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** Overview ** ** Overview **
-This proposal continues the joint work of two very successful projects: The +In 1996, the Paradigms in Physics Project at Oregon State University reformed the entire upper-division curriculum for physics majors.  This reform involved both a rearrangement of content to better reflect the way professional physicists think about the field and also the infusion of a number of evidence-based interactive pedagogies that are known to engage students more effectively. The resulting curriculum has become a local and national model for curricular reform and includes a variety of active-engagement teaching strategiesThe holistic approach of the Paradigms Project represents an essential complement to curriculum development projects that focus on a single course or subdiscipline of physics and to education research that focuses on a single concept at a time. The proposal activities are divided into two strands:
-Paradigms in Physics Project, a complete redesign of the physics major, now in +
-its sixteenth year, and the Vector Calculus Bridge Project, an effort to +
-``bridge the gap'' between the mathematics and physics of vector calculus, now +
-in its twelfth yearCurricular materials produced by these projects+
-including group activities, instructor's materials, and three published and +
-one online textbook are currently in use at OSU and a number of other +
-institutions.+
-The next phase of this project looks at representations of the quantification +Strand 1: Research on Student Learning: 
-of change, particularly partial derivatives, across many STEM disciplines, +Research questions about how multiple representations can be leveraged to support student learning will be investigated through formal physics education research. New curricular materials will be developed and refined through a cycle of reflective practice.
-with the goal of aiding students in moving toward the robust and multi-faceted +
-understandings typical of STEM professionals. The project will include +
-strands that explore the ways in which STEM experts use and represent change, +
-that develop and test curricular materials for middle-division math and +
-physics courses, that establish students' initial and ongoing levels of +
-understanding as they progress through the curricular materials, and that make +
-these curricular materials freely available online to the education community.+
-** Intellectual Merit **+Strand 2: Learning Progression Development: 
 +A learning progression for quantum mechanics will be developed using a process established by the research group in its current project on partial derivatives, including empirically validating expert upper anchors and levels of students' ideas.
-This project will advance knowledge within physics and mathematics education +** Intellectual Merit **
-as well as across other science, technology, and engineering fields that +
-engage undergraduates in learning how to use partial derivatives to model +
-changing quantities in complex environments.  Success in upper-level +
-undergraduate and graduate courses in these fields requires understanding what +
-partial derivatives are and how to use them.  Drawing upon expertise in +
-mathematics, physics, and education, the team is tracing learning trajectories +
-from what novice students write, draw, and say when encountering partial +
-derivatives in upper-level courses through various representations experts use +
-as they identify and interpret ways that variables change under different +
-circumstances. In analyzing such data, the team is extending and adapting ways +
-of thinking from other fields, such as identifying the different ``epistemic +
-games'' students and experts ``play'' when solving problems involving partial +
-derivatives.  Based on such research, the curricular materials will include +
-prompts for encouraging metacognition, ways to help students become aware of +
-their own thought processes while transferring their emerging expertise from +
-one context to another.+
-Led by the PIs of the Paradigms and Bridge projects, the team includes +This project will produce new knowledge about (1) how students understand and use multiple representations to learn and do quantum mechanics, (2) how to sequence representations in a spins-first approach to support student reasoning about quantum systems, and (3) how computation may be leveraged to support student learning in quantum mechanics. This project is aligned with the research agenda for discipline-based education research recently set by of The National Research Council, including: research in upper division courses examining a range of pedagogical techniques and learning progressions, instructional approaches that help students use visualizations, and investigations of teaching and learning across multiple quantum mechanics courses.
-curriculum developers, education researchers, and recent adopters of +
-curriculum materials from previous projects. This team has published 29 papers +
-and 3 books based on previous grants in this ongoing project.+
** Broader Impact ** ** Broader Impact **
-This project will directly impact mathematics and physics education at the +Paradigms curricular materials are open source and freely available on the Portfolioswiki and linked to the Compadre national digital library and PhysPort. Instructors can easily adapt materials to local contexts and in multiple grain sizes.
-middle-division undergraduate level by providing classroom-tested curricular +
-materials and associated instructor resources to the education community +
-through existing, proven online resources (an activities wiki and textbook). +
-Mathematics materials will support learning trajectories in +
-multiple STEM disciplines, not just mathematics and physics.  The addition of +
-the new materials will make the existing resources easier to adopt by +
-providing more complete coverage, in line with most common course structures. +
-The project structure itself provides a model of how to advance STEM education +
-holistically, combining an influential national advisory committee with a +
-local interdisciplinary panel of experts drawn from affiliates in OSU's new +
-Center for Research in Lifelong STEM Learning.  All of these experts were +
-chosen in part because of their potential to use the intellectual results of +
-the work synergistically in their own related projects.+
 +The new learning progression will help adopting faculty to understand how instructional activities are linked to learning goals and will articulate a trajectory for sequencing activities based on education research of these materials.  This work to increase students' representational fluency and understanding of quantum mechanics is intended to increase the retention of all students, especially including underrepresented populations in physics, as well as to make upper-division physics and other representationally rich disciplines more accessible to a wider range of students.  By improving student learning in physics, this project addresses the increasing economic need for STEM graduates who understand the quantum mechanics of contemporary and emerging technologies.  A ``second-generation'' effect in which student who learn using advanced pedagogies become teachers who use those approaches amplifies the impact of both our teaching here at OSU and those faculty who adopt our materials.

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