CAREER: Developing a Mathematical Knowledge Base for Teaching and Learning Generalization in Basic Algebra at the Middle-Grades in Urban Contexts

职业：为城市环境中的中年级基础代数的教学和学习泛化开发数学知识库

• 批准号: 0448649
• 负责人: Ferdinand Rivera
• 金额: $ 50.1万
• 依托单位: San Jose State University Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0448649&HistoricalAwards=false
• 关键词: CAREER; Developing; Mathematical; Knowledge; Base

Intellectual Merit The proposed study develops a mathematical knowledge base for teaching and learning generalization in basic algebra at the middle school level in an urban context. It involves analyzing children's generalizing processes based on individual and social activity. Classroom teaching experiments shall be developed, implemented, tested, and revised with the goal of articulating models of generalization in children. The project shall also address relevant instructional strategies and factors that will enable children to learn about the generalizing process, including ways the factors can all be coordinated properly so that teachers are able to provide their students with successful experiences. The study shall start with a class of 5th graders in a school in California whose thinking processes will be closely monitored for one semester. If it is possible, the same group of 5th graders will be investigated longitudinally for a period of four years. The overall theoretical framework of the study is drawn from an emergent perspective in which children's strategies of generalization are viewed as being constructed from individual and social processes. Further, the instructional theory of realistic mathematics education (RME), developed at the Freudenthal Institute, will be used in the design of classroom teaching experiments. The study has a developmental research focus. Children will perform activities that will allow them to engage in complex chains of reasoning and signification leading to the emergence of models for generalization. Also, classroom teaching experiments are developed using a development cycle. This cycle assumes a symbiotic relationship between instructional theory and actual practice. Data sources include video recordings of all classroom and small group discussions, audiotape recordings of project meetings and debriefing sessions with participating teachers, copies of student's written work, and individual clinical interviews. Data analyses of individual and collective learning in a classroom community shall use a method developed by Cobb, Stephan, McClain, and Gravemeijer (2001). Broader Impact The integrated research and education plan involves developmental research activities. The first activity concerns the development of structures of generalization among urban middle school children, including usable instructional theories that middle school teachers in such contexts may be able to adapt in their own classrooms. The five-year project is school-based and will be conducted in a collaborative partnership with teachers and their students who agree to participate in the study. Classroom teaching experiments will be designed, tested, and revised with a particular emphasis on how instructional resources and the classroom social context can be coordinated so that students succeed in algebra-related tasks involving generalization. The middle school mathematics curriculum provides the important formal foundation in algebra that needs to be strengthened at least in the area of formulating generalizations so that students are able to successfully transition to high school algebra. In the second activity, an ongoing circular process of describing, analyzing, and testing of strategies that children employ to generalize will be conducted in order to establish developmental models. Research-based and classroom-tested instructional materials that contain lessons and analyses drawn from the two activities shall be prepared and disseminated for public use by way of: presentations in various research and teachers. conferences; presentations in faculty in-service programs in urban middle schools; incorporation of research findings in various mathematics education courses in the university and in professional in-service programs with the aim of developing urban teachers whose instructional practices have been drawn from research; journal articles for teachers and researchers; CDs; and a website that will include activities, think pieces, and relevant publications in order to provide all teachers, students, and concerned stakeholders with ways in which to assist all middle-school students develop effective generalization skills. The proposed project shall also benefit from a diverse panel of experts whose expert knowledge has been drawn from having extensively worked with children in local, statewide, and international contexts.

智力优点拟议的研究开发了一个数学知识库，用于城市环境中中学基础代数的教学和学习概括。它涉及根据个人和社会活动分析儿童的概括过程。课堂教学实验的开发、实施、测试和修订应以阐明儿童的泛化模型为目标。该项目还应解决相关的教学策略和因素，使儿童能够了解概括过程，包括如何正确协调这些因素，以便教师能够为学生提供成功的经验。该研究将从加利福尼亚州一所学校的五年级学生开始，他们的思维过程将在一个学期内受到密切监控。如果可能的话，将对同一组五年级学生进行为期四年的纵向调查。该研究的总体理论框架是从一种新兴的角度得出的，其中儿童的概括策略被视为是由个人和社会过程构建的。此外，弗洛伊登塔尔研究所开发的现实数学教育教学理论（RME）将用于课堂教学实验的设计。该研究有一个发展研究重点。孩子们将进行一些活动，使他们能够参与复杂的推理和意义链，从而导致泛化模型的出现。此外，课堂教学实验是使用开发周期开发的。这个循环假设教学理论和实际实践之间存在共生关系。数据来源包括所有课堂和小组讨论的视频记录、项目会议和与参与教师的汇报会的录音、学生书面作业的副本以及个人临床访谈。对课堂社区中个人和集体学习的数据分析应使用 Cobb、Stephan、McClain 和 Gravemeijer (2001) 开发的方法。更广泛的影响 综合研究和教育计划涉及发展研究活动。第一项活动涉及城市中学生泛化结构的发展，包括中学教师在这种情况下可以在自己的课堂上采用的可用教学理论。这个为期五年的项目以学校为基础，将与同意参与该研究的教师和学生合作进行。课堂教学实验的设计、测试和修订将特别强调如何协调教学资源和课堂社会背景，以便学生成功完成涉及泛化的代数相关任务。中学数学课程为代数提供了重要的正式基础，至少在概括概括方面需要加强，以便学生能够成功过渡到高中代数。在第二项活动中，将进行一个持续的循环过程，描述、分析和测试儿童所采用的概括策略，以建立发展模型。应准备并通过以下方式传播基于研究和课堂测试的教学材料，其中包含从这两项活动中得出的经验教训和分析：在各种研究和教师中进行演示。会议；在城市中学教师在职项目中的演讲；将研究成果纳入大学的各种数学教育课程和专业在职课程中，目的是培养城市教师，其教学实践来自于研究；教师和研究人员的期刊文章； CD；一个包含活动、思考和相关出版物的网站，以便为所有教师、学生和相关利益相关者提供帮助所有中学生发展有效的概括技能的方法。拟议的项目还将受益于多元化的专家小组，他们的专业知识来自于在当地、全州和国际范围内与儿童进行的广泛工作。