When mathematics is used to help people cope with real-life situations, a three-stage intellectual process is involved. An operational instrument for assessing how a person moves from the first to the second and third stage is proposed. (Author)

Formally states the Thick Point Theorem and explicates the proof. Explores the key point for use of the Theorem. (GEA)

Displays that by themselves always elicited chance judgment of number were shown to three- to four-year-olds and six- to seven-year-olds. The first display was transformed into the second, and so on. Results indicated that three- to four-year-olds do not understand conservation of number because judgements of successive displays were independent…

One of the major sources of mathophobia is the great gap between the universally valid arithmetic of abstract numbers and the arithmetic that people use for describing concrete quantities. (Author/IRT)

This study examined the effect of language on acquiring the concept of place value. The sample for the study consisted of 211 Arabic-speaking children aged between 6.6 years and 7.8 years. Children were interviewed individually and asked to represent written two-digit numbers using base-10 blocks. A new approach for testing the linguistic…

The aim of the study (Johnsen Hoines 2002) reported here was to shed light on the process through which student teachers express and interpret their understandings about mathematical notions and thereby gain insight into them. This paper focuses on how students cooperate and move between different ways of understandings. It emphases in particular…

The paper looks into visualisation in learning mathematics from three perspectives: It starts from a discussion what it takes to make a sign, an inscription on the blackboard, on paper or on a computer screen to an image. Here we will look into the question of "similarity" and point to the possibility of having different perspectives on the same…

Vygotsky posed a variety of meaningful ideas for education in his short life. This paper focuses on everyday concepts and mathematical concepts or scientific concepts from his theory, reorganizing these ideas according to a new idea of sublated concepts. Using a series of interviews from a third grade fraction class in Japan, the paper discusses…

In this paper we put forward a theoretical position that, in cognitive terms, a differentiation should be made between a correspondence and a function. Important in understanding this difference is the role of an assignation rule; the correspondence acts as a way to identify a rule in context, whilst the function accommodates the rule in a more…

The ability of students to interpret from, represent mathematical problems in, and interact with, a number of differing representations appears to be a crucial part of understanding mathematical concepts. Here we consider the role of representation in student understanding of derivative and present an outline framework for determining its…

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, plane and spherical trigonometry, and mensuration. [This book was translated by David Brewster. It was revised and adapted by Charles Davies.]

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, plane and spherical trigonometry, and mensuration. [This book was translated by David Brewster. It was revised and adapted by Charles Davies.]