UpperLevel Curriculum Lessons from the Paradigms Program http

Upper-Level Curriculum Lessons from the Paradigms Program http: //physics. oregonstate. edu/portfolioswiki Corinne Manogue & the whole Paradigms Team 11/19/2016 New Faculty Workshop

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 11/19/2016 New Faculty Workshop

Top Down/Bottom Up On your small whiteboard: • What is the purpose of education? 11/19/2016 New Faculty Workshop

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. 11/19/2016 New Faculty Workshop

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 11/19/2016 New Faculty Workshop

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. 11/19/2016 New Faculty Workshop

Reflective Judgment “…the ability to understand the nature of illstructured 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 11/19/2016 New Faculty Workshop

Reflective Judgment/Sensemaking • • • order of magnitude? dimensions? type of “beast”? limiting cases? symmetry? time dependence? 11/19/2016 • 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

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? 11/19/2016 New Faculty Workshop

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? 11/19/2016 New Faculty Workshop

On your small whiteboard • List one characteristic of middle-division students? 11/19/2016 New Faculty Workshop

Novice Expert —Problem-Solving • Moving away from templates • Using advanced notation • Breaking-up complicated problems • Harmonic reasoning 11/19/2016 • Problem-solving confidence • Using Reflective Judgment New Faculty Workshop

Novice to Expert • How do I use this method to solve problems? • How do I get from this step to this step? 4/27/2012 • How will I know if this will work? • What else can I do if this won’t work? Seoul National University

My Agenda Today • Discuss a few “teaching principles” and related “teaching suggestions. ” • Model and discuss different types of activities. 11/19/2016 New Faculty Workshop

Teaching Principles • It is your responsibility to ensure that everyone is comfortable in your class. • It takes courage to be publically wrong. 11/19/2016 New Faculty Workshop

Suggestions to Build Community • Multiple faces of diversity • Vivid examples – Picking up someone else’s baby. • Storytelling – Falling asleep. – Being brave. 11/19/2016 New Faculty Workshop

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 11/19/2016 New Faculty Workshop

PER Result • Most students know triangle trigonometry • But not circle trigonometry 11/19/2016 New Faculty Workshop

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 11/19/2016 New Faculty Workshop

Spin 1/2 Systems • Choose a partner. • Together, show the quantum spin ½ state 11/19/2016 New Faculty Workshop

Spin 1/2 Systems • Show the states that are physically equivalent to this state. 11/19/2016 New Faculty Workshop

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. 11/19/2016 New Faculty Workshop

Multiple Representations 11/19/2016 New Faculty Workshop

Ket Function Hamiltonian Eigenstate Coefficient 11/19/2016 New Faculty Workshop Matrix

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. 11/19/2016 New 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. 11/19/2016 New Faculty Workshop

Potential Due to Charged Disk What is the electrostatic potential at a point, on axis, above a uniformly charged disk? 11/19/2016 New Faculty Workshop

One Physics Concept • Coulomb’s Law: 11/19/2016 New Faculty Workshop

Superposition • Superposition for solutions of linear differential equations: 11/19/2016 New Faculty Workshop

Chopping and Adding Integrals involve chopping up a part of space and adding up a physical quantity on each piece. 11/19/2016 New Faculty Workshop

Computational Skill • Can the students set-up and do the integral? 11/19/2016 New Faculty Workshop

Limits (Far Away) 11/19/2016 New Faculty Workshop

Constants vs. Variables • Which of these symbols are constants and which are variables? 11/19/2016 New Faculty Workshop

Teaching Principle • Plan for a concept to build over time. • • 11/19/2016 New juxtapositions within a single course. Important concepts across several courses. New 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) • Periodic Systems – Band Structure 11/19/2016 New Faculty Workshop Hydrogen (3 -D)

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 11/19/2016 New 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. 11/19/2016 New Faculty Workshop

Eigenvector Definition • An eigenvector is a vector whose direