6/22/2016New Faculty Workshop Interactive Engagement in Upper-Level Physics Lessons from the Paradigms Program Corinne Manogue & the whole Paradigms Team

6/22/2016New Faculty Workshop Support National Science Foundation –DUE , , –DUE , , –DUE , , Oregon State University Oregon Collaborative for Excellence in the Preparation of Teachers Grinnell College Mount Holyoke College Utah State University

The Upper-Division On your small whiteboard give one way that the upper-division is different from the lower division. 6/22/2016New Faculty Workshop

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. 6/22/2016New Faculty Workshop

6/24/2014New Faculty Workshop Novice Expert Moving away from templates Using advanced notation Breaking-up complicated problems Harmonic reasoning Problem-solving confidence Using Reflective Judgment

4/27/2012Seoul 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?

My Agenda Today Discuss a few “teaching principles” and related “teaching suggestions.” Model and discuss different types of activities. 6/22/2016New Faculty Workshop

Teaching Principle Students are smarter than you think, but know far less. 6/22/2016New Faculty Workshop Suggestions 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.

6/22/2016New Faculty Workshop The Vertical Axis: Quantum Particle on a Ring

6/22/2016New Faculty Workshop The Radial Axis: Quantum Rigid Rotor

6/22/2016New Faculty Workshop Hydrogen Atom

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. 6/22/2016New Faculty Workshop

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 6/22/2016New Faculty Workshop Suggestion Use activities that require students to go back and forth between multiple representations.

6/22/2016New Faculty Workshop Multiple Representations

6/22/2016New Faculty Workshop KetFunctionMatrix Hamil- tonian Eigen- state Coeff- icient

Teaching Principle Students have little experience with geometric visualization. 6/22/2016New Faculty Workshop Suggestion Use kinesthetic activities to tap into students’ embodied cognition.

Kinesthetic Activities Stand up. Each of you represents a point charge. Make a linear charge density. 6/22/2016New Faculty Workshop

4/27/2012Seoul National University Two Messages I.Plan for a concept to build over time. New juxtapositions within a single Paradigm. Important concepts across several Paradigms.

4/27/2012Seoul National University Central Forces

4/27/2012Seoul National University ODE’s vs. PDE’s

4/27/2012Seoul National University 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

4/27/2012Seoul National University Effective Potential

6/24/2014New Faculty Workshop Teaching Principle Plan for a concept to build over time. New juxtapositions within a single course. Important concepts across several courses.

6/24/2014New Faculty Workshop 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

6/24/2014New Faculty Workshop 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.

Eigenvector Definition An eigenvector is a vector whose direction is not changed by the transformation. 6/24/2014New Faculty Workshop

6/24/2014New Faculty Workshop Eigenstates on the Ring

6/24/2014New Faculty Workshop 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

Teaching Principle It takes effort to bring information into working memory. 6/22/2016New Faculty Workshop Suggestion Use small whiteboards to help students activate the relevant information.

Small Whiteboards On your small whiteboard, write something you know about the dot product. 6/22/2016New Faculty Workshop

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. 6/22/2016New Faculty Workshop

6/22/2016New Faculty Workshop 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.

Teaching Principle Don’t try to answer a question that students don’t yet have. 6/22/2016New Faculty Workshop Suggestion Use active engagement to prime “the teachable moment.”

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 Compare and Contrast Activities 6/22/2016New Faculty Workshop

6/22/2016New Faculty Workshop 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.

6/22/2016New Faculty Workshop 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.

4/27/2012Seoul National University Plane Wave Representations

6/24/2014New Faculty Workshop 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.

6/22/2016New Faculty Workshop 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.

6/22/2016New Faculty Workshop Potential Due to Charged Disk What is the electrostatic potential at a point, on axis, above a uniformly charged disk?

6/22/2016New Faculty Workshop One Physics Concept Coulomb’s Law:

6/22/2016New Faculty Workshop Superposition Superposition for solutions of linear differential equations:

6/22/2016New Faculty Workshop Chopping and Adding Integrals involve chopping up a part of space and adding up a physical quantity on each piece.

6/22/2016New Faculty Workshop Computational Skill Can the students set-up and do the integral?

6/22/2016New Faculty Workshop Limits (Far Away)

6/22/2016New Faculty Workshop Constants vs. Variables Which of these symbols are constants and which are variables?

6/24/2014New Faculty Workshop 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

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? 6/24/2014New Faculty Workshop

4/27/2012Seoul National University 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

4/27/2012Seoul National University 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.

6/22/2016New Faculty Workshop Socratic vs. Groups How does it feel to teach in these ways? vs. Everyone knows everything vs. No one knows anything

6/22/2016New Faculty Workshop 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)