Search

This conceptual paper proposes a model to describe the quality of student dialogue during participative collaborative problem solving. Drawing on the participation metaphor of learning, we argue that the construct of mathematical sophistication is useful to describe the quality. We then present two frameworks, mathematical competencies and mathematical practices, as ways to operationalise the construct in the collaborative problem-solving setting. We argue that by using a networking theories approach, the two frameworks will provide nuances of levels of mathematical sophistication that can be observed in student interaction. In addition, they could provide an analysis of both individual and group contributions to mathematical sophistication in a collaborative task setting. Implications of using two approaches for conceptualizing mathematical sophistication for future mathematics education research and teaching practices are provided.

This investigation monitored the perceived effectiveness of a professional development program, called Facilitating Effective Learning and Teaching, in improving teacher practice. The program assumes that improvement is likely when the participants understand and value the learning process and themselves as learners and teachers. Program components included a challenge for change on the part of individual teachers, teachers operating as learners, and implementation of learned ideas in the classroom. The program examined the following aspects of learning: the meaning of learning; individual ways of learning; attitudes; students displaying what they know; facilitating the learning of new ideas; managing concentration; learning by reading, writing, and listening; facilitating remembering; learning in different contexts; students learning to organize themselves as learners; and monitoring learning. Evaluation of the program with 78 secondary teachers in Melbourne (Australia) showed that the quality of teaching and learning can be improved by increasing the school community's understanding and valuing of the learning process and individual variation in learning. Positive outcomes from the program included an increased preparedness to examine change by teachers, the fostering and legitimizing of positive attitudes towards classroom change, and a preparedness to be involved in change processes. (JDD)

Facilitating Effective Learning and Teaching (FELT) is a program that involves the systematic analysis of learning by students. It identifies the processes of reflection and making implicit knowledge explicit in changing one's understanding of learning. The present investigation examines the prediction that students can enhance their self-perception and effectiveness as learners by understanding and valuing both the learning process and themselves as learners. The FELT program affords the opportunity for students to evaluate and to modify the concepts of learning in the light of increasing knowledge and experience as learners. The basis of the FELT program is an examination of the learning process by learners. The following aspects of the learning experience are examined: (1) the meaning of learning; (2) individual ways of learning; (3) feelings of the learner; (4) displaying knowledge; (5) learning new ideas; (6) concentrating; (7) learning by reading, writing, and listening; (8) remembering; (9) learning in different contexts; and (10) organizing. The FELT program is based on eight assumptions. One assumption of the FELT program is knowledge is acquired through active construction. An investigation of 137 students in grades 5-8 reports an evaluation of the effect of studying the first aspect of learning on students's knowledge of learning and beliefs about themselves as learners. (KDP)

This paper examines a model of individual ways of learning and its implications for mathematics teaching. Topics discussed include: alternative ways that students use to represent mathematical ideas, management or control mechanisms, related models of learning preferences, ways in which students relate and manipulate ideas, and implications of this model of individual learning preferences for the teaching of mathematics. Contains 10 references. (MKR)