This qualitative case study in a rural school in Umgungundlovu District in KwaZulu-Natal, South Africa, explored Grade 12 learners' mental constructions of mathematical knowledge during engagement with optimisation problems. Ten Grade 12 learners who do pure Mathemat-ics participated, and data were collected through structured activity sheets and…

In some higher education courses that focus on case studies, teachers can provide situated scenarios (such as business bottlenecks and medical cases) and problem-solving discussion tasks for students to promote their cognitive skills. There is limited research on the content, performance, and behavioral patterns of teaching using online…

Proposes that conceptual change is constrained by the child's conceptual structures and the structures inherent in problem-solving tasks. Uses a microgenetic case study and group data to examine how interaction between strategies children bring to a task and the detailed task structure redirect children's attention and create the possibility of…

Argues that the dichotomy between domain-specific and general theories of cognitive development addressed in the "Merrill-Palmer Quarterly" special issue is unproductive. Suggests that polarities of generality and specificity exist in creative tension as seen through developmental processes. (Author/BB)

Examines the role of case methods in teacher education, noting that the use of case methods depends upon an understanding of teaching and the learning-to-teach process. Three frameworks for using cases in teacher education are examined (precept and practice, problem solving and decision making, and knowledge and understanding). (SM)

This study examines the construct of problem representation and the processes used by learners to construct or modify problem representations in problem-solving situations. Students (n=14) from freshman calculus courses at the University of California at San Diego participated in videotaped interviews in which they were asked to think aloud as…

The processes by which conceptual knowledge is constructed during mathematical problem solving were studied, focusing on the cognitive activity of learners (i.e., the ways they elaborate, reorganize, and reconceptualize their solution activity). Underlying this research is the view that learners' mathematical conceptions evolve from their activity…

Reports case studies using personal construct psychology and the logic of fuzzy sets to elucidate the content and organization of two elementary school teachers' knowledge of fractions and mathematical pedagogy. Results identified four personal constructions that affected classroom events; knowledge of fractions, general pedagogical knowledge,…

This paper examines students' mathematics learning in a social context as two versions of an instructional sequence designed to facilitate students' development of a conceptual foundation for place-value numeration are enacted in two third grade classrooms. The same instructional sequence is used in each classroom with the regular classroom…

Epistemological perspectives are the ways students interpret or make meaning of their educational experience. Research has stressed the need to develop strategies to counter traditional mathematics pedagogy and epistemology because they have alienated many girls and women. An integrated framework of two cognitive developmental models describe…

The IADIS CELDA 2012 Conference intention was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There had been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a…