String art on an octahedron provides a viable way to teach and illustrate geometric concepts, while correlating mathematics and art. How to use straws and string, and suggestions for investigating the related geometry, are given. (MNS)

The discussions of the theme group on Technology and Cognitive Development at the Fifth International Congress on Mathematical Education are summarized. How computers can be used to engage students actively, to promote problem-solving skills, and to achieve better understanding is discussed. (MNS)

An example is given for deriving mathematical content from a game. The game and eight activities are included for both basic and advanced versions. (MNS)

Examines hypotheses and strategies used by children at the kindergarten, second-, fourth- and sixth-grade levels in making proportional judgements. The task involved 36 trials in which the child had to choose between two groups to obtain a target-color "chip." Results generally conformed to the developmental sequence proposed by Piaget…

Recent thinking about the mathematics being used in science courses, with an emphasis on problem solving, is reviewed. Data from a survey of the mathematics content in secondary science textbooks are then presented, with suggestions for science instruction. (MNS)

Discussed are the roles played by anticipation, belief, and motivation in two young children's problem-solving activity. It is argued that a solver's beliefs and motivations are intimately related, and that the discussion of the two children's behaviors may have some generality. (Author/MNS)

Instructional strategies that will develop the concept of a fraction are presented. Fractions as counting numbers, measures, and subdivisions are included, with a combination of regions and number lines suggested as a teaching aid. (MNS)

Results from an English assessment of achievement on two geometric topics, line symmetry and angles, are reported. Contrasts in the patterns of responses to related items, and to the same items by pupils aged 11 or 15, are highlighted. (MNS)

The development of proportional reasoning has long been recognised as a central but problematic aspect of mathematics learning. In a Year 6 teaching intervention the part/whole notion of fractions was distinguished from the part: part notion of ratio, and the "between" and "within" relationships in ratio were emphasised.…

This study investigated the development of an additive schema from the perspective of the schema's flexibility in coping with new context and unfamiliar semantic structure. It followed 27 first graders who learned addition and subtraction using an experimental curriculum. The instruction involved a didactical model combining the context of two…

This study addressed the problem of how a prospective mathematics teacher's active engagement in a scientific inquiry can deepen the meaning of her extant mathematical concepts. We used a constructivist framework to analyze a 2-hour interview with a prospective mathematics teacher as she solved an open-ended problem of graphing a 3-D landform. We…

There are two purposes in this study. One is to compare how 7th and 8th graders reason on linear and quadratic geometric number patterns when they have not learned this kind of tasks in school. The other is to explore the hierarchical relations among the four components of reasoning on geometric number patterns: understanding, generalizing,…

We report research on meanings of scale generated by pairs of 14 year-old students engaged in joint map-construction. Characteristics of the learning environment, such as the communicational orchestration, the use of experientially familiar objects in space as starting points for creating figural representations and the interrelated…

This report explores first year undergraduate mechanical engineering and mathematics students' conceptions of the derivative and the contribution that membership of different departments may have on these conceptions. Quantitative results suggest that mechanical engineering students develop a proclivity for rate of change aspects of the derivative…

This is a study of how urban elementary grades students develop and express functions. Data were analyzed according to the forms of representations students used, the progression in students' mathematical language and the operations they employed, and how they attended to one or more varying quantities. Findings indicate that students are capable…