Investigates the thinking process underlying students' improper linear reasoning and how this process is affected by their mathematical conceptions, beliefs, and habits. Explores the actual process of problem solving from students falling into the linearity trap and the mechanism behind it. Discusses specific mathematical conceptions, habits, and…

Describes how elementary linear algebra can be taught successfully while introducing students to the concept and practice of mathematical proof. Suggests exploring the concept of solvability of linear systems first via the row echelon form (REF). (Author/KHR)

Investigates proficiencies when students work on mathematics problems and the extent captured by knowledge categories. Explores competency that goes beyond knowledge to include mathematical 'dispositions' and 'practices' in which students engage. Considers ways in which research knowledge is conceived and developed, reflecting upon the role of…

Analyzes articles in "Educational Studies in Mathematics" since 1990. Reviews production and use of theories of teaching and learning mathematics. Outlines the theoretical framework of the tools of analysis and discusses methodological difficulties. Presents findings from the analysis of the journal and gives one example of how to read an article,…

Reanalyzes data obtained in 1987 on mental calculation strategies used by 11-year-olds in England, Wales, and Northern Ireland. Classifies mental strategies developed in the past decade in international research. Compares frequency and effectiveness of the strategies used by pupils of different levels of attainment. Discusses basic arithmetic…

Analyzes data from observations of first year university mathematics tutorials to elicit characteristics of teaching using the teaching triad, a tool developed in earlier research. Explores sensitivity to students and mathematical challenges. Provides insight into related pedagogic processes and shows approaches to analyzing teaching that address…

Describes formative and self-regulating evaluation, developed by Citogroep and used for primary schools in the Netherlands to signal the progress of 6-12-year-old students and monitor their learning. Presents the structure, principles, and tools of the management of the improvement of differential pedagogy and key ideas for teacher education.…

Investigates adults' long-term memory of mathematics learned in high school. Reports findings regarding the subjects' attempts to draw graphs of simple linear functions. Categorizes diverse responses to the task of drawing a graph of a linear function. Analyzes in detail three cases based on recall theories that explain the mechanism of recalling…

Reports on a study in which three 3rd grade students were presented with the volume of cuboids. Examines the problem solving actions students demonstrate and analyzes students' strategies and solutions. Explores the connection between spatial structuring and the use of numerical operation. Considers perseverance and control emerging when solving…

Suggests that strategy choice is a misleading characterization of efficient mental calculation and that teaching mental calculation methods as a whole is not conducive to flexibility. Proposes an alternative in which calculation is thought of as an interaction between noticing and knowledge. Presents an associated teaching approach to promote…

Analyzes the hypothesized biasing effect of teachers' gender stereotypes on their impressions of their students' competence and effort in mathematics. Teacher perceptions were consistent with stereotypes of gender differences. Discusses student performance level as an essential mediator-variable in the transmission of teachers' gender stereotypes.…

Undertakes, from a poststructuralist perspective, a meta-analysis of two short episodes from a paper by Manouchehri and Goodman (2000). Explores how mathematical knowledge and identities are produced in teaching/learning interactions in the classroom and the wider practical implications of this productive power of process for mathematics education…

Classifies ethnomathematics in relation to the teaching of formal, academic mathematics. Investigates whether ethnomathematics should replace academic mathematics, be a supplement to the mathematics curriculum, be used as a springboard for academic mathematics, or be taken into consideration when preparing learning situations. Suggests that only…

Reports the findings of a study aimed at learning from students and teachers in Black schools what classroom practices lead to success in school mathematics in their impoverished context. (Author/KHR)

Explores written calculation methods for division used by pupils in England (n=276) and the Netherlands (n=259). Analyses informal strategies and identifies progression towards more structured procedures that result from different teaching approaches. Comparison of methods used shows greater success in the Dutch approach which is based on…