The give-"n" task is widely used in developmental psychology to indicate young children's knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and…

This paper reports on concept images of 38 secondary school mathematics prospective teachers, regarding the evenness of numbers. Written assignments, individual interviews, and lesson transcripts uncover salient, erroneous concept images of even numbers as numbers that are two times "something" (i.e., "2i" is an even number),…

Discussed are the results of interviews with 63 Australian children (interviewed in English) and 62 Nigerian children (62 interviewed in English and 60 interviewed in Yoruba) to determine how they used number concepts in discussing five demonstrations manipulating physical matter. Differences between the two groups are considered. (RH)

Analyzes from an historical perspective the extension of the natural-number domain to integers in students' transition from arithmetic to algebra in the context of word problems. Extracts four levels of acceptance of these numbers--subtrahend, relative number, isolated number and formal negative number--from historical texts. The first three…

Presented is a report on four 45-minute sessions with a group of 17-year-old students in Poland. Sessions were the first of a series organized with aim of exploring the possibilities of elaborating didactical situations that would help students overcome epistemological obstacles related to limits. Students' attitudes pertinent to the development…

The author cites observations of his own children that reflect their concept of fractions and analyzes their conduct in each case. (MN)

A semiotic perspective on mathematical activity provides a way of conceptualizing the teaching and learning of mathematics that transcends and encompasses both psychological perspectives focussing exclusively on mental structures and functions, and performance-focussed perspectives concerned only with student's behaviours. Instead it considers the…

The theoretical and reference frameworks developed in a 1982 study proved effective for developing a constructivist approach leading children to build a meaningful and efficient symbolism of number. Results of a three-year longitudinal study are described. (MNS)

Compares mathematics achievement of children in Taiwan and the United States by analyzing the arithmetical learning contexts of each. Interviews with parents and teachers identify cultural beliefs about learning arithmetic; interviews with students identify level of sophistication of arithmetical concepts. Found greater understanding by Chinese…