Below are the proposal summaries from the many grants that have funded the Paradigms in Physics project.

**NSF Proposal Summary: DUE--1836604**

1/19--12/20; $299,282

**PARADIGMS IN PHYSICS: REPRESENTATIONS IN QUANTUM MECHANICS**

*Elizabeth Gire, Tevian Dray, Corinne A. Manogue, & David Roundy*

**Overview**

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 strategies. The 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:

Strand 1: Research on Student Learning: 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.

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.

**Intellectual Merit**

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.

**Broader Impact**

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.

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.

**NSF Proposal Summary:
DUE-1836603**

1/19--12/20; $298,984

**PARADIGMS IN PHYSICS: REPRESENTATIONS OF PARTIAL DERIVATIVES**

*David Roundy, Tevian Dray, Elizabeth Gire, & Corinne A. Manogue*

**Overview**

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 strategies. The 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.

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.

**Intellectual Merit**

Strand 1: Improved Online Dissemination of Curricular Materials: 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 information. Employing a relational database for the structure underneath will allow for adding new layers of information about sequences of activities and courses.

Strand 2: Modular Online Mathematical Methods Text: 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.

**Broader Impact**

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.

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.

**NSF Proposal Summary:
DUE-1323800**

9/13--8/16; $649,293

**PARADIGMS IN PHYSICS: REPRESENTATIONS OF PARTIAL DERIVATIVES**

*Corinne A. Manogue, Tevian Dray, David Roundy, & Emily H. van Zee*

**Overview**

This proposal continues the joint work of two very successful projects: The 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 year. Curricular 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 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**

This project will advance knowledge within physics and mathematics education 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 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**

This project will directly impact mathematics and physics education at the 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.

**NSF Proposal Summary:
DUE-1141330**

6/12--5/15; $124,236

**DEVELOPING A COMPUTATIONAL PHYSICS LAB INTEGRATED WITH UPPER-DIVISION
PHYSICS CONTENT**

*David Roundy*

An upper-division computational physics course is being developed which runs parallel to and in synchrony with the existing junior-year physics courses that are being developed within the "Paradigms in Physics" project at Oregon State University (OSU).

Computation in physics courses is commonly treated in one of two ways. Either students run existing simulations in order to aid their understanding of physics, or physics examples are introduced ad hoc as applications of the numerical methods that students are learning to use in performing their own computations. While both of these approaches have value, this project serves to create a course that teaches students physics by having them create their own computations within the context of upper division courses. To this end, a project-driven laboratory experience in computational physics (utilizing course-integrated Python oriented modules) is introduced at an advanced level. In this laboratory course, students are learning to use important computational tools in the same manner as a professional physicist. In view of the importance of computation to the professional scientist, the course seeks to teach at a level that is accessible to all physics majors, with particular care taken for those who are least comfortable using computers.

This project is producing a set of six computational laboratory modules (with corresponding curricular materials) that are being evaluated and made available for use at other colleges and universities. Although the content is tailored and organized to fit the junior-year curriculum at OSU, the materials are designed to be sufficiently modular so as to be readily incorporated into the upper-division physics curriculum at other colleges and universities. Workshops are being developed for AAPT national meetings that will directly increase the visibility of these computational modules for other users.

**NSF Proposal Summary:
DUE-1023120**

9/10--9/14; $440,606

**PARADIGMS IN PHYSICS: INTERACTIVE ELECTROMAGNETIC CURRICULAR MATERIALS**

*Tevian Dray, Corinne A. Manogue, & Emily H. van Zee*

**Intellectual Merit**

This project builds on the joint work of two projects: The Paradigms in Physics Project, a complete redesign of the physics major, and the Vector Calculus Bridge Project, an effort to bridge the gap between the mathematics and physics of vector calculus.

The focus of this project is on the upper-division content in the area of electromagnetism. The goal is to increase the usability of the materials in four distinct ways: improving the effectiveness of the classroom materials; continuing development of a resource wiki, including descriptions of sequence of activities; adding narratives and video of classroom practice; and creating a modular online text. Both the text and the wiki are designed to be modular, allowing maximum flexibility in use. Both also contain a "meta" layer extensively documenting multiple pathways through the individual modules. The wiki further encourages faculty users to design and document alternatives, tailored to the needs of their own students. Pilot versions of all four pieces have been tested by instructors both at Oregon State University and elsewhere; extensive feedback is guiding further development.

This project includes an established team, an experienced science education researcher, recent adopters of the materials, a National Advisory Panel, and an external evaluator.

**Broader Impact**

The primary goal of this project is to provide online resources to a large audience, with most of the resources freely accessible to the general public. In the long run, the materials generated by this project can be used by many students and faculty well beyond the immediate adopters, both in the classroom and for professional development of TAs and other teachers. Furthermore, project research results and case studies are being disseminated to the education research community, not only on the project website, but also through presentations at conferences and publication in appropriate refereed journals.

