The Purpose of Education: Fostering Reflective Judgment and Problem-Solving Skills

1. Upper-Level CurriculumLessons 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. Top Down/Bottom Up On your small whiteboard: • What is the purpose of education? New Faculty Workshop

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. New Faculty Workshop

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 New Faculty Workshop

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. New Faculty Workshop

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 http://www.umich.edu/~refjudg/index.html New Faculty Workshop

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? New Faculty Workshop

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? New Faculty Workshop

10. Speaking Writing Community Building Professional Identification Career Development Non-academic Careers Future Teachers Modern Topics The Hidden Curriculum Where in your curriculum? Courses, Advising, SPS, Projects, Research, Senior Thesis, Internships, Special Days? New Faculty Workshop

11. On your small whiteboard • List one characteristic of middle-division students? New Faculty Workshop

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

13. 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

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

15. Teaching Principles • It is your responsibility to ensure that everyone is comfortable in your class. • It takes courage to be publically wrong. New Faculty Workshop

16. Suggestions to Build Community • Multiple faces of diversity • Vivid examples • Picking up someone else’s baby. • Storytelling • Falling asleep. • Being brave. New Faculty Workshop

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 New Faculty Workshop

18. PER Result • Most students know triangle trigonometry • But not circle trigonometry New Faculty Workshop

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 New Faculty Workshop

20. Spin 1/2 Systems • Choose a partner. • Together, show the quantum spin ½ state New Faculty Workshop

21. Spin 1/2 Systems • Show the states that are physically equivalent to this state. New Faculty Workshop

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. New Faculty Workshop

23. Multiple Representations New Faculty Workshop

24. New Faculty Workshop

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. New Faculty Workshop

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. New Faculty Workshop

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

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

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

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

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

32. Limits (Far Away) New Faculty Workshop

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

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

35. 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

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 New Faculty Workshop

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. New Faculty Workshop

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

39. Eigenstates on the Ring New Faculty Workshop

40. Socratic vs. Groups How does it feel to teach in these ways? vs. Everyone knows everything vs. No one knows anything New Faculty Workshop

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) New Faculty Workshop

42. physics.oregonstate.edu/portfolioswiki New Faculty Workshop

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. New Faculty Workshop