Collaborative Research: POGIL Math - Guided Inquiry Materials for Gatekeeper Courses in Mathematics

该合作项目将在化学领域取得成功的过程导向引导探究学习（POGIL）方法应用于本科微积分预科和第一学期的微积分课程。该团队的工作以三个主要目标为指导：i)创建新的POGIL学习材料，用于微积分预科和微积分，改革将产生巨大而明显的影响；ii)通过在国家数学会议和POGIL夏季研讨会上举办数学专用POGIL研讨会，在数学界发展教师专业知识，以实施这些新材料；iii)通过实施案例研究设计来检查POGIL MATH课堂环境下的学习情况，对本科数学教育进行深入研究。有几个因素促成了这个项目强大的智力价值。首先，PI团队汇集了以下方面的专业知识：(1)编写高质量的POGIL化学活动；(2)数学课程创新；(3)数学教育研究；(4)评价。第二，POGIL项目的国家办事处在培训和传播方面提供支助。此外，由于POGIL是一项经过全国测试和验证的教学策略，基于对学生学习方式的研究，作为拟议项目的一部分生成的课堂材料预计将在数学方面产生类似于化学方面的结果：a)改善学生的学习；B)减员（特别是在代表性不足的少数民族学生中）；C)改善了对数学的态度；d)增加了教师的采用率。该项目正在几个方面发挥其更广泛的影响。首先，该项目研究部分的案例研究设计告知数学界，POGIL活动如何挑战数学教育文献中发现的学生对微积分的误解，以及课堂环境如何影响POGIL活动的实施。其次，在这个项目中开发的材料正在由作者和beta测试人员在不同的环境中进行课堂测试，因此增加了这些POGIL数学活动到任何教员课堂的潜在可移植性。此外，在直接参与编写POGIL微积分材料的几个机构中，有很大比例的代表性不足的学生在学习微积分，因此，任何课程变化都会对保留少数民族学生和妇女产生重大影响。最后，合作和试点测试站点中的各种机构正在扩大POGIL专家网络，跨越各种高等教育机构，美国各地和学科，从而对本科STEM教育社区的数学教学产生潜在的变革性影响。

This collaborative project is applying the approach of Process Oriented Guided Inquiry Learning (POGIL), which has been successful in chemistry, to undergraduate pre-calculus and first semester calculus courses. The team's work is guided by three main goals: i) to create new POGIL learning materials for pre-calculus and calculus where reform will have a large and visible impact; ii) to develop faculty expertise within the mathematics community to implement these new materials by presenting math-specific POGIL workshops at national mathematics meetings and POGIL summer workshops; and iii) to conduct in depth research on undergraduate mathematics education by implementing a case study design to examine learning in POGIL MATH classroom contexts. Several factors contribute to the strong intellectual merit of this project. First, the PI team brings together combined expertise in (1) authoring high quality POGIL chemistry activities; (2) curricular innovations in mathematics; (3) mathematics education research; and (4) evaluation. Second, the POGIL Project's National Office is lending support in training and dissemination. Moreover, because POGIL is a nationally tested and proven pedagogical strategy based on research on how students learn, classroom materials generated as part of the proposed project are expected to generate results in mathematics similar to those in chemistry: a) improved student learning; b) decreased attrition (especially among underrepresented minority students); c) improved attitudes toward mathematics; and d) increased faculty adoptions. The project is exercising its broader impact in several ways. First, the case study design of the project's research component is informing the mathematics community about how POGIL activities can challenge student misconceptions in calculus as identified in the mathematics education literature, as well as how classroom context affects implementation of POGIL activities. Second, the materials developed in this project are being classroom tested in diverse settings, both by the authors and by beta-testers, hence increasing the potential transportability of these POGIL mathematics activities to any faculty member's classroom. In addition, several of the institutions directly involved in the development of the POGIL calculus materials have large percentages of underrepresented students taking calculus, and thus any curricular change is in the position to have a significant impact on retention of minority students and women. Finally, the variety of institutions both in the collaborative and among the pilot test sites are expanding the network of POGIL experts, spanning a variety of post-secondary institutions, regions throughout the U.S., and disciplines, thus having a potentially transformative effect on mathematics instruction in the undergraduate STEM education community.