Outlines 10 math activities involving students in measuring, using numbers, sorting, classifying, investigating, and reasoning in the outdoors and helping students develop concepts and determine meaningful relationships between mathematics and the world around them. (ERB)

Orienteering involves navigating over an unfamiliar route with a map and a compass and locating control markers as quickly as possible. Originating in Sweden, orienting began primarily as a military event and has grown into "a sport for all." Suggested activities in orienteering to conduct in school conclude the article. (ERB)

Points out difficulties experienced by developmental students in dealing with abstractions in language and mathematics. Shows how students can be taught mathematical concepts by using concrete examples and their own colloquial language to better grasp abstractions. (DMM)

Research findings on children's understanding of fractions, gleaned from interviews, are briefly noted. (MNS)

Describes an approach to generating graphs that represent the relationship between pieces of quantitative information and play upon the reader's perception of those relations. (AEA)

Some strategies for avoiding misconceptions about the greatest common factor and the least common multiple are presented. Several alternative methods for computing each are given. (MNS)

The author argues that the existence and uniqueness theorems of elementary differential equations must be taught prior to some simple initial value problems. (SD)

The author discusses curriculum planning and reform, especially the theory of Mathematics education outlined by T. P. Nunn prior to 1920. This article is a continuation of SE 515 504, 516 064, and 516 353. (SD)

This paper presents the conceptualisation of infinity as a multi-faceted concept, discussing two examples. The first is from history and illustrates the work of Euler, when using infinity in an algebraic context. The second sketches an activity in a school context, namely students who approach the definite integral with symbolic-graphic…

The present study aims to explore the secondary teachers' understanding and reasoning about the concepts of limit and continuity. The findings suggest that teachers have not developed a rich relational understanding of these notions. They exhibited disturbing gaps in their conceptualizations of limit and continuity. [For complete proceedings, see…

This paper introduces the reader to the concepts of binomial probability and simulation. A spreadsheet is used to illustrate these concepts. Random number generators are great technological tools for demonstrating the concepts of probability. Ideas of approximation, estimation, and mathematical usefulness provide numerous ways of learning…

This book is designed to help teachers in the elementary grades deepen their understanding of the mathematics they have to teach. It is based on the belief that teachers cannot teach what they do not understand well, and it addresses several fundamental questions: (1) What math concepts and skills are important in the elementary grades?; (2) Why…

In this article, which is part of an ongoing research, a classification is proposed for ratio comparison problems, according to their context, their quantity type, and their numerical structure. Deriving from this classification, an interview protocol was designed, and guidelines for the interpretation of answers into strategies were decided. A…

This report considers the reasoning of sixth grade students as they explore problem tasks concerning the fairness of dice games. The particular focus is the students' interactions, verbal and non-verbal, as they build and justify representations that extend their basic understanding of number combinations in order to model the outcome set of a…

In this paper, we explore the role of polygonal shapes as geometrical models in teaching mathematics, so as to elicit and interpret children's geometric conceptions and understanding about shapes. Primary pupils were asked to draw a stairway of figures (triangles, squares and rectangles) each one bigger than the preceding one. Pupils use two…