Establishes six levels from an inductive proof to an algebraic demonstration on the bases of three axes in lower secondary school mathematics. Examines the meanings of demonstration and proof in lower secondary school mathematics and shows the relationships between them. Illustrates the discussion with a seventh grade student's activities.…

Presents findings that identify components of the practices of teachers acting as assessors of students' mathematics in the normal course of classroom work. Indicates that even teachers who have undergone some assessment training may underestimate the role of evidence interpretation, and questions about equity in the uses of teachers' judgements…

Proposes that children progressively recognize deeper and deeper similarities between their physical angle experiences, and classify them firstly into specific situations, then into more general contexts, and finally into abstract domains. Indicates that the standard angle concept first develops in situations where both arms of the angle are…

Discusses the problems of conceptualization of the function limit in technological environments (principally graphing calculators today and symbolic calculators tomorrow) that are gradually being adopted in precalculus teaching. Explains how the instrumentation process and the conceptualization process are dependent on each other. Sets forth a…

Presents a study using a module of work based on a graphing calculator that provided an environment where students could experience some aspects of variables and begin to build an understanding of them. Graphing calculators proved to be an instrument for achieving significant improvement in student understanding, which had often proved difficult…

Presents the story of a mathematics teacher's transformation that resulted from her engagement in collaborative action research. Discusses issues related to the broader study of collaborative action research in the mathematics classroom that are connected to teachers' transformation. (Contains 31 references.) (Author/ASK)

Analyzes student construction of function-based problem solving methods in introductory algebra. Describes longitudinal observation of a pair of students that studied algebra for three years using the function approach including intensive use of graphing technology. Offers terms for describing and explaining what and how do learners appreciate and…

Proposes a model to study the interaction between cognition and affect in mathematics. Develops important dimensions related to affect and cognition. Explains the importance of taking into account such dimensions in this kind of research, referring to students who are failing academically through a case study. (Contains 21 references.) (Author/ASK)

Identifies and explores the difficulties in the novice mathematician's encounter with mathematical abstraction. Observes 20 first-year mathematics undergraduates and extracts sets of episodes from the transcripts of the tutorials and interviews within five topics in pure mathematics. Discusses issues related to the learning of one mathematical…

Studies knowledge of young children's partitioning strategies by setting out not only to identify new partitioning strategies, but also to develop taxonomy for classifying young children's partitioning strategies in terms of their abilities. Provides taxonomy utilizing children's informal partitioning strategies as the foundation upon which to…

Draws from research studies on the introduction of symbolic systems on computers and calculators and considers 'new' techniques that accompany new technological instruments, their role in conceptualizing, and their links with 'usual' paper/pencil techniques as the key to analyzing the role of technology in education. This view implies non-obvious…

Reports on a statistical study of English and Hungarian teachers' conceptions of mathematics and its teaching. Distributed questionnaires to 200 English and 40 Hungarian mathematics teachers. Significant similarities emerged with both countries sharing, with similar strengths, a general conception of mathematics teaching that incorporates the…

Describes a research project that had two goals: to design and develop a tool with which to investigate pupils' images of mathematicians, and to use the device to compare those images held by lower secondary pupils in five countries. Reports that with small cultural differences, certain stereotypical images of mathematicians were common to pupils…

Presents a study by the International Commission on Mathematical Instruction (ICMI) on mathematics education in different cultural traditions. Investigates problems in mathematics education including issues such as curriculum; assessment; policy; the influences of information, communication technology (ICT), and multimedia; and community and…

Explores mathematical identity or self-concept through two classroom episodes in a senior high school class. (MM)