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

微积分之路：微积分预科水平教学专业发展模式的传播和扩展第二阶段MSP涉及四个核心伙伴；亚利桑那州立大学，以及梅萨，钱德勒和斯科茨代尔学区。支持合作伙伴有：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。第二阶段项目以“项目路径”的工作为基础，该项目是一个有针对性的MSP，确定了中学数学和科学教师的专业发展属性，这些属性导致了学生学习方面的实质性和持续的改善，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以探究为基础和以概念为导向。第二阶段建立在第一阶段的五大类发现的基础上，这些发现对于支持数学教师实现学生对数学关键思想学习的重大转变至关重要。这些是教师：1)他们所教的数学知识；2)关于什么是有效的数学学习和教学的信念；3)在教学中对学生的思考和学习进行反思的能力；4)使用课程支持材料，促进以探究为基础和概念为导向的教学；5)参与路径专业学习社区（plc）。第一阶段的结果是发展了Pathways学前微积分专业发展模型（P3DM），其中包括课堂上的学生活动，有详细的老师笔记，电脑动画和评估。这有助于微积分预科教师进行教学转换，从而在学生学习中获得显著收益。第二阶段通过三种方式扩展P3DM来扩展这项工作：1)在社区学院和大学层面实施P3DM， 2)在更大的班级中实施该模型；3)包括系主任在内的学校管理人员的参与，支持核心合作学区（11所学校）的所有教师在微积分预备课程中采用P3DM。第二阶段研究了以三种方式分别缩放P3DM的过程，并继续研究P3DM体验如何影响教师在其他微积分预科课程（如代数II、大学代数和三角学）中的教学。第二阶段研究议程涉及以下内容：学校的哪些制度因素会抑制或支持Pathways学前微积分教材的高质量实施？需要哪些外部资源来减轻抑制因素和利用支持因素？2. 教师理解和掌握Pathways学前微积分教材的典型发展轨迹是什么？教师需要什么样的支持来促进这种发展？3. 教师对Pathways微积分预科教材中核心数学概念的理解，以及在课堂上准确评估学生对这些概念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？4. 什么样的行政支持能使教师有效地实施微积分预备课程的材料？除了大学和社区学院的教师外，至少有150名高中数学教师将参与其中。本研究的成果将为微积分预科课程（微积分预科、大学代数、三角和高中代数II）中的P3DM提供知识和工具。这些调查还将产生对促进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，并对课程的中心思想建立更深入和更紧密的理解。

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.