Transition to Algebra: A Habits of Mind Approach

向代数过渡：思维习惯方法

• 批准号: 0917958
• 负责人: E. Paul Goldenberg
• 金额: $ 349.61万
• 依托单位: Education Development Center
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0917958&HistoricalAwards=false
• 关键词: Transition; Algebra; Habits; Mind; Approach

DRL: DR K-12PI: GoldenbergAbstractThis project, Transition to Algebra: A Habits of Mind Approach, led by professionals in the mathematics group at the Education Development Center, is developing a collection of modules introducing key ideas of algebra in ways that complement the core curriculum when a school is offering double period algebra. The key habit of mind being developed is abstracting from calculation. Modules deal with the transition from arithmetic to algebra, rational numbers, expressions/equations/word problems, graphs and equations, geometry of algebra, and proportional reasoning. The target population is students in urban high poverty schools with a significant ELL sector.The proposers' hypothesis is that instructional materials focused on developing conceptual understanding and mathematical habits of mind can complement traditional skill-focused algebra instruction in ways that are engaging to students. Furthermore, they argue that using materials with such meta-cognitive aims will actually strengthen the learning of core algebraic concepts and skills. The supplementary algebra modules are being developed by a form of design research. Concurrent with development and field test of the student and teacher materials, the investigators are addressing four research questions. The first two questions are focused on the effects of the intervention in developing student habits of mind and in improving their competence and confidence in algebra. The other two address the feasibility of implementing the new approach to double-period algebra in a variety of school settings. A small-scale quasi-experimental field test is being used to give preliminary estimates of the effectiveness of the instructional materials and the implementation guidelines. The core purpose of these research activities is to inform development and refinement of the student and teacher instructional materials.Products of this development effort will be a valuable resource to schools as they devise strategies for helping all students master the essentials of elementary algebra.

DRL：DR K-12PI：Goldenberg摘要这个项目，过渡到代数：思维习惯方法，由教育发展中心数学组的专业人员领导，正在开发一系列模块，介绍代数的关键概念，以补充学校提供双周期代数的核心课程。培养思维的关键习惯是从计算中抽象出来。模块处理从算术到代数的转换、有理数、表达式/方程式/应用题、图形和方程式、代数几何和比例推理。研究的目标人群是英语学习领域较多的城市高中的学生。提出者的假设是，注重发展概念理解和数学思维习惯的教学材料能够以吸引学生的方式补充传统的以技能为中心的代数教学。此外，他们认为，使用具有这种元认知目的的材料实际上会加强核心代数概念和技能的学习。补充代数模块正在以一种设计研究的形式开发。在开发和实地测试学生和教师材料的同时，调查人员正在解决四个研究问题。前两个问题集中在干预在培养学生思维习惯和提高他们在代数方面的能力和信心方面的效果。另外两个讨论了在不同的学校环境中实施双周期代数新方法的可行性。目前正在进行小规模的准实验实地测试，以初步评估教学材料和实施指南的有效性。这些研究活动的核心目的是为学生和教师的教学材料的发展和完善提供信息。这种发展努力的成果将是学校制定策略帮助所有学生掌握初等代数的基本要素时的宝贵资源。