Research on Informal Mathematics Learning

这项拟议的为期三年的研究项目的目的是调查非正式、课外和城市环境中数学学习的特点及其促进作用。研究项目由两个相互关联的研究组成，一个关注中学生的学习，另一个探讨促进者的干预。第一个研究的重点是(1)中学生在研究定义明确的开放式任务时发展和使用的数学思想和数学推理的形式；(2)学生在构建每个任务的解决方案时的话语模式；(3)在学习过程中，学生对数学的看法和对自己作为数学思考者的看法发生的变化。第二项研究记录和分析了促进者干预及其对学生与学生之间的话语互动和学生个体学习的影响。

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.