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Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Making decisions is a daily act in the human being, to greater uncertainty more difficult it is to decide. From a learning situation, consisting of deciding between two random games with dices, the relationship between proportional thinking and probabilistic thinking is studied, considering three states for proportional thinking and three types of probabilistic thinking. Under the focus of an instrumental case study, the decisions and arguments of Chilean high school students are analyzed. The results indicate that there are both beneficial and harmful relationships between proportional and probabilistic thinking, and that the difficulties in determining probabilities are not necessarily due to the absence of the use of proportions. A teaching that considers argumentation and learning of the sample space is recommended to channel the use of intuitive resources. [ABSTRACT FROM AUTHOR]

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The intuitions and heuristics about the probability are evaluated in 257 engineering students through a questionnaire of eight closed items, and the 148 arguments of them in an open item, are analized. The results indicate a high variation in the qualitative assignment of the probabilistic intuition in situations of uncertainty and the existence of correct and incorrect intuitions of the students. We propose a teaching of probability that relates theoretical and practical understanding of meanings of probability, from the intuitive to the axiomatic, through the qualitative estimation of probabilistic intuitions as a degree of personal belief, and the explicit confrontation of diverse heuristics with formal knowledge of probability. [ABSTRACT FROM AUTHOR]

Arguing and representing are abilities promoted in the school curricula of many countries. This paper presents the arguments used by six students from grades one to four regarding external representations they created. The structure of the arguments is analyzed with respect to some of the components presented in these representations using Toulmin's simple model, interpreting the arguments, and integrating the representation created with the argumentation. Verbal and gestural argumentative elements appear to be influenced by the students' oral expression abilities and numerical and geometrical knowledge. The arguments about the logical component, the variable, and about the numerical component, the frequency, were verbalized by the students, while the linear components, the linear basis and the graphical linearity, were argued for using spoken language, gestures, and metaphors. [ABSTRACT FROM AUTHOR]

Copyright of Magis: Revista Internacional de Investigación en Educación is the property of Pontificia Universidad Javeriana and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper analyzes the open responses to a problem situation used in research on the mean with data containing outliers. The results reveal correct and incorrect perceptions and show that statistical notions regarding the context and representativeness of a data set are far removed from teacher training. Elementary teacher educators could draw from these perceptions and help to improve them so that future teachers may gain a full understanding of the concept, which will give them the skills they need to teach statistics in schools. [ABSTRACT FROM AUTHOR]

We present a descriptive study about the knowledge of eight mathematics teacher educators in the context of a Lesson Study group, in the field of number sense, for primary teacher training. The objective is to identify elements of knowledge through the double perspective of the educators, when their practices consider both their future teachers and primary school students (double-look). Fragments were analyzed in a top-down and bottom-up process. The double-look scenarios appear useful to identify elements of the educator's knowledge, of a different nature from that of a teacher, although associated with it. [ABSTRACT FROM AUTHOR]