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1.
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
2.
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
3.
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
4.
12-and 13-year-olds were tested with two types of tasks to test their understanding of applications of the multiplication and division of positive numbers: (i) writing down calculations required to solve verbal problems, and (ii) making up stories to fit given calculations. Selected pupils were interviewed to investigate further the thinking processes involved. The results indicate (a) the pervasive nature of certain numerical misconceptions, (b) the effects of structural differences among the items; particularly whether multiplication can be conceived as repeated addition or not, and whether division has the structure of partition, quotition or rate, (c) specific effects of context attributable to such aspects as relative familiarity, and (d) various interactions between these three sets of factors.With the collaboration of Joanna Rigg and Malcolm Swan. 相似文献
5.
It has been assumed, on historical and psychological grounds, that the concept of irrational numbers faces two major intuitive obstacles: a) the difficulty to accept that two magnitudes (two line segments) may be incommensurable (no common unit may be found); and b) the difficulty to accept that the set of rational numbers, though everywhere dense, does not cover all the points in an interval: one has to consider also the more rich infinity of irrational points. In order to assess the presence and the effects of these obstacles, three groups of subjects were investigated: students in grades 9 and 10 and prospective teachers.The results did not confirm these hypotheses. Many students are ignorant when asked to classify various numbers (rational, irrational, real) but only a small part of the subjects manifest genuine intuitive biases. It has been concluded that such erroneous intuitions (a common unit can always be found by indefinitely decreasing it and in an interval it is impossible to have twodifferent infinite sets of points [or numbers]) have not a primitive nature. They imply a certain intellectual development. 相似文献
6.
Analysing the various misconceptions held by students with regard to the mathematical set concept, the authors hypothesized
that these misunderstandings may be explained by the initial ‘collection’ model. Even after learning the formal properties
of a set in the mathematical sense, the students are still influenced in their reactions by the collection representation,
which acts ‘from behind the scenes’ as a tacit model. If the mathematical concept is not continually reinforced through systematic
use, it is the initial figural interpretation which will replace, as an effect of time, the formal one. The findings confirmed
this hypothesis.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
7.
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
8.
Tacit Models and Infinity 总被引：2，自引：0，他引：2
Efraim Fischbein 《Educational Studies in Mathematics》2001,48(2-3):309-329
The paper analyses several examples of tacit influences exerted by mental models on the interpretation of various mathematical
concepts in the domain of actual infinity. The influences of the respective tacit models, being generally uncontrolled consciously,
may lead to erroneous interpretations, to contradictions and paradoxes. The paper deals especially with the unconscious effect
of the figural-pictorial models of statements related to the infinite sets of geometrical points (on a segment, a square,
or a cube) related to the concepts of function and derivative and to the spatial interpretation of time and motion in Zeno's
paradoxes.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
The paper opens with the theoretical construct of figural concepts. It is argued that geometrical figures are characterized by both conceptual and sensorial properties. A geometrical figure is a mental abstract, ideal entity, the meaning of which is governed by a definition. At the same time, it is an image: it possesses extensiveness (spatiality), shape and magnitude. In geometrical reasoning the two categories of properties should merge absolutely, with the sensorial components providing the dynamics of invention and the conceptual component guaranteeing the logical course of the mathematical process. The paper investigates the effects of interaction between the conceptual and the figural components of a number of geometrical figures under the impact of age and mathematical competence. It has been found that age does not improve the control of the conceptual component on the interpretation of figures (between ages 14 and 17) in contrast to what one could expect. Usually, as an effect of age (grade) the interpretation gets worse. On the other hand, there are striking differences between the three competence levels considered. Strong mathematical students are characterized by their capacity to overcome the apparent contradiction between the figural, direct, impressions and the definitory properties. Their decision is, ultimately, determined according to the formal constraints (axioms and definitions). 相似文献
10.
This article seeks to analyze certain questions concerning the protests mounted against the 1978 World Cup. After a brief review of the military government's efforts to use the World Cup to legitimize its dictatorship, to Argentine society as well as the rest of the world, we examine the reactions of world public opinion to the fact that this event was being held in a country ruled by a repressive, criminal regime. Our focus, however, is on the people and groups in Israel who used the occasion of the World Cup to protest and denounce the crimes committed in Argentina. The Israeli case is particularly interesting because of the close relations between Israel and the Argentine dictatorship, as well as the fact that Israel had a large community of Latin American immigrants, most of them Argentines. Their numbers steadily increased as several hundred exiles fled the horrors of the military dictatorship. 相似文献