Pathways to Calculus: Disseminating and Scaling a Professional Development Model for Algebra Through Precalculus Teaching and Learning

微积分之路：通过微积分教学传播和推广代数专业发展模型

• 批准号: 1050721
• 负责人: Marilyn Carlson
• 金额: $ 210万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1050721&HistoricalAwards=false
• 关键词: Pathways; Calculus; Disseminating; Scaling; Professional

The Pathways to Calculus: Disseminating and Scaling a Professional Development Model for Precalculus Level Instruction Phase II MSP involves four Core Partners; Arizona State University, as the lead, and the Mesa, Chandler, and Scottsdale school districts. Supporting partners are: Brigham Young University, the University of Northern Colorado, the University of Georgia, Northern Arizona University, and Scottsdale Community College.This Phase II project builds on the work of Project Pathways, a targeted MSP that identified attributes of professional development for secondary mathematics and science teachers that resulted in substantive and sustained improvements in student learning, as documented by student performance on district exams, state exams and research-based tools. The Phase II project leverages the research-based processes and tools that emerged in Phase I research to be highly effective for shifting teachers' instruction to be more inquiry-based and conceptually oriented. Phase II builds on Phase I findings in five broad categories that are critical for supporting mathematics teachers to realize significant shifts in their students' learning of key ideas of mathematics. These are teachers': 1) knowledge of the mathematics they teach; 2) beliefs about what constitutes effective mathematics learning and teaching; 3) ability to engage in reflection on student thinking and learning in relation to their teaching; 4) use of curricular support materials that promote inquiry-based and conceptually oriented instruction; and 5) participation in Pathways Professional Learning Communities (PLCs).Phase I resulted in the development of the Pathways Precalculus Professional Development Model (P3DM), which includes in-class student activities with detailed teacher notes, computer animations and assessments. This supported Precalculus teachers in making instructional transitions that realized significant gains in student learning. Phase II extends this work by scaling the P3DM in three ways: 1) implementation of the P3DM at the community college and university levels, 2) implementation of the model in larger classes; 3) engagement of school administrators, including department chairs, to support all teachers in Core Partner school districts (11 schools) in adopting P3DM in Precalculus. Phase II studies the process of scaling P3DM in each of the three ways, and continues to examine how the P3DM experience affects teachers' instruction in other Precalculus level courses such as algebra II, college algebra and trigonometry.The Phase II Research Agenda addresses the following: 1. What institutional factors of a school inhibit or support quality implementation of Pathways Precalculus materials? What external resources are needed to mitigate inhibiting factors and capitalize on supportive factors? 2. What is the typical developmental trajectory of teachers understanding and taking ownership of Pathways Precalculus materials? What support do teachers need to enable this development? 3. What is the typical developmental trajectory of teachers' understanding of the core mathematical ideas in the Pathways Precalculus materials and ability to accurately assess students' reasoning about these ideas in the classroom setting? What support do teachers need to understand these concepts and effectively assess student reasoning? 4. What administrative support enables teachers to effectively implement Pathways Precalculus materials?A minimum of 150 high school mathematics teachers will be involved in addition to university and community college instructors and faculty. The products of this research will contribute knowledge and tools for scaling up the P3DM in the Precalculus strand (precalculus, college algebra, trigonometry and high school algebra II) of mathematics. The investigations will also produce insights about the factors that contribute to a mathematics department's transformation to support students in developing the capacity and confidence to solve novel problems and construct deeper and more connected understanding of the central ideas of a course.

微积分之路：传播和扩展专业发展模式的Precalculus水平教学第二阶段MSP涉及四个核心合作伙伴;亚利桑那州立大学，作为领导，和梅萨，钱德勒，和斯科茨代尔学区。 支持伙伴包括：杨百翰大学、北方科罗拉多大学、格鲁吉亚大学、北方亚利桑那大学和斯科茨代尔社区学院。该第二阶段项目建立在路径项目的工作基础上，路径项目是一个有针对性的MSP，它确定了中学数学和科学教师专业发展的属性，这些属性导致了学生学习的实质性和持续性改善，正如学生在地区考试中的表现所记录的那样，国家考试和研究工具。 第二阶段项目利用第一阶段研究中出现的基于研究的过程和工具，非常有效地将教师的教学转变为更加基于探究和以概念为导向。 第二阶段建立在第一阶段的调查结果在五个大类是至关重要的支持数学教师实现重大转变，在他们的学生学习的关键思想的数学。 这些是教师的：1）他们所教的数学知识; 2）对有效的数学学习和教学的信念; 3）反思与教学相关的学生思维和学习的能力; 4）使用促进探究和概念导向教学的课程支持材料;和5）参与路径专业学习社区（PLC）。第一阶段导致了路径Precalculus专业发展模型（P3 DM）的发展，其中包括课堂上的学生活动，详细的教师笔记，电脑动画和评估。 这支持Precalcus教师进行教学转型，实现学生学习的显着收益。 第二阶段通过以下三种方式扩展P3 DM：1）在社区学院和大学层面实施P3 DM，2）在较大的班级中实施该模型; 3）学校管理人员，包括部门主席的参与，以支持核心合作伙伴学区（11所学校）的所有教师在普雷库斯采用P3 DM。 第二阶段研究P3 DM在三种方式中的每一种方式的扩展过程，并继续研究P3 DM的经验如何影响教师在其他Precalculus级别课程，如代数II，大学代数和三角学的教学。第二阶段研究议程涉及以下内容： 1. 学校的哪些制度因素抑制或支持高质量地实施路径Precalculus材料？ 需要哪些外部资源来缓解抑制因素并利用支持因素？ 2. 教师理解和掌握Pathways Precalcus教材的典型发展轨迹是什么？ 教师需要什么样的支持才能实现这一发展？ 3. 教师对Pathways Precalcus教材中核心数学思想的理解以及在课堂环境中准确评估学生对这些思想的推理能力的典型发展轨迹是什么？ 教师需要什么支持来理解这些概念并有效地评估学生的推理能力？ 4. 什么样的行政支持使教师能够有效地实施Pathways Precalcus材料？除了大学和社区学院的教师和教员外，至少有150名高中数学教师将参与其中。 这项研究的产品将有助于扩大P3 DM在Precalculus链（前微积分，大学代数，三角和高中代数II）的数学知识和工具。 调查还将产生有关有助于数学系转型的因素的见解，以支持学生发展解决新问题的能力和信心，并构建对课程中心思想的更深入，更紧密的理解。