The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)

Describes aspects of research conducted with two secondary mathematics teachers and seven senior students, which explored their perceptions of mathematics from their experiences and beliefs about personal excellence in school mathematics. Identifies three categories of excellent students: the student excellent-in-mathematics, the student…

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)

Case studies of two students detail contrasting passive and active learning behaviors. Examples of strategic learning behaviors illustrate that having students involved in activities such as discussions, question answering, and seatwork problems does not automatically guarantee successful knowledge construction. The nature of a student's…

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)

Examines the effects of cooperative homework on mathematics achievement, taking into account team characteristics. Results showed that three-member teams high in ability seem preferable in organizing cooperative learning for mathematics homework. Middle- and low-achievers all benefited from cooperative mathematics homework, whereas high achievers…

Introduces a theoretical framework--a language of description --which has been developed for the sociological analysis of school texts, mathematics texts in particular. The language is introduced through the practical description of extracts from the texts which were analyzed in its development. Also indicates how the language of description is…

Describes a method whereby data are first analyzed episode-by-episode in comparison to each other. Conjectures thus generated are then meta-analyzed to create chronologies structured by general assertions grounded in students' mathematical activity. Clarifies the relation between psychological and social processes. (TO)

Describes a study of 2 secondary students working problems over a 10-week period. Information on metacognitive awareness, confidence, and ability were collected through two videotaped sessions and questionnaires. Results suggest impulsiveness and perceived order of merit inhibit effective problem solving. (MTE)

Longitudinal teaching experiment engaged students in activities to produce fraction problems using specific terminology and satisfying certain criteria. Classroom interactions developed a common system of meanings and required negotiation of new social norms, leading to a new didactic contract. (SW)

Purposeful sampling was used to select six English-Korean bilingual students to investigate language difficulties and cognitive processes in solving mathematics word problems. These six case studies revealed distinct patterns of difficulties in solving problems written in English and Korean, especially for students in transition stage. (Author/KMC)

Investigated development of turn and turn measurement concepts within a computer-based instructional unit. Written assessments, interviews, and interpretive case studies of third and fourth graders found that turns were less salient for children than forward and back motions; students evinced a progressive construction of imagery and concepts…

Comparison of the effectiveness of two computerized environments, Schemes for Problem Analysis (SPA) and Algebraic Proposer (AP), with two sixth-grade classes found that in solving easy word problems, both software systems were equally helpful, but in harder word problems, those students who learned with SPA experienced more success than those who…

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)

Spatial tests involving the comparison of diagrams of interlaced ropes or knots at varying orientations were given to (n=21) subjects, mostly English college undergraduates, to determine an ordering in terms of complexity of tasks involving the mental manipulation of the knots. Certain knot shapes were processed faster than others and greater…