Enhancing Physics Engagement: Upper Division Paradigms

1. Interactive Engagementin Upper-Level PhysicsLessons from the Paradigms Program http://physics.oregonstate.edu/portfolioswiki Corinne Manogue & the whole Paradigms Team New Faculty Workshop

2. Support • National Science Foundation • DUE-9653250, 0231194, 0618877 • DUE-0837829, 1023120, 1323800 • DUE-0088901, 0231032, 0837829 • Oregon State University • Oregon Collaborative for Excellence in the Preparation of Teachers • Grinnell College • Mount Holyoke College • Utah State University New Faculty Workshop

3. The Upper-Division • On your small whiteboard give one way that the upper-division is different from the lower division. New Faculty Workshop

4. The Upper-Division • Examples of how the upper-division is different from the lower division: • Smaller classes. • More invested students. • More complicated content. • More time/courses. • Opportunity to spiral. • Many students are timid/concerned. New Faculty Workshop

5. Moving away from templates Using advanced notation Breaking-up complicated problems Harmonic reasoning Problem-solving confidence Using Reflective Judgment Novice Expert New Faculty Workshop

6. 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? Novice to Expert Seoul National University

7. My Agenda Today • Discuss a few “teaching principles” and related “teaching suggestions.” • Model and discuss different types of activities. New Faculty Workshop

8. Teaching Principle Suggestions • Students are smarter than you think, but know far less. • Ask yourself when students would have learned something you expect them to know. • Keep a list of “surprising” things that students don’t know and use it to choose activities (PCK). • How to interpret the vertical axis. New Faculty Workshop

9. The Vertical Axis:Quantum Particle on a Ring New Faculty Workshop

10. The Radial Axis:Quantum Rigid Rotor New Faculty Workshop

11. Hydrogen Atom New Faculty Workshop

12. Simulations • Design experiences based on known student problems. • Choose thoughtfully: • “black box” (e.g. PhETs, OSP) • “open” (e.g. Mathematica/Maple) • “student code writing” • Avoid “Ooooh-Aaahh!!!” by asking students to answer specific questions. New Faculty Workshop

13. Teaching Principle • To become good problem-solvers, students must LEARN to move smoothly between multiple representations. • Students must develop a “rich concept image” for many physical concepts Suggestion • Use activities that require students to go back and forth between multiple representations. New Faculty Workshop

14. Multiple Representations New Faculty Workshop

15. New Faculty Workshop

16. Teaching Principle • Students have little experience with geometric visualization. Suggestion • Use kinesthetic activities to tap into students’ embodied cognition. New Faculty Workshop

17. Kinesthetic Activities • Stand up. • Each of you represents a point charge. • Make a linear charge density. New Faculty Workshop

18. Two Messages • Plan for a concept to build over time. • New juxtapositions within a single Paradigm. • Important concepts across several Paradigms. Seoul National University

19. Central Forces Seoul National University

20. ODE’s vs. PDE’s Seoul National University

21. Central Forces Classical Orbits & Quantum Hydrogen Atom • ODE’s PDE’s (interpretation of QM) • Use reduced mass • Use spherical symmetry to simplify equations • Conservation—Angular momentum & Energy • Effective potential • Symmetric potential but asymmetric solutions Seoul National University

22. Effective Potential Seoul National University

23. Teaching Principle • Plan for a concept to build over time. • New juxtapositions within a single course. • Important concepts across several courses. New Faculty Workshop

24. 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 New Faculty Workshop

25. 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. New Faculty Workshop

26. Eigenvector Definition • An eigenvector is a vector whose direction is not changed by the transformation. New Faculty Workshop

27. Eigenstates on the Ring New Faculty Workshop

28. Eigenstates • Preface • 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 New Faculty Workshop

29. Teaching Principle • It takes effort to bring information into working memory. Suggestion • Use small whiteboards to help students activate the relevant information. New Faculty Workshop

30. Small Whiteboards • On your small whiteboard, write something you know about the dot product. New Faculty Workshop

31. Using Small Whiteboards • Make it safe to be wrong: • Insist that students answer, but allow a question mark. • Make answers anonymous at first. • Different types of questions: • Review, comparing multiple representations. • Bring out common problems. • Model professional problem-solving. New Faculty Workshop

32. Affordances of Small White Board Questions • Allow the instructor to see if everyone is on the same page. • “Quiet” members of the class are encouraged to participate. • Students vie to have their answers chosen. • Keep everyone engaged and awake. • Professional development: communication skills. New Faculty Workshop

33. Teaching Principle • Don’t try to answer a question that students don’t yet have. Suggestion • Use active engagement to prime “the teachable moment.” New Faculty Workshop

34. Compare and Contrast Activities • On your medium whiteboards, construct a square grid of points, approximately two inches apart, at least 7 by 7. • I will draw an origin and a vector • For every point on your grid, imagine drawing the position vector • Calculate and label the point. • Connect the points with equal values of New Faculty Workshop

35. Effective Activities • Are short, containing approximately 3 questions. • Ask different groups to apply the same technique to different examples. • Involve periodic lecture/discussion with the instructor. New Faculty Workshop

36. Affordances of Medium Whiteboards • Provide the opportunity: • to develop and practice problem-solving strategies, • to compare and contrast answers, • for mini-presentations, • to discuss synthesis, evaluation, decision-making, etc. New Faculty Workshop

37. Plane Wave Representations Seoul National University

38. 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. New Faculty Workshop

39. 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. New Faculty Workshop

40. Potential Due to Charged Disk What is the electrostatic potential at a point, on axis, above a uniformly charged disk? New Faculty Workshop

41. One Physics Concept • Coulomb’s Law: New Faculty Workshop

42. Superposition • Superposition for solutions of linear differential equations: New Faculty Workshop

43. Chopping and Adding Integrals involve chopping up a part of space and adding up a physical quantity on each piece. New Faculty Workshop

44. Computational Skill • Can the students set-up and do the integral? New Faculty Workshop

45. Limits (Far Away) New Faculty Workshop

46. Constants vs. Variables • Which of these symbols are constants and which are variables? New Faculty Workshop

47. Teaching Principle—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 http://www.umich.edu/~refjudg/index.html New Faculty Workshop

48. 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? New Faculty Workshop

49. Active Engagement • Effective but Slow • Precious commodity • Use wisely • Special Needs of Upper-Division • Easily Over-Scheduled • Can Get Out-of-Synch • Short Activities Mid-Lecture • Moving Rooms: awkward but possible Seoul National University

50. The Instructor: Paints big picture. Inspires. Covers lots fast. Models speaking. Models problem-solving. Controls questions. Makes connections. The Students: Focus on subtleties. Experience delight. Slow, but in depth. Practice speaking. Practice problem-solving. Control questions. Make connections. Lecture vs. Activities Seoul National University