*Summary*

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 analyzes facilitator interventions and their consequent influence on student-to-student discursive interactions and individual student learning. The two studies employ curricular materials, pedagogical ways of working, as well as methodological and analytic tools developed at the Robert B. Davis Institute for Learning of Rutgers University. The setting for both studies will be an informal after-school program for students of Hubbard Middle School in Plainfield, an economically depressed, urban school district with 98% African American and Latino students.

*Intellectual Merit*

Our research will address important education and other social issues concerning the potential of informal mathematics learning and facilitation in urban contexts and, in this setting, the possibilities of students to develop deep subject matter understanding. Widespread practice is based on the assumption that minority children in urban school settings require a building of skills in a structured environment. With this focus, the nature of those students' mathematical reasoning and how it develops remains unexplored. Through the careful analysis of student-to-student discourse initiated by students themselves or stimulated by teacher questioning, our research studies will investigate the growth of mathematical understanding and reasoning of minority students in an after-school setting when conditions that invite unrestricted thinking and individual agency have been established.

*Broader Impact*

The results of the proposed research will contribute to fundamental knowledge about the mathematical reasoning of urban minority students. This research will provide (a) fundamental knowledge about mathematical ideas and forms of reasoning that students of middle school age can build in an informal environment; (b) insights into patterns of student-to-student discourse as they build mathematical ideas and forms of reasoning; (c) deeper understanding of changes in students' view of mathematics and themselves as mathematics learners; (d) documentation of efficacious interventions that facilitate students' building of mathematical ideas and reasoning as well as growth in understanding of particular mathematical concepts; (e) an electronic database that can be used for future research and for materials development; and (f) a replicable model for large-scale studies on mathematics learning in informal environments. Within the ROLE program, our study focuses directly on Quadrants II and III and provides insights into the issues of Quadrant IV, as well.