This paper describes changes in students' geometrical knowledge and their creativity associated with implementation of Multiple Solution Tasks (MSTs) in school geometry courses. Three hundred and three students from 14 geometry classes participated in the study, of whom 229 students from 11 classes learned in an experimental environment that…

The paper introduces an exploratory framework for handling the complexity of students' mathematical problem posing in small groups. The framework integrates four facets known from past research: task organization, students' knowledge base, problem-posing heuristics and schemes, and group dynamics and interactions. In addition, it contains a new…

This interview study takes place in the context of a single small district in the United States. In the algebra curriculum of this district, there was a shift in the conception of equation, from a statement about unknown numbers to a question about the comparison of two functions over the domain of the real numbers. Using two of Shulman's…

The significance of discussion in mathematics classes has been prominently debated in the research literature. Different studies have stressed the importance of teacher flexibility in orchestrating the discussion. We introduce an operational definition of teacher flexibility. In a case study with one secondary-school mathematics teacher, we…

During individual interviews, secondary school mathematics teachers were asked to plan teaching an unfamiliar and challenging mathematics problem. Each teacher watched a special video-clip showing a pair of pupils successfully coping with the task. Teachers' planning was analyzed at three stages: before they solved the problem, after solving it,…