1. Upper-Level Curriculum Lessons from the Paradigms Program
Corinne Manogue
& the whole
Paradigms Team
Paradigms in Physics
Revising the Upper-Division Curriculum
Paradigms in Physics is a project at Oregon State University to revise the entire upper-division curriculum for physics and engineering physics majors to make our program more modern, integrated, and flexible and to increase students’ success.
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2. Support National Science Foundation DUE-9653250, 0231194, 0618877
Oregon State University
Oregon Collaborative for Excellence in the Preparation of Teachers
Grinnell College
Mount Holyoke College
Utah State University
Acknowledgements
This material is based upon work supported by the National Science Foundation under Grants No. DUE and DUE Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The project has also received support from the Department of Physics, College of Science, and Academic Affairs at Oregon State University and the Hutchcroft Fund at Mount Holyoke College.
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3. Top Down/Bottom Up On your small whiteboard:
What is the purpose of education?
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4. The Purpose of Education —Many purposes
To become a useful citizen.
To become a productive member of society.
To achieve happiness.
To find work.
To improve one’s standard of living.
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5. The Purpose of Education —A challenging vision
“…the purpose of your education is your growth as an individual and the development of your capacity to contribute to the transformation of society.”
—FUNDAEC
Fundación para la Aplicación y Enseñanza de las Ciencias
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6. The Purpose of Education —Implications
To be able to work with others.
To feel safe and help others to feel safe to participate and to take risks.
To be able to communicate effectively.
To be able to do complex problem-solving.
To do sensemaking.
To exercise reflective judgement.
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7. Reflective Judgment
“…the ability to understand the nature of ill-structured problems and to construct solutions for them.” —King & Kitchner
Stages:
Pre-reflective: knowledge from authority
Quasi-reflective: knowledge is uncertain
Reflective: evaluation of proposed solutions
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8. Reflective Judgment/Sensemaking
order of magnitude?
dimensions?
type of “beast”?
limiting cases?
symmetry?
time dependence?
How do I decide what is correct?
Does this answer conflict with something else I “know?”
Is this the problem I should be solving?
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9. Reflective Judgment
How do we structure/implement our curriculum so as to encourage our students to engage in this reflection?
How do we structure/implement our departments so as to encourage ourselves to engage in this reflection?
Why is this important?
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10. The Hidden Curriculum Where in your curriculum?
Speaking
Writing
Community Building
Professional Identification
Career Development
Non-academic Careers
Future Teachers
Modern Topics
Courses, Advising, SPS, Projects, Research, Senior Thesis, Internships, Special Days?
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11. On your small whiteboard
List one characteristic of middle-division students?
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12. Novice Expert —Problem-Solving
Moving away from templates
Using advanced notation
Breaking-up complicated problems
Harmonic reasoning
Problem-solving confidence
Using Reflective Judgment
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13. Seoul National University
Novice to Expert
How do I use this method to solve problems?
How do I get from this step to this step?
How will I know if this will work?
What else can I do if this won’t work?
4/27/2012
Seoul National University

14. My Agenda Today
Discuss a few “teaching principles” and related “teaching suggestions.”
Model and discuss different types of activities.
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15. Teaching Principles
It is your responsibility to ensure that everyone is comfortable in your class.
It takes courage to be publically wrong.
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16. Suggestions to Build Community
Multiple faces of diversity
Vivid examples
Picking up someone else’s baby.
Storytelling
Falling asleep.
Being brave.
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17. Teaching Principles Develop pedagogical content knowledge (PCK)
Use the results of PER
Talk with other faculty
Talk to advanced students
In the classroom: increase communication FROM students TO you
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18. PER Result Most students know triangle trigonometry
But not circle trigonometry
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19. Spin 1/2 Systems Stand up. Your left shoulder is the origin.
Rotate your left arm to show the whole complex plane.
Straight out in front of you, represents reals.
Straight up represents the pure imaginaries.
Show
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20. Spin 1/2 Systems Choose a partner.
Together, show the quantum spin ½ state
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21. Spin 1/2 Systems
Show the states that are physically equivalent to this state.
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22. Teaching Principles
Students must develop a “rich concept image” for many physical concepts
To become good problem-solvers, students must LEARN to move smoothly between multiple representations.
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23. Multiple Representations
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24. Ket Function Matrix Hamil- tonian Eigen- state Coeff- icient
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25. Teaching Principles
Students must learn how to break a problem up into manageable pieces.
Students must understand that solving physics problems is not just “doing math” about physics problems.
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26. An Example
Typical of EARLY upper-division work for physics majors and many engineers.
Solution requires:
many mathematical strategies,
many geometrical and visualization strategies,
only one physics concept.
Demonstrates different use of language.
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27. Potential Due to Charged Disk
What is the electrostatic potential at a point, on axis, above a uniformly charged disk?
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28. One Physics Concept
Coulomb’s Law:
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29. Superposition
Superposition for solutions of linear differential equations:
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30. Chopping and Adding
Integrals involve chopping up a part of space and adding up a physical quantity on each piece.
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31. Computational Skill Can the students set-up and do the integral?
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32. Limits (Far Away) 11/19/2016 New Faculty Workshop
You MUST expand in terms of something dimensionless!
(This is the potential due to a point charge!)
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33. Constants vs. Variables
Which of these symbols are constants and which are variables?
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34. Teaching Principle Plan for a concept to build over time.
New juxtapositions within a single course.
Important concepts across several courses.
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35. Eigenstates Preface Spin & Quantum Measurements 1-D Waves
2-D eigenvectors in Bra-Ket notation
Spin & Quantum Measurements
2 state systems
1-D Waves
Fourier series and 1-D Schrödinger
Central Forces
Ring (1-D) Sphere (2-D) Hydrogen (3-D)
Periodic Systems
Band Structure
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36. Eigenvectors Activity
Draw the initial vectors below on a single graph
Operate on the initial vectors with your group's matrix and graph the transformed vectors
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37. Eigenvectors Activity
Note any differences between the initial and transformed vectors. Are there any vectors which are left unchanged by your transformation?
Sketch your transformed vectors on the chalkboard.
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38. Eigenvector Definition
An eigenvector is a vector whose direction is not changed by the transformation.
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39. Eigenstates on the Ring
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40. Socratic vs. Groups How does it feel to teach in these ways? vs.
Everyone knows everything vs. No one knows anything
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41. We Can Help!
We have developed lots of materials: contact us and check out our wiki and ComPADRE.
physics.oregonstate.edu/portfolioswiki
Try our new online text:
physics.oregonstate.edu/BridgeBook
And published texts:
McIntyre (QM), Dray (SR)
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42. physics.oregonstate.edu/portfolioswiki
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43. Take-home Messages
Think about the curriculum and your department as a whole, but break each task into small, doable pieces.
Make it safe for each person to grow in their own way.
Use reflective practice: If it worked, figure out why so you can do it again and share it. If it didn’t work, figure out why so you can do it differently next time.
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