There is evidence that spontaneous learning leads to relational understanding and high positive affect. To study spontaneous abstracting, a model was constructed by combining the RBC model of abstraction with Krutetskii's mental activities. Using video-stimulated interviews, the model was then used to analyze the behavior of two Year 8 students…

Uses the notion of focusing phenomena to explain how a teacher's actions were connected to her students' interpretations of a linear equation. Conducts interviews and analyzes a high-school classroom that emphasized dependency relationships in real-world situations. Describes how the teacher directed attention away from functional relationships…

Presents findings from a research project in two high school mathematics classrooms. Focuses on the ways in which teachers' classroom interventions promote the growth of students' mathematical understanding. Describes 'blocking' as one of the major interventions of mathematics teachers. Discusses implications of the intervention strategy for…

Investigates 15-16-year-old students' interruptions in participation in mathematics class. Focuses on how the students construe normative meaning for the classroom episodes and how they value others and the knowledge construed. Indicates that some interruptions in the students' participation can be understood as an active contestation to the…

Investigates the connection between epistemology and openness to equity issues in the thinking of beginning secondary mathematics teachers. Analyzes teachers' responses around four themes: (1) beliefs about the nature of mathematics; (2) how those beliefs affect their pedagogy; (3) how they explain student failure; and (4) views on initial teacher…

Explores the extent and nature of students' calculator usage as determined from examination scripts in the Western Australian Calculus Tertiary Entrance Examination. Discusses errors made and understanding called upon for seven questions. Discusses instruction and assessment of skills associated with graphical interpretation. (Author/KHR)

Focuses on the state of mathematics as exemplified in New Zealand schools rather than the level of mathematical understanding of students. Regards the picture of mathematics presented in curriculum documents as healthy with respect to mathematics, but criticizes implementation of the curriculum. Suggests teaching by presenting a wider picture of…

Reports an analysis of videotape and interview data from four Year 8 mathematics lessons from the perspective of student cognitive engagement. Reports that cognitive engagement can be consistently recognized by specific linguistic and behavioral indicators. (Author/MM)

Explores secondary school students' conceptions of division by zero. A substantial number of the participating secondary school students argued that division by zero results in a number, and concrete arguments were generally regarded as valid for justifying the impossibility of division by zero. (Contains 30 references.) (Author/ASK)

Discusses collecting which occurs when students know what is needed to solve a problem, and yet their understanding is not sufficient for the automatic recall of useable knowledge. Presents exemplars of classroom discourse to describe the collecting phenomenon and discusses the implications for teacher and learners. (Contains 24 references.)…

Reports on how students managed some technical aspects of graphics calculators as they used them to study graphs of straight lines and parabolas. Identifies three common student difficulties: (1) tendency to be unduly influenced by the jagged appearance of graphs; (2) poor understanding of the zoom operation; and (3) limited grasp of the processes…

Draws on data from a three-year longitudinal study of secondary school classrooms to examine pedagogical issues in using technology resources in mathematics teaching, graphing calculators and overhead projection panels in particular. Theorizes four roles for technology in relation to teaching and learning interactions. Illustrates how technology…

Presents a study in which three classes of grade 10 students worked with graphics calculators throughout, five classes used them for approximately two months, and four classes did not use them at all. Posttest results showed that students who had worked with graphics calculators tended to attempt more problems and obtain higher test scores than…

Reports on the strategies adopted by a group of teachers in Ontario, Canada as they implemented de-streaming with grade 9 classes. Indicates that teachers were found to be making special provisions for both low- and high-achieving students and employing a wide range of techniques for assessing student progress. (Contains 20 references.)…

Investigates first year prospective secondary school teachers' beliefs about and attitudes toward mathematics. Finds that prospective teachers generally perceived good mathematics teaching to include the provision of enjoyable experiences. (Contains 31 references.) (Author/ASK)