**NSF Proposal Summary:
DUE-0837829**

2/09--1/13; 44,563

**COLLABORATIVE RESEARCH: PARADIGMS IN PHYSICS: CREATING AND TESTING
MATERIALS TO FACILITATE DISSEMINATION OF THE ENERGY AND ENTROPY MODULE**

*David Roundy & Corinne A. Manogue*

Topics in statistical and thermal physics have long been problematic in the undergraduate curriculum. To many students, the subject matter is abstract and theoretical and often requires mathematical tools they lack. This project addresses the challenge of teaching upper-division thermal and statistical mechanics by building on the Energy and Entropy (E&E) paradigm developed through the Paradigms in Physics Project at Oregon State University and a physics education research project at the University of Maine. E&E takes a radically different approach to statistical mechanics, incorporating the issues of quantum mechanics and measurement at its core and focusing on entropy as the Principle of Least Bias. In the approach, thermodynamic systems are treated as large, i.e. macroscopic, quantum systems that are not perfectly isolated from the remainder of the universe. This external interaction has enormous consequences that when taken into account clarifies thermodynamics' substance, with thermal variables now understood as macroscopic quantum averages and thermal probabilities as macroscopic quantum probabilities. An entropy postulate then plays the ultimate and crucial role of match maker in this marriage. As part of the current project, E&E curricular materials are being further refined and the materials are being field tested at Oregon State University and at collaborator sites at Ithaca College and Pacific University, a detailed instructor's manual is being prepared, and an education research project is being conducted to examine the efficacy of the approach and materials in supporting student learning of these concepts in advanced courses.

**NSF Proposal Summary:
DUE-0618877**

9/06--8/11; $498,124

**PARADIGMS IN PHYSICS: MULTIPLE ENTRY POINTS**

*Corinne A. Manogue, Tevian Dray, Barbara S. Edwards, David H. McIntyr*
& Emily H. van Zee//

**Intellectual Merit**
This proposal merges two very successful projects: The Paradigms in Physics
Project, a complete redesign of the physics major, now in its ninth year, and
the Vector Calculus Bridge Project, an effort to "bridge the gap" between the
mathematics and physics of vector calculus, now in its fifth year. The merged
project will be run by an established team, with two new members in education
research, appropriate to its expanded role.

The primary thrust of this proposal is to design materials that provide multiple entry points to our successful curriculum, aimed not only at encouraging full adoption of our 18 redesigned courses, but also at supporting faculty teaching more traditional courses who may wish to experiment with one or more pieces, be it a single activity or an entire course. We have identified four main strands:

- New content: We plan to develop textbooks for quantum mechanics and for vector calculus, emphasizing our nonstandard approach to these topics, while encouraging, but not requiring, the use of active engagement.
- Case studies: We plan to expand our existing websites to provide the information necessary for successful adoption of one or more of our activities, showing how to combine lectures and active engagement in a coherent way.
- Community of scholars: We plan to host a small number of visitors, who would be immersed in, and contribute to, the entire Paradigms package.
- Education Research: We plan to do research into students' ability to reason harmonically and metacognitively, and how these skills are affected by our materials.

**Broader Impact**

In addition to the impact on students, faculty, TAs, and visitors directly involved in the project, the primary goal of this project is to make what we have learned available to as wide an audience as possible. We expect to see impacts as a formal part of the project, but also in other, perhaps surprising ways, due to the use of multiple forms of dissemination. Each strand has the potential to reach beyond the boundaries of the project. We anticipate for example that the textbooks we develop will be used by many students and faculty beyond the immediate adopters of the Paradigms program. And the case studies on the website might be used for training TAs and other teachers. Our visitors will surely infuse our vision with unexpected insights and knowledge that will spin off in new directions. And the information gained by our research into student learning will be available to the entire education research community.

**NSF Proposal Summary:
DUE-0231194**

5/03--4/07; $99,941

**PARADIGMS IN PHYSICS--FACULTY MATERIALS**

*Corinne A. Manogue, David McIntyre, & Allen Wasserman*

The Paradigms in Physics Project is an ongoing complete revision of the upper-division physics curriculum. By tying the junior-year content to case-studies of paradigmatic physical situations, the curriculum is more modern and flexible enough to meet students' diverse career needs. By utilizing more student centered pedagogies including integrated laboratories, small-group problem-solving, computer simulations, and project-based courses, the project is improving students' analytical and problem-solving abilities, as well as their integration of mathematics and physics. By spiraling to revisit topics and concepts at a higher level in the senior year, the project is enhancing student learning. This phase involves national dissemination of this successful project. However dissemination of a project of this scale has never been attempted by a single department. Thus the present project focuses on two of the new Paradigms courses. Beyond the student materials that have already been developed, faculty will need additional support as they adopt these courses, including written Instructor's Guides to both the content and the activities, and Faculty Development Workshops. Successful implementation and evaluation of this project will provide the experience necessary to outline a more ambitious dissemination plan for the Paradigms project.

