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)

This paper offers a critical analysis of Dubinsky et al. (On Learning Fundamental Concepts of Group Theory; 1994) and proposes, as an alternative to the four axioms and the standard definitions, that permutation and symmetry may be regarded as the fundamental concepts of group theory. (Author)

Investigates different types of procedures used by students (N=108) to simplify certain algebraic expressions. Findings indicate seven types of procedures including automatization, formulas, guessing-substituting, preparatory modification, concretization, rules, and quasi-rules. Contains 30 references. (JRH)

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…

Interviews 53 sixth grade students individually in an attempt to discover whether wrong interpretations of the algebraic structure found in an algebraic context occurs in a purely numerical context. Concludes that students' difficulties with the algebraic structure were also found in purely numerical contexts. (Contains 27 references.) (Author/ASK)

Investigates ways in which students use signs and endow them with meaning in their very first encounter with the algebraic generalization of patterns. Provides accounts of students' emergent algebraic thinking. Uses ethnographic qualitative methodology supported by historic epistemological research. Focuses on a discussion held by a small group of…

Examines a theoretical perspective on the ways in which children progress in learning mathematics. Suggests that there is difficulty in associating teaching discourses with the mathematics they locate that can result in an incommensurability between alternative perspectives being offered. Resists attempts to privilege any particular account but…

Presents and investigates a theoretical perspective on the development of understandings of mathematical operations with a particular focus on addition. Presents a case study on the development of a young boy and concludes that his attainment of aspects of operation sense supported transitions into algebraic ways of thinking. Contains 46…

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 a theory of the development of algebraic abstraction that extends Sfard's and Mason's ideas on learners' progress from operational or process-oriented thinking to the abstract or structural perspective. Analyzes secondary school students' approaches to classifying a set of complex equations. (Author/MKR)

Reports on a case study of a 16-year-old student working on transformations of functions in a computer-based, multirepresentational environment. Presents an analysis of the work during the transition from the use of visualization and analysis of discrete points to the use of algebraic symbolism. (AIM)

Examines possibilities for learning offered by a piece of software, Fonctuse, likely to encourage the linking of algebraic and graphical representations of functions. Studied the influence of prior algebraic knowledge on the cognitive processes and constructions of knowledge at play in this environment. (Author/MKR)

Presents a model of rational number using pairs of line segments which can embody ratios of numbers. Actions upon these segments can embody arithmetical operations. Discusses tasks in a computer environment for bringing out diverse algebraic and geometric meanings of rational numbers. (Contains 23 references.) (MKR/Author)

Investigates four seventh-grade teachers' awareness of students' tendency to conjoin or "finish" open expressions and teachers' ways of coping with this tendency. Concludes that two experienced teachers were aware of this tendency, whereas the novices were not, and teaching approaches related to this tendency differed considerably. Contains 24…

Discusses effectiveness of hints given to (n=100) ninth-grade students solving nonstandard problems on functions. Hints that stimulated concrete action were effective if the action modeled the required solution method. Hints that only warned against certain mistakes were ineffective. Appendix includes problems and hints. (MKR/Author)