1. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Active-Engagment Strategies that help students learn how to 'Think Like a Physicist' Corinne Manogue http://physics.oregonstate.edu/portfolioswiki

2. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Support National Science Foundation –DUE-9653250, 0231194, 0618877 –DUE-0088901, 0231032, 0837829 Oregon State University Oregon Collaborative for Excellence in the Preparation of Teachers Grinnell College Mount Holyoke College Utah State University

3. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Purpose of Education —Reflection “For an educational process to be truly successful, it must encourage students to reflect on the conceptual foundation of their own education.” —FUNDAEC Fundación para la Aplicación y Enseñanza de las Ciencias—Colombia

4. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA A Question for the Audience

5. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Main Differences Physics is about things. Physics is about geometry. Physicists can’t change the problem.

6. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Visualization—Table

7. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Visualization—Level Curves

8. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Visualization—Graph

9. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Curvilinear Coordinates

10. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Curvilinear Basis Vectors

11. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Curvilinear Basis Vectors

12. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Vector Differential

13. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Vector Differential

14. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Geometry of Change

15. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Master Formula where

16. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Hill

17. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Visualization—Gradient

18. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Cross Product

19. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Cross Product

20. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA

21. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 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.

22. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Potential Due to Charged Disk What is the electrostatic potential at a point, on axis, above a uniformly charged disk?

23. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA One Physics Concept Coulomb’s Law:

24. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Superposition Superposition for solutions of linear differential equations:

25. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Chopping and Adding Integrals involve chopping up a part of space and adding up a physical quantity on each piece.

26. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Computational Skill Can the students set-up and do the integral?

27. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Constants vs. Variables Which of these symbols are constants and which are variables?

28. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Limits (Far Away)

29. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Spinning Ring Consider a very thin ring of charge with constant charge density, and total charge Q. The ring has radius R and is rotating about its axis with period T. For all groups: Create an integral expression for the vector potential caused by this ring everywhere in space. The expression should be complete enough to put into Maple or a similar mathematics package.

30. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Spinning Ring - Limits Approximate this vector potential near the center of the ring, in the plane of the ring. Approximate this vector potential near the center of the ring, along the z-axis. Approximate this vector potential far from the ring, in the plane of the ring. Approximate this vector potential far from the ring, along the z-axis.

31. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Active Engagement

32. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Summary of Strategies Make the students do it/checking in –Small white boards –Kinesthetic activities Multiple reps –Cross Products Geometric Reasoning –Maple Activities Breaking apart complicated expressions –Small group activities—Potential due to a disk What kind of a beast is it –Parameters vs constants Chunking –Unifying ideas—Master formula Organization –Build the concept over time. –Concept Maps Content ordering –Math & physics together

33. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Lecture vs. Activities 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.

34. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Socratic vs. Groups How does it feel to teach in these ways? vs. Everyone knows everything vs. No one knows anything

35. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA KetFunctionMatrix Hamil- tonian Eigen- state Coeff- icient

36. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Classroom Practice — Content Talking at the level of syllabi is not enough. –Curvilinear coordinates –Exp(ikr) Know what your students know –Many surprises—use PER –Notation exp(ik.r)

37. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Classroom Practice —Resources Seating Tables and chairs Walls Large white boards Small white boards Projectors, etc. Time Slots Daily schedule Chunks Course names Credits

38. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Hidden Curriculum —Professional Development Speaking Writing Modern Topics Professional Identification Career Development Non-academic careers Future teachers Where in your curriculum? Courses, Advising, SPS, Projects, Research, Senior Thesis, Internships, Special Days?

39. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Hidden Curriculum —Problem-solving What is problem-solving?

40. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Hidden Curriculum —Problem-Solving Moving away from templates Using advanced notation Breaking-up complicated problems Harmonic reasoning Novice Expert Problem-solving confidence Using Reflective Judgment

41. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Hidden Curriculum —Changing the frame What are your students expectations for what will happen in the classroom?

42. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Hidden Curriculum —Changing the frame Respect Rapport Encouragement Discipline Humor Expectation of success “Not knowing” is our initial state

43. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Purpose of Education —Changing the frame What is the purpose of education?

44. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Purpose of Education —Many purposes To become a useful citizen. To contribute to the progress of one’s country. To become a productive member of society. To achieve happiness. To find work. To improve one’s standard of living.

45. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Purpose of Education —Education vs. Science The purpose of science is narrow. The purpose of education is not. If we want our students to believe that they can/should USE science to solve the world’s problems, then we must recognize that in our courses. We are educators as much as we are scientists. We must educate the next generation of EVERYBODY.

46. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 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

47. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Purpose of Education —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

48. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Purpose of Education —Reflection 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?

49. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Classroom Practice — Content Resources vs. misconceptions. Talking at the level of syllabi is not enough. –Curvilinear coordinates –Exp(ikr) Know what your students know –Many surprises – Notation exp(ik.r) Compare and contrast Students always point to checking in with them. What is your own frame? Changing the students frame?

50. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Active engagement in the upper-division classroom Better learning (why) –Awake –Building own knowledge –Quick feedback is most effective. –Developing reflective judgment –Multiple representations

51. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Pedagogy Encourages both collaborative and independent learning: –Small group activities –Integrated laboratories –Projects –Learning cycles –Journal research –Visualization

52. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Integrated Laboratories

53. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Early Quantum Mechanics 1-D Waves –cf. classical waves on string –1-d Schrödinger—particle-in-a-box Spin & Quantum Measurement –Successive Stern-Gerlach Measurements Central Forces –cf. classical orbits –3-d Schrödinger—the hydrogen atom Energy & Entropy –Thermodynamics describes a quantum system

54. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Early Quantum Mechanics 1-D Waves –cf. classical waves on string –1-d Schrödinger—particle-in-a-box Spin & Quantum Measurement –Successive Stern-Gerlach Measurements Central Forces –cf. classical orbits –3-d Schrödinger—the hydrogen atom

55. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Early Quantum Mechanics Energy & Entropy –Thermal physics describes a quantum system Periodic systems –Introduction to solid state

56. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA ODE’s vs. PDE’s

57. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Central Forces Classical Orbits & Quantum Hydrogen Atom –Use reduced mass –ODE’s PDE’s (interpretation of QM) –Use spherical symmetry to simplify equations –Conserved—Angular momentum & Energy –Effective potential –Symmetric potential but asymmetric solutions

58. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Effective Potential

59. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Central Forces—Activities Students draw potentials for 2-d air table Interactive orbits in Maple Ring (1d) Sphere (2d) Hydrogen (3d) Use color for value of probability density Time dependent superpositions

60. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Eigenstates on the Ring

61. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Using Color to Visualize Spherical Harmonics

62. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Using Color..\OSU\mathphys\mathphys\paradigm6\flatylm.mws

63. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Constraints Diverse Student Interests –Industry-bound students –Interdisciplinary interests –Modern topics needed Timing Constraints –Coop program –Transfer students –GRE timing Fewer Credit Hours

64. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Logistics Fitting Traditional Schedule –Prefaces & Postscript –Three Week Classes Other Departments Scheduling The Administration

65. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Learning Cycles Interest Experience Analysis Experiment Overview

66. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Breaking Barriers Flexibility Communication Making It Work Active Engagement

67. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Communication Faculty Communicate Faculty Listen to Students Formative Evaluation

68. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Making It Work Registrar Use Resources as Allocated Rhythm Collaborative Solitaire Time More Innovation $

69. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 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

70. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 1-D Waves (Classical) Waves in electrical circuits, waves on ropes. (Quantum) Matter waves of quantum mechanics. (Math) Fourier analysis to begin the study of eigenstates.

71. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 1-D Waves Coax Cable: –Standing waves. –Traveling waves. –Wave packets. –Dispersion. –Energy. –Reflection. –Transmission. –Impedance.

72. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Spin & Quantum Measurement Uses sequential Stern-Gerlach experiments as a concrete context for exploring the postulates of quantum mechanics. Probability, eigenvalues, operators, measurement, state reduction, Dirac notation, matrix mechanics, time evolution, spin precession, spin resonance, neutrino oscillations, the EPR experiment. J. S. Townsend, A Modern Approach to Quantum Mechanics (McGraw-Hill, New York, 1992).

73. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Spin & Quantum Measurement Students infer wave function from “data.” Measurement based. D. V. Schroeder and T. A. Moore, "A computer-simulated Stern- Gerlach laboratory," Am. J. Phys. 61, 798-805 (1993).

74. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Central Forces (Classical) Orbits. (Quantum) Unperturbed hydrogen atom. (Math) Special functions.

75. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Energy & Entropy Wave functions for macroscopic systems are unknowable. A statistical entropy function is a unique, objective measure of bias (“fairness”). Probabilities can be calculated from a postulate of least bias (“maximum fairness”). The inferred probabilities are identical with Gibbs probabilities.

76. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Energy & Entropy Throw loaded and unloaded dice to calculate the fairness function. Maximum fairness method applied to a model polymer to deduce an equation of state deduced. Students apply the equation of state to predict outcome of heating a rubber band.

77. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Periodic Systems Coupled classical oscillators, Dispersion relations for 1,2,3 oscillator types, Phonons in a solid. Specific heats of a solid using various models. Schrödinger equation in a periodic potential. Band structure of the electron energy spectrum. Connection to molecular orbital theory. Other systems such as semiconductors.

78. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Two Messages I.Plan for a concept to build over time. New juxtapositions within a single Paradigm. Important concepts across several Paradigms.

79. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Two Messages I.Plan for a concept to build over time. New juxtapositions within a single Paradigm. Important concepts across several Paradigms.

80. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Central Forces

81. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA ODE’s vs. PDE’s

82. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 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

83. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Effective Potential

84. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Central Forces

85. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Two Messages I.Plan for a concept to build over time. New juxtapositions within a single Paradigm. Important concepts across several Paradigms.

86. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 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

87. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Two Messages I.Plan for a concept to build over time. II.Use an appropriate mixture of lecture and active engagement.

88. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Lecture vs. Activities 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.

89. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 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

90. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 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.

91. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 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.

92. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Eigenstates on the Ring

93. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Effective “Maple” Activities Transparent vs. black box. Interactive vs. demo. Oh… Ahhh…! Short vs. long. –Break up to force synthesis. One vs. several questions. –What is that extra dimension? –Pure states vs. superpositions. –Time evolution.

94. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Advice to Curriculum Developers The problem is often not what you think— listen to the students. PER does not yet tell you which problem to solve. Sometimes solving a small early problem solves lots of bigger later problems. Don’t be afraid of confusion in the classroom.

95. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Requests to the Audience Replacements for old CUPS software. (Mario Belloni—Physlets). Request for Adopters for: –Spin & Quantum Measurements –Energy & Entropy Request for Activities Testers for: –Symmetries & Idealizations –Static Vector Fields –Multi-variable & Vector Calculus

96. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Central Forces—Activities Students draw potentials for 2-d air table Interactive orbits in Maple Ring (1d) Sphere (2d) Hydrogen (3d) Use color for value of probability density Time dependent superpositions

97. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Planes

98. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Mathematics Physics Mathematics Physics

99. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Grand Canyon MathematicsPhysics

100. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Simple Curriculum Additions Equations describe the relationship of physical quantities to other physical quantities. Emphasize superposition of solutions to linear differential equations. Integrals involve chopping a part of space and adding up a physical quantity on each piece. “Limits” require one to say what dimensionless quantity is small.

101. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physics is about things What sort of a beast is it? Physics is independent of coordinates. Graphs are about the relationships of physical things. Fundamental physics is highly symmetric.

102. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physics is about things What sort of a beast is it? –Scalar vs. vectors –Individual vectors vs. fields –Units –Coordinate systems –Time. Physics is independent of coordinates. Graphs are about the relationships of physical things. Fundamental physics is highly symmetric.

103. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physics is about things What sort of a beast is it? Physics is independent of coordinates. –Vectors as arrows –Geometry of dot and cross products. Graphs are about the relationships of physical things. Fundamental physics is highly symmetric.

104. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physics is about things What sort of a beast is it? Physics is independent of coordinates. Graphs are about the relationships of physical things. –Fundamental physics is 3 dimensional. –Graphs of waves are misinterpreted. –3-d graphs of functions of 2-variables are misleading. –Hills are not a good example of functions of 2 variables. –Use of color. Fundamental physics is highly symmetric.

105. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physics is about things What sort of a beast is it? Physics is independent of coordinates. Graphs are about the relationships of physical things. Fundamental physics is highly symmetric. –Spheres and cylinders vs. parabolas. –Interesting physics problems can involve trivial math. –

106. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physicists can’t change the problem. Physics involves the creative synthesis of multiple ideas. Physics problems may not be well-defined math problems. Physics problems don’t fit templates. Physics involves the interplay of multiple representations.

107. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physicists can’t change the problem. Physics involves the creative synthesis of multiple ideas. Physics problems may not be well-defined math problems. –No preferred coordinates or independent variables. –No parameterization. –Unknowns don’t have names. –Getting to a well-defined math problem is part of the problem. –If you can’t add units, it’s a poor physics problem. Physics problems don’t fit templates.

108. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physicists can’t change the problem. Physics involves the creative synthesis of multiple ideas. Physics problems may not be well-defined math problems. Physics problems don’t fit templates. –Template problem-solving vs. skills. –A few key ideas are remembered best later. Physics involves the interplay of multiple representations.

109. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physicists can’t change the problem. Physics involves the creative synthesis of multiple ideas. Physics problems may not be well-defined math problems. Physics problems don’t fit templates. Physics involves the interplay of multiple representations. –Dot product. –Words, graphs, symbols

110. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Context Rich Problems Just as you turn onto the main avenue from a side street with a stop sign, a city bus going 30-mph passes you in the adjacent lane. You want to get ahead of the bus before the next stoplight which is two blocks away. Each block is 200-ft long and the side streets are 25-ft wide, while the main avenue is 60-ft wide. If you increase your speed at a rate of 5-mph each second, will you make it? (No Picture) Patricia Heller and Kenneth Heller, University of Minnesota

111. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Advice to Curriculum Developers The problem is often not what you think— listen to the students. Sometimes solving a small early problem solves lots of bigger later problems. Don’t be afraid of confusion in the classroom.

112. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Group Activities Task Master Keeps group on track: “What you had for lunch doesn’t seem relevant.” Cynic Questions everything: “Why?” “Why?” “Why?” Recorder Reporter

113. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA What Are Vectors? Mathematics: Triples of numbers Physics: Arrows in space

114. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Sample Group Activity Find the angle between a diagonal of a cube and an edge

115. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Group Activity Emphasizes that vectors are arrows Combines geometry and algebra Uses multiple representations geometry: algebra: memory:

116. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Relating Multiple Representations

117. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Importance of Interactive Classroom

118. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Collaborative Learning

119. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Importance of Interactive Classroom

120. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Student Quotes I can't believe I thought it was possible to succeed in this class without doing the labs! (This student chose not to do the labs, dropped out, then retook the course.) The concepts are simple and powerful. You just have to think. Excellent! Five stars for learning and head-scratching value. Studying in a group is so important. Learned how to do problems in more than one way. Took awhile, but started to make sense at the end. (All of it.) Smile. I just want to mention that this lab section has been very valuable to my understanding of the material. Although I initially felt it would be ``just another thing to get done'', I now see it to be a very beneficial component to this course. I was very surprised that I knew more than I thought. Surprised by how much we had to recall from last week. This is a good thing. What I want to know is... Why does it always seem so obvious after the fact? I learned that math was all interlinked. I can list a whole lot of methods and theorems that all use different ideas, but the math ends up all the same.

121. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Integrals

122. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Symmetry

123. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Ignoring Symmetry

124. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Mathematician’s Line Integrals Start with theory Do examples starting from next to last line –Need parameterization

125. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physicist’s Line Integrals Theory: –Chop up the line into little pieces. – Add up the components of parallel to (times the length of ). Do examples directly from –Need along the curve.

126. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Mathematics Example

127. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physics Example points in the direction of. is constant along the curve. Therefore,

128. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physics

129. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Bridging Project Differentials (Use what you know!) Exploiting multiple representations Symmetry (adapted bases, coordinates) Geometry (vectors, div, grad, curl) Computer visualization (Maple, Excel) Active engagement (groups, flashcards)

130. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Do You Do This?Or This?

131. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Goals Mathematics: Visualization Arbitrary surfaces 2-D is primary example Immediate sophistication Domain is important End point flexible Physics: Visualization Simple geometries only 3-D is primary example Many years later Surface is important End point fixed –Divergence theorem –Stokes’ theorem

132. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Student Problems Visualizing in 3-dimensions (new tools) Using algebra!! Understanding introductory calculus Doing trigonometry as triangles (increasing) Exploiting multiple representations

133. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Opportunities Beta testers are being sought to test materials: Vector Calculus (lower-division math) http://www.physics.oregonstate.edu/bridge  MathFest (8/12-14/04)  Summer Workshops (6/18-22/04 MA) (8/7-11/04 OR) Thermodynamics and Quantum Mechanics http://www.physics.oregonstate.edu/paradigms  Summer Workshop (6/25-28/04)  AAPT Workshop (1/05)

134. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA We have the best experimental facility in the world!

135. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Curriculum Reform The Paradigms Project PhysTEK

136. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Physics Education Research The Vector Calculus Bridge Project Making Connections

137. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Why Should You Do This?

138. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Two Curriculum Projects The implications of what we have learned for the structure of classical mechanics courses: Paradigms in Physics: complete reenvisioning of the upper-division major (more later). The Bridge Project: to bridge the vector calculus gap between mathematics and physics.

139. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Two Curriculum Projects The implications of what we have learned for the structure of E & M courses: Paradigms in Physics: complete reenvisioning of the upper-division major http://www.physics.oregonstate.edu/paradigms http://www.physics.oregonstate.edu/paradigms http://www.physics.oregonstate.edu/portfolios The Bridge Project: to bridge the vector calculus gap between mathematics and physics. http://www.physics.oregonstate.edu/bridge

140. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Mathematics Is Not About Things Students may not think of equations as telling about the relationships of physical quantities to other physical quantities. Traditional introductory courses do not teach this. This is a common “hidden curriculum” goal in upper-division classical mechanics.

141. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA What’s so important about units? Do you mean units, or dimensions? “What sort of a beast is it?” Generalized coordinates

142. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Geometry Are surfaces real? Imagine doing a flux integral over a hemisphere… What are Which example surface is more important— sphere or paraboloid? Other client fields are less geometric.

143. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Mathematician’s & Differentials Many calculus texts gloat about the fact that they have eliminated the differential from differential calculus. Definition of a differential, importance of limits.

144. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Use What You Know Line Integrals—mathematician’s always use parameterizations:

145. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA What is the electrostatic potential due to this point charge?

146. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Point Charge—Potential

147. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA What is the electrostatic potential due to this pair of point charges?

148. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Shifting/Superposition Superposition for solutions of linear differential equations:

149. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA What is the electrostatic potential due to this ring of charge?

150. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Idealization Make the students think about the source:

151. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Deconstruction

152. 4 October 2010 XIII SEMANA DE LA ENSENANZA DE LA FISICA Why so long? The professor’s “simple” solution involves lots of hidden resources. Our list: Like charges repel, unlike attract Attractions and repulsions are forces Forces can add and cancel (one does not “win”; one is not “blocked”) “Equilibrium” corresponds to balanced, opposing forces (not a single strong “holding” force) Electric force both increases with charge and decreases with distance from charge Objects respond to the forces they feel (not those they exert) Charges may be of indeterminate sign and still exert balancing forces on the test charge “Fixed” objects don’t give visible indication of forces acting on them; “free” ones do Only forces on the test charge require analysis Each other charge exerts one force on test charge Each force may be represented by a vector “Equilibrium” corresponds to opposing vectors Vertical and horizontal dimensions are separable One dimension is sufficient for analysis Electric force both increases with charge and decreases with distance from charge Electric force decreases with the square of the distance

153. 4 October 2010 XIII SEMANA DE LA ENSENANZA DE LA FISICA Reverse engineering expert knowledge In this case, I had failed to appreciate how much knowledge I had compiled into my “simple” solution. Watching these students helped me “reverse engineer” what I had built over many years into a tight, automatic knowledge structure. The students are not only solving the problem. They are compiling the knowledge required for the problem and are learning how to do problems in general.

154. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA What is the electrostatic field due to this ring of charge?

155. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Potentials or Fields Should students study the electric field first (conventional) or electrostatic potentials (Paradigms)?

156. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Cognitive Blending Putting together of two locally coherent mental spaces in a way that has elements not present in either one separately. Example: Complex Numbers –2-D vectors –Addition & multiplication of real numbers

157. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Spinning Ring Consider a very thin ring of charge with constant charge density, and total charge Q. The ring has radius R and is rotating about its axis with period T. For all groups: Create an integral expression for the vector potential caused by this ring everywhere in space. The expression should be complete enough to put into Maple or a similar mathematics package.

158. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Current Kinesthetic Knowledge Explicit Idealization

159. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Redish Cognitive Model 1.1. 2.2. 3.3. 4.4.

160. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA What are Functions?

161. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA After 1 Week S2:It’s been kind of frustrating actually. It’s a new way of looking at things. Especially because we’re used to just repeating whatever people tell us in class.... I learn that way pretty well. I’m not used to this way of learning yet. It’s so hard for me to understand what’s going on sometimes.

162. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 5 Weeks Later S2: I think I wouldn’t understand the material very well if I just had to read it in a book by myself, because I don’t get the interaction and I don’t get the projects and I wouldn’t get the correlation between the physics and the math. It just wouldn’t be there at all. And I think doing a bunch of different activities kind of makes you a more well rounded person as well. Because you can say, “Oh, well I can explain Gauss’s Law Like six different ways, let me show you the ways or something.” Because we’ve done stuff like that, like Gauss’s Law And Coulomb’s Law and all these different laws all together, I guess, and we’ve done them so many different ways.

163. 4 October 2010 XIII SEMANA DE LA ENSENANZA DE LA FISICA Expectations: Framing a situation An individual’s expectations activate what he/she pays attention to and what he/she ignores in response to the 10,000 things and their interactions – a selective filter. A college student has had many years of schooling and (thinks) he/she knows what to expect when he/she walks into a classroom. If the students’ expectations about what they are supposed to do fail to match the teacher’s expectations about what the student should do, both may be disappointed.

164. 4 October 2010 XIII SEMANA DE LA ENSENANZA DE LA FISICA Food in mouth: Eat Use hands Use knife and fork Select food Pay Menu on paper Menu on wall In a Restaurant:1

165. 4 October 2010 XIII SEMANA DE LA ENSENANZA DE LA FISICA Framing Framing is the process of  perceiving  interpreting  activating a particular set of long-term memories for dealing with a situation.

166. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Changing the Frame

167. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Star Trek S1: I think part of what was interesting. It was completely different than what you might be implicitly expecting about even regular group work might be like. So preconceptions about what class was going to be like, It was effective at probably shattering a lot of those. You don’t terribly often have your professor standing on the table role playing a fictional character for educational purposes. And I thought that was good as a way to sort of expand our expectations of what we might be doing at any given time. rather than just sort of sit here, take notes, then do something and then sit here some more.

168. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Experts vs. Novices Experts –Have a lot of knowledge –Have well structured knowledge –Plan their work –Choose strategies by “deep structure” –Frequently evaluate their progress Novices –Have less knowledge –Have weak knowledge organization –Just “go” without much planning –Choose strategies by “surface structure” –Rarely evaluate their work

169. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Long-term Memory Long-term memory is not well indexed.

170. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Chunking & Compiling When we are learning new things, they each appear in our memory as separate facts. This makes the load on working memory extremely high. What happens when the buffer gets full? Chunking/compiling.

171. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Dot Products

172. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Concept Maps

173. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Summarizing

174. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 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?

175. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Future Instructor:…How do you imagine your future careers to be? S2:Kind of like this class, I think, is what I imagine my future career to be if it’s research or something Because you’re not given a set homework or list of things to do And honestly this class probably prepares me a lot more for my job than a rote memory, like a strictly lecture type of class because my life is not going to be a lecture and my like work I take home with me is not going to be homework In strictly the sense that you pull it out of a book to get the answer (?) Let’s turn to page 675, here the answer really is It’s like you’re exploring things And you’re trying to find the answer using whatever method you have And if that method is like “oh I’ll use angle (?) to find like whatever the graph is supposed to be like” and “Oh we have to take it out to the 100th term to see like “Oh it really does (?) this graph” and that’s just the way it’s going to be.

176. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Take-home Messages? What have you learned? What will you try? Do we need to teach this way all the time? How can you take advantage of the new student frame?

177. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA S2:I think it helps if there is like a lecture first to tell us what we’re supposed to figure out. Because for me the most frustrating thing in school, especially in high school and in elementary school, is like when they’re “explore and figure this out” and I like can’t figure it out if you don’t... tell me what I’m trying to find... I get so frustrated and it’s just the same thing. Like if I just had guidance into the thing we’re trying to find.... I think some sort of lecture in the beginning, like a really quick, little like “this is what we’re trying to find, now explore it yourself, try to find it yourself, using whatever various methods we’re using today” that might help me personally a little more.

178. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA S2:I’m the opposite. Like difficult homework problems, they frustrate me.... Seriously, if I’m told how to do something, that’s like it, then I can equate to what I’m trying to do on my homework later It’s just easier that way, especially in (class), with like (Professor) Like he’d tell us in class, oh you do it this way. And then there’d be like 15 homework problems on it. It’s just easier for me to remember, it’s like rote memory.

179. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Len:What is it about dealing with that wrong way of doing things that you find valuable? S1:I’m not sure how to articulate other than that generally having made a mistake, especially a mistake where it leaves me to feel stupid about it afterwards I tend to remember not to do that better than I’m going to remember to do something that worked Because if it worked, then I don’t have to think about it very much because it wasn’t that hard, If I do it wrong, I actually have to think about it and put more effort into it And hopefully I’ll remember because I put more thought into what I was doing

180. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA EVZ And suppose that happened to you on a homework problem rather than in class… S1:It was good to do it in class because we were able to get nudged in the right direction so we actually did eventually succeed On the homework problem, it would have been more likely that I would have just run into a wall and not been able to get all the way to the right solution if it was too different from what I was trying to do If I had been able to figure it out and finally get to the end it probably would have been equally effective but there’s a good chance that I would have gotten stuck and given up at some point which would not have been effective at all.

181. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Things to Try Black box visualization—Talks Here Metacognition—Summaries, Concept Maps Collaborative Activities—Ring Kinesthetic—Densities & Currents Maple/ Mathematics Visualization—Flux They construct visualization—Electrostatic Potentials Multiple Representations—Plane Waves Compare & Contrast Summaries—Gauss & Ampere Repetition—Boundary Conditions Small White Boards—Everywhere!

182. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA

183. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA

184. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Four Key Ideas 1.Resources 2.Association / Activation 3.Compilation / Binding 4.Control / Selective Attention

185. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Spinning Ring - Limits Approximate this vector potential near the center of the ring, in the plane of the ring. Approximate this vector potential near the center of the ring, along the z-axis. Approximate this vector potential far from the ring, in the plane of the ring. Approximate this vector potential far from the ring, along the z-axis.

186. 4 October 2010 XIII SEMANA DE LA ENSENANZA DE LA FISICA An example The pair of coupled ODEs are referred to as the Lotka-Volterra equations and are supposed to represent the evolution of the populations of a predator and its prey as a function of time.  Which of the variables, x or y, represents the predator?  Which represents the prey?  What reasons do you have for your choice?  What’s left out of this model?

187. 4 October 2010 XIII SEMANA DE LA ENSENANZA DE LA FISICA A New Research Project Learning the Language of Science: Advanced Math for Concrete Thinkers 4 year NSF supported project (DTS program) (2005-2009) In this project we are observing physics majors working on problems in upper division physics courses. We hope to develop a better understanding of student difficulties and to provide guidance to create new materials to help overcome them.

188. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Motto My Agenda Is Irrelevant If I Can’t Take The Students With Me

189. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Active Engagement Colloquium How did your frame change over the course of the colloquium? –How was this accomplished ? –Were you comfortable? Uncomfortable? When? –Was the frame appropriate for the goals? Did you feel engaged? –Did this aid your learning? What have you learned? –Are there techniques you want to use in your class? –Why? Is the context appropriate? –How would your establish an appropriate frame 7. –What are your goals? –Do we need to use active engagement in every class? –Hidden curriculum goals?

190. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA

191. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Challenges Understanding Fields Field vectors vs. field lines vs. line integral convolution Understanding 3-D Visualization Describing Spatial Dependence Curvilinear Coordinates Equation interpretation Densities Adding Vectors Integration as Chopping & Adding Limiting Cases Gauss & Ampère –Symmetries –Imaginary Surfaces & Loops

192. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Thinking About Curriculum Content Matters Transitions Matters Metacognition Matters Pedagogy Matters

193. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Content Matters What we teach? What do we leave out? Do we teach concepts, facts, problem- solving, …? What order do we teach it in? How do the pieces contribute to our overall goals?

194. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Order/Repetition (Syllabi) Power Series Approximations using power series Potentials for E & g Position Vector Dot Products Superposition of Discrete Sources Visualizing Potentials Curvilinear coordinates Cross & Triple Products Total Charge Idealization: Edges Idealization: Infinite Thinness Superposition of Continuous Sources Quantifying Change E & g Fields Back to Potentials Curl & Conservative Fields Flux Gauss's Law and Symmetry Divergence Maxwell's Equations 1 Energy & Conductors Boundary Conditions for E Product Rules & Second Derivatives Griffiths Triangle Currents B Vector Potentials B Fields Biot-Savart Law B Fields Ampère's Law and Symmetry Maxwell's Eqns 2, 3, 4 Griffiths Triangle Boundary Conditions for B

195. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Transitions Matter From subdiscipline to subdiscipline From concept to concept From novice to expert From mathematics to physics From one representation to another From easier to harder

196. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Pedagogy Matters Computer Simulations –Many talks here Projects –Wave Guides Collaborative Activities –Ring Repetition –Boundary Conditions Compare & Contrast Summaries –Gauss & Ampere Maple/ Mathematica Visualization –Flux They construct visualization –Electrostatic Potentials Multiple Representations –Plane Waves Small White Boards –Dot products Kinesthetic –Densities & Currents –Curvilinear basis vectors

197. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Flux Maple Worksheet Initially, define the location of the point charge to be at the origin of a rectangular coordinate system: > Point:=[0,0,0]; > a:=Point[1];b:=Point[2];c:=Point[3]; Find the electric field of the point charge: > r:=sqrt((x-a)^2+(y-b)^2+(z-c)^2); > Efield:=(q/(4*Pi*epsilon))*grad(-1/r,[x,y,z]);

198. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Flux Maple Worksheet

199. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Equipotential Surfaces Draw the equipotential surfaces for each of the following static charge configurations: Four positive charges arranged in a square. Two positive charges and two negative charges arranged in a square, with like charges diagonally opposite each other. A line segment with constant charge density. A flat, circular ring with constant charge density.

200. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Plane Wave Activity Students connect points with equal value of What is

201. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Plane Wave Representations

202. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Multiple Representations Write on your small white board something about dot products.

203. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Steady Current

204. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Curvilinear Basis Vectors

205. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Metacognition Matters How do you know that you know something? Why am I doing this to you? What are the facets of problem-solving? How far have you come? How do you organize the content in your head?

206. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Summarizing

207. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Concept Maps

208. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA

209. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Things to Try Black box visualization—Talks Here Metacognition—Summaries, Concept Maps Collaborative Activities—Ring Kinesthetic—Densities & Currents Maple/ Mathematics Visualization—Flux They construct visualization—Electrostatic Potentials Multiple Representations—Plane Waves Compare & Contrast Summaries—Gauss & Ampere Repetition—Boundary Conditions Small White Boards—Everywhere!

210. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Interactive Engagement vs. Traditional Lecture FCI scores from N = 6542 students from 60 intro physics courses. Hake, AJP 1992

211. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Food in mouth: Eat Use hands Use knife and fork Select food Pay Menu on paper Menu on wall In a Restaurant:1

212. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Changing the Frame

213. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Hidden Curriculum —Lecture vs. Activities 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.

214. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 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?

215. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Large-enrollment Classrooms

216. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA 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

217. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Voting What are the three most important sources of energy for the United States currently?

218. 4 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Large Whiteboards Provide the opportunity: –to compare and contrast answers, –for mini-presentations, –to discuss problem-solving strategies, synthesis, evaluation, decision-making, etc.