This paper elaborates the notion of a personal example space as the set of mathematical objects and construction techniques that a learner has access to as examples of a concept while working on a given task. This is different from the conventional space of examples that is represented by the worked examples and exercises in textbooks. We refer to…

Students incorporate and use the implicit and explicit parameter time to support their mathematical reasoning and deepen their understandings as they participate in a differential equations class during instruction on solutions to systems of differential equations. Therefore, dynamic reasoning is defined as developing and using conceptualizations…

Attempts to examine the place of mathematics in terms of the goals within education and in particular to seek reconsideration regarding who has the right to make such decisions. Stresses that there is no one answer because many influences change over time, and students may decide they do not wish to learn a subject. (AIM)

This study examines the assessment beliefs and practices of four middle school mathematics teachers implementing a reformed mathematics curriculum for the first time. The constraints on change in assessment include time available to develop, implement, and interpret alternative assessments, as well as parent and student beliefs about what it means…

Describes a project-based situation in mathematics with 12- and 13-year-old students in 2 schools in Edinburgh, Scotland. The main theme of the project, its results, and afterthoughts are presented to illustrate differences in the behavior and attitudes between students in the last year of primary school and those in the first year of secondary…

Argues that the organization of cognitive structures for technical domains can be visualized as a network of connected thinkable models. Describes a taxonomy of models that has been developed and discusses the issue of how representations relate to human modes of perception and action. Contains 25 references. (DDR)

Describes two experiments that investigate how "buggy algorithms" in multi-digit subtraction are used. The first experiment tested third grade students (N=110) and repeated the test two years later. The second experiment tested students in grades 3-6 (N=301). Contains 21 references. (DDR)

Discussed are the range and balance of learning activities in the classroom, including discussion of the various roles of the people involved. The analysis is based on records of observations of 174 mathematics lessons with students aged 12-14; microcomputer use was integrated as a teaching aid. (MNS)

The range of problems associated with learned helplessness in mathematics is introduced through three hypothetical case studies. Then the basic theory of, the evidence for, and variables affecting learned helplessness are described. Issues of cure and prevention are discussed, and some suggestions are offered for teachers. (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)

A learning sequence is sketched that enables children to have valid experiences in music, language, mathematics, and movement, more or less simultaneously. The activity starts with a short tune and works toward a song as the solution to the problem. The creation of a dance follows the writing of the song. (RH)

Presents a constructivist view of mathematics, mathematics teaching, and mathematics achievement, and differentiates this view as an alternative to the typical traditional perspective of these terms. Discusses the roots of this approach in contemporary information-processing psychology. (TW)

Presented is an overview of "Boxer," a multipurpose computational user-friendly medium, the focus of this special issue presenting research involving its use. With its roots in LOGO, the design of Boxer is described and an overview of the articles in the issue is given. (MDH)

A longitudinal study followed Brian from grade five through grade seven to examine his representation and development of mathematical knowledge. Some observations over the four years were that Brian liked to figure things out, responded poorly to suggestions not fitting the representation he constructed, and changed attitudes from purposeful and…

This field study represents a departure from structured, or directed, computer-mediated communication as used in its natural environment, the computer lab. Using observations, interviews, and the computer medium itself, the investigators report how high school students interact with computers and create their own agendas for computer usage and…