**NSF Proposal Summary:
DUE-0321032**

4/03--3/07; $217,039

**BRIDGING THE VECTOR CALCULUS GAP: EPISODE II**

Tevian Dray & Corinne A. Manogue

There is a "vector calculus gap" between the way vector calculus is usually taught by mathematicians and the way it is used by other scientists. This material is essential for physicists and some engineers due to its central role in the description of electricity and magnetism.

The two basic underpinnings of this proposal are the use of geometric reasoning rather than algorithmic computation -- a new emphasis for lectures -- and the use of open-ended small group activities -- a new emphasis for recitations. We believe that our major success so far has been the identification of geometric reasoning, using the vector differential, as the common theme underlying all of vector calculus. In the Proof-of-Concept phase of this project, we developed small group activities based on this approach, some intended for use in a vector calculus course, and some for use in upper-division physics courses on related material. These activities have been used successfully, by us and others, at several institutions.

It is the goal of this Full Development proposal to "bottle" our success by training other faculty in the use of our materials. We intend to offer workshops for those using these materials, and to write an Instructor's Guide containing information about this geometric approach to vector calculus, advice on using small group activities effectively, and tips on the individual activities. Four institutions have so far agreed to beta test these materials.

Enhancing students' geometric understanding of vector calculus will help to bridge the "vector calculus gap".

**NSF Proposal Summary:
DUE-0088901**

1/01--7/03; $112,513

**BRIDGING THE VECTOR CALCULUS GAP**

Tevian Dray & Corinne A. Manogue

There is a "vector calculus gap" between the way vector calculus is usually taught by mathematicians and the way it is used by other scientists. This material is essential for physicists and some engineers due to its central role in the description of electricity and magnetism. It is the goal of this proposal to bridge this gap.

The vector calculus gap goes much deeper than a difference in emphasis. Ask a physicist or engineer what topics should be covered in vector calculus, and the answer will pretty much agree with the existing syllabus used by mathematicians. But the traditional language used by mathematicians to teach this material is so different from the way it is used in applications that students are often unable to translate.

A major part of the problem is the traditional mathematics emphasis on Cartesian coordinates to describe vectors as triples of numbers, rather than emphasizing that vectors are arrows in space. This leads to the all-important dot and cross products being memorized as algebraic formulas, rather than statements about projections and areas, respectively. It is hardly surprising that many students are then barely able to compute line and surface integrals, or the divergence and curl of a vector field, let alone understand their geometric interpretation.

The traditional approach has one big advantage: It provides a single framework for handling quite general problems, the classic example being problems involving a paraboloid. But most practical applications, including virtually all at the undergraduate level, fall into a small number of special cases, such as those with spherical or cylindrical symmetry. There are no paraboloids in undergraduate physics! Problems with a high degree of symmetry become much more intuitive when the computations are not only done in appropriate coordinates, but also using a vector basis adapted to those coordinates. This emphasizes the geometry of the particular problem, rather than a brute force algebraic computation which many students fail to find illuminating.

We propose to develop supplemental materials, especially small group activities, which emphasize the geometry of highly symmetric situations, some of which are intended for use with an otherwise traditional vector calculus course, and some of which are intended for use in a new, upper-division physics course on related material. Such activities will introduce students to the types of problems -- and methods of solution -- which they will encounter in their chosen specialization, while at the same time increasing their understanding of traditional vector calculus and its applications, thus bridging the gap.

**NSF Proposal Summary:
DUE-9653250**

6/97--11/02; $497,063

**PARADIGMS IN PHYSICS**

*Corinne A. Manogue, Philip Siemens, & Janet Tate*

We are developing materials for a new curriculum for Junior-year Physics majors, learning by example in case-study format. Today's upper-division curricula currently require more advanced analytical and problem-solving skills than can be taught in a lower-division course dominated by the needs of non-major students, as typically offered by most departments. The objective is a double-tiered upper-division course of study, allowing students to consider the main topics twice: first emphasizing analytical skills, then emphasizing deductive and disciplinary integration. The curriculum, Paradigms in Physics, is to be a sequence of case studies of paradigmatic physical situations and conceptual examples, typically spanning two or more sub-disciplines. The teaching methodology of each Paradigm is being chosen to develop analytical and problem-solving skills. The topics are being chosen to span many of the principal examples usually developed while teaching the deductive disciplines. These Paradigms are to be followed in the senior year by survey courses which systematically present the deductive systems of Physics in a condensed format, as well as courses describing the phenomena and methodology of modern research areas. The dual-function (topic and method) design of the case studies will improve students' comprehension of the deductive disciplines, not only because they have enhanced analytical skills, but also because they are familiar with the central examples. Textbooks are being chosen for use throughout both years. Additional instructional materials is being sought and, as necessary, developed for each Paradigm; the content and medium of these materials is being chosen according to the specific demands of each topic, as will the instructional methodology. This flexibility allows appropriate use of group work, collaborative learning, and new technological resources. Evaluation is being performed by collaboration with a specialist as well as by external review; non-sighted access will be facil itated. Results will be made available at AAPT meetings, as published articles and on the Web.