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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.
-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 +
-The next phase of this project looks at representations of the quantification +Key to the ongoing success of the Paradigms program has been a vibrant learning community of physics faculty that constantly adapts both the curriculum and the groups' processes and methods as the physics education research community progresses.  The project team includes curriculum developers, education researchers, textbook authors, online textbook designers, recent adopters of curriculum materials from previous projects, and web development experts.
-of change, particularly partial derivatives, across many STEM disciplines, +
-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 ** ** Intellectual Merit **
-This project will advance knowledge within physics and mathematics education +Strand 1: Improved Online Dissemination of Curricular Materials: 
-as well as across other science, technology, and engineering fields that +Using a rigorous user-centered design process this project will redesign the Paradigms Project's online curriculum dissemination website on the outside to make it more intuitive for users to find needed informationEmploying a relational database for the structure underneath will allow for adding new layers of information about sequences of activities and courses.
-engage undergraduates in learning how to use partial derivatives to model +
-changing quantities in complex environmentsSuccess 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 +Strand 2: Modular Online Mathematical Methods Text: 
-curriculum developers, education researchers, and recent adopters of +Employing state-of-the-art software, this project will develop an open source, modular, online mathematical methods book for use in a just-in-time fashion in upper-division courses.  Using PreTeXt and Sage will allow the inclusion of multiple types of collapsible text alongside embedded computer algebra coding and high-quality, interactive graphics.
-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 +The gold standard for web dissemination of curricular materials is changing rapidly. For example, the National Science Digital Library has in many ways been superceded by modern search engines. The project activities represent second generation dissemination techniques.
-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.+
 +Strand 1 will create a more effective website that will be used by faculty teaching upper-division physics courses across the nation.  Many curriculum development groups are struggling to create a website that can be used effectively.  The complex structure of our long-term project is a further challenge.  One of the two major aggregators, PhysPort, simply links to our site.  Making our site more usable for those wishing to adopt various aspects of the Paradigms materials will also make our site a model for how other curriculum development projects might achieve the same goals.
 +The textbook in Strand 2 will document the content, language, and interactive nature of Paradigms courses as a living curriculum, whose continuous further development is driven by what happens in the classroom, thus providing  a resource not only to our own students, but also to our colleagues in mathematics, physics, and science education, both at OSU and at other institutions.
 +Furthermore, our deliberate choice to present mathematical concepts in physics language provides both mathematics and physics instructors with a window into the culture of the other discipline.  Not only does it help students to see familiar concepts in linear algebra expressed in the bra/ket language of quantum mechanics, but it is equally enlightening for mathematics instructors to be exposed to this usage.

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