The purpose of this research was to investigate the evolution, with age, of probabilistic, intuitively based misconceptions We hypothesized, on the basis of previous research with infinity concepts, that these misconceptions would stabilize during the emergence of the formal operation period The responses to probability problems of students in Grades 5, 7, 9, and 11 and of prospective teachers indicated, contrary to our hypothesis, that some misconceptions grew stronger with age, whereas others grew weaker Only one misconception investigated was stable across ages An attempt was made to find a theoretical explanation for this rather strange and complex situation

The Evolution with Age of Probabilistic, Intuitively Based Misconceptions.

The article presents a report on four 45 minute sessions with a group of 17 year old humanities students. These sessions were the first of a series organised with the aim of exploring the possibilities of elaborating didactical situations that would help the students overcome epistemological obstacles related to limits. Students' attitudes pertinent to the development of the notion of limit, as well as changes of these attitudes, are described and analysed.

Humanities students and epistemological obstacles related to limits

Never getting to zero: Elementary school students' understanding of the infinite divisibility of number and matter.

The paper is based on extensive research carried out on students of mathematics who had completed a university course of calculus. The basic purpose of the research was to determine the students' images of the concept of limit, that is to find out their associations, conceptions and intuitions connected with limits and to determine the degree of their efficiency and the sources of their formation. To achieve the objectives an expanded set of selected problems — simple but not quite standard — and various other research instruments were used. Several classes of images of the limit concept have been identified and described, according to their main foci: neighborhoods, graph approaching, values approaching, being defined at x0, limit of f atx0 equals f(x0), and algorithms.

Images of the Limit of Function Formed in the Course of Mathematical Studies at the University.

This theoretical paper provides: (1) a presentation of some tasks that maybe regarded as typical sources for forming students' intuitions and first understandings about limiting processes of real sequences, (2) an analysis of the formal definition of limit via identifying roles for each symbol that occurs to achieve a mental image firmly consonant with the definition, and (3) a description of how this mental imagery may be used to re-examine the validity of some intuitive beliefs. In particular a persistent issue found in (1) is that the sources encourage an intuitive image of a sequence as having an ultimate term associated with the limit; it is this belief that is mostly discussed in (3).

Letting the intuitive bear on the formal; a didactical approach for the understanding of the limit of a sequence

The intuition of infinity

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The intuition of infinity