Transition to Algebra: A Habits of Mind Approach

这个名为“向代数过渡：思维习惯方法”的项目，由教育发展中心数学小组的专业人员领导，正在开发一系列模块，介绍代数的关键思想，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的。模块处理从算术到代数，有理数，表达式/方程/单词问题，图形和方程，代数几何和比例推理的过渡。目标人群是城市高中贫困学校的学生，其中有大量的ELL部门。提议者的假设是，侧重于培养概念理解和数学思维习惯的教学材料可以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标的材料实际上会加强对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，研究人员正在解决四个研究问题。前两个问题集中在干预对培养学生思维习惯和提高他们在代数方面的能力和信心的影响。另外两篇论述了在各种学校环境中实施双周期代数新方法的可行性。目前正在进行一项小规模准实验实地测试，以初步估计教学材料和执行准则的效力。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。这一开发成果将成为学校设计策略帮助所有学生掌握基本代数知识的宝贵资源。

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.