are; in fact, manipulated'behind the scenes' (correctly or incorrectly) by schemata. This implies that, in order to influence, didactically, students' intuitions, those schemata on which these intuitions are based should be identified and acted upon. 相似文献