The purpose of the proposed three-year research project is to investigate characteristics of mathematics learning and its facilitation in an informal, after school, and urban environment. The research project consists of two interconnected studies, one focusing on the learning of middle-school students and the other inquiring into facilitator interventions. The first study focuses in-depth on (1) the mathematical ideas and forms of mathematical reasoning that middle school students develop and use as they investigate well defined, open ended tasks; (2) the patterns of discourse among the students as they build solutions to each task; and (3) over the course of the study, changes that occur in students' views about mathematics and about themselves as mathematical thinkers. The second study documents and analyses facilitator interventions and their consequent influence on student-to-student discursive interactions and individual student learning.
