CAREER: Fostering "Mathematical Practices" In Urban Classrooms: Focus On Representation And Justification

职业：在城市课堂中培养“数学实践”：关注表征和论证

• 批准号: 0447542
• 负责人: Despina Stylianou
• 金额: --
• 依托单位: CUNY City College
• 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: 2005-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0447542&HistoricalAwards=false
• 关键词: CAREER; Fostering; Mathematical; Practices; Urban

The learning of mathematical practices, that is, the specific processes that successful mathematics learners engage in when doing mathematics, such as the use of justifications and various representations, is as important in achieving high performance in mathematics as it is to know the theory of mathematics. Yet, the role of these practices in school mathematics has been peripheral at best. Many students' experience with mathematics is limited to the memorization and practice of facts and procedures and little emphasis is placed on the development of these practices. This is particularly true in diverse, urban environments where students have been traditionally under-performing in mathematics. However, recent reform efforts are calling for a shift of mathematics instruction to foster the development of such practices in all students. If these practices are to become a meaningful part of school mathematics programs, we must advance our understanding of students' development of these practices and the conditions that promote that development. While research has provided us with valuable insights on several of these practices, there has been little understanding of how these practices develop as a whole and over time especially in challenging instructional settings.I am proposing a study that will address this topic. This study will trace the development of middle school students' competencies in the mathematical practices of representation and justification and will identify conditions that influence that development. I will begin first with a broad analysis of a large number of urban students' conceptions of mathematical practices. This will be followed by a focused and detailed analysis of the development of 6th to 8th grade students, using a variety of instruments and classroom observations. The goal is to go beyond documentation of the current conditions, and to trace and understand changes in students' competencies over time. Furthermore, the study will analyze classroom-teaching practices that influence these changes. To achieve this, the students' teachers will participate in concurrent professional development activities designed to enhance their understandings of middle school students' development of mathematical reasoning and classroom practices that promote that development, and will also be studied in parallel with their students.Intellectual Merit. The proposed work addresses calls for new research programs in emerging areas, including those that attend to the development of mathematical practices. The study will lead to conceptual frameworks that coordinate social and cognitive perspectives on mathematics learning with much-needed work in the urban schools' context and in the area of middle school students' development of mathematical practices (and not only skills and facts) and how to engage in professional development for teachers that supports this. The result will be deeper insight into the forms of pedagogy and content that support student learning in urban mathematics programs.Broader Impacts. I expect the proposed work to open new avenues in the learning and teaching of middle school mathematics, in particular, in the teaching and learning of mathematical practices, in ways, which resonate with overall progressive trends in the mathematics education community. A better understanding of the processes associated with students' developing conceptions of these practices can lead to recommendations for curriculum development and instruction. This study will suggest how instruction on representation and justification might be more effectively incorporated in middle school mathematics and will provide some insights on the nature of the cognitive and social obstacles that inhibit the development of efficient mathematical reasoning in more advanced levels. The proposed research setting is situated in a major urban area with a diverse student population for whom traditional mathematics instruction has not proven fruitful. Thus, understanding how to build mathematically successful students and how to support teachers within this context can support learning across multiple and diverse student populations. Findings will be broadly disseminated to enhance the field's understanding and to assist teachers in their everyday activities. Overall, the activities of the project will directly impact the diverse urban community of New York and will mentor pre-service teachers and graduate students who are members of underrepresented groups.Finbarr C. Sloane Ph.D.Program Director REC: ROLE & IERI

数学实践的学习，也就是成功的数学学习者在做数学时所从事的特定过程，例如使用证明和各种表示，对于在数学方面取得高成绩与了解数学理论一样重要。然而，这些实践在学校数学中的作用充其量只是外围的。许多学生的经验与数学是有限的记忆和实践的事实和程序和很少强调放在发展这些做法。这在多样化的城市环境中尤其如此，在这些环境中，学生的数学成绩一直不佳。然而，最近的改革努力呼吁数学教学的转变，以促进所有学生发展此类实践。如果这些做法是成为学校数学课程的一个有意义的一部分，我们必须推进我们的理解学生的发展，这些做法和促进发展的条件。虽然研究已经为我们提供了宝贵的见解，对这些做法，特别是在具有挑战性的教学环境中，这些做法如何发展作为一个整体，随着时间的推移，一直很少了解。本研究将追踪中学生在数学表征和证明实践中能力的发展，并将确定影响这种发展的条件。我将开始首先与大量的城市学生的数学实践的概念进行广泛的分析。接下来将使用各种仪器和课堂观察，对6至8年级学生的发展进行重点和详细的分析。其目标是超越当前条件的文件，并跟踪和了解学生的能力随着时间的推移发生的变化。此外，本研究将分析影响这些变化的课堂教学实践。为了实现这一目标，学生的教师将参加同时进行的专业发展活动，这些活动旨在加强他们对中学生数学推理发展的理解，以及促进这种发展的课堂实践，并且还将与学生一起进行研究。拟议的工作解决了在新兴领域，包括那些参加数学实践的发展新的研究计划的要求。这项研究将导致概念框架，协调社会和认知角度的数学学习与急需的工作在城市学校的背景下，在中学生的数学实践（而不仅仅是技能和事实）的发展领域，以及如何从事专业发展的教师，支持这一点。其结果将是更深入地了解支持城市数学课程学生学习的教学法和内容的形式。 我希望拟议的工作开辟了新的途径，在学习和教学的中学数学，特别是在教学和学习的数学实践，在方式，这与整体进步的趋势，在数学教育界的共鸣。更好地理解与学生发展这些实践概念相关的过程，可以为课程开发和教学提供建议。本研究将建议如何在表示和理由的教学可能会更有效地纳入中学数学，并将提供一些见解的认知和社会障碍的性质，抑制发展的有效的数学推理在更先进的水平。拟议的研究设置是位于一个主要的城市地区与不同的学生群体，传统的数学教学并没有被证明是富有成效的。因此，了解如何建立数学上成功的学生，以及如何在这种情况下支持教师可以支持跨多个和不同的学生群体的学习。调查结果将广泛传播，以加强实地的了解，并协助教师开展日常活动。总的来说，该项目的活动将直接影响到纽约多样化的城市社区，并将指导任职前教师和研究生，他们属于代表性不足的群体。斯隆博士项目主任REC：ROLE IERI