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

微积分之路：传播和推广微积分基础阶段教学的专业发展模式第二阶段MSP涉及四个核心伙伴；亚利桑那州立大学作为牵头，以及梅萨、钱德勒和斯科茨代尔学区。支持伙伴是：杨百翰大学、北科罗拉多大学、佐治亚大学、北亚利桑那大学和斯科茨代尔社区学院。这一第二阶段项目建立在路径项目工作的基础上，路径是一个有针对性的MSP，它确定了中学数学和科学教师的专业发展属性，导致学生学习的实质性和持续改善，学生在地区考试、州考试和基于研究的工具中的表现证明了这一点。第二阶段项目利用第一阶段研究中出现的以研究为基础的过程和工具，非常有效地将教师的教学转变为更以探究为基础和以概念为导向。第二阶段建立在第一阶段五大类调查结果的基础上，这五大类对支持数学教师实现学生对数学关键思想的学习的重大转变至关重要。这些是教师应具备的条件：1)所教数学的知识；2)对有效的数学学习和教学的信念；3)反思学生对教学的思考和学习的能力；4)使用课程辅助材料，促进以探究和概念为导向的教学；以及5)参与路径专业学习社区(PLC)。第一阶段导致了路径微积分专业发展模式(P3 DM)的发展，其中包括学生在课堂上的活动，包括详细的教师笔记、计算机动画和评估。这支持了微积分预科教师进行教学转型，实现了学生学习的显著收获。第二阶段通过三种方式扩展这项工作：1)在社区学院和大学一级实施P3 DM；2)在大班中实施该模式；3)动员学校管理人员，包括系主任，支持核心伙伴学区(11所学校)的所有教师在Precarculus中采用P3 DM。第二阶段研究P3DM在三种方式下的扩展过程，并继续考察P3DM经验如何影响教师在其他微积分基础课程如代数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阻碍或支持路径微积分基础材料的高质量实施？需要什么样的外部资源来缓解抑制因素和利用支持因素？2.教师理解和掌握路径演算前材料的典型发展轨迹是什么？教师需要什么支持才能实现这一发展？3.教师对《路径基础》材料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核心思想的推理能力的典型发展轨迹是什么？教师需要什么支持才能理解这些概念并有效地评估学生的推理？4.什么行政支持使教师能够有效地实施路径微积分预科材料？除了大学和社区学院的教师和教职员工外，至少有150名高中数学教师将参与其中。这项研究的成果将提供知识和工具，以扩大P3 DM的数学基础(微积分预科、大学代数、三角学和高中代数II)。调查还将深入了解有助于数学系转型的因素，以支持学生发展解决新问题的能力和信心，并建立对课程核心思想的更深层次和更紧密的理解。

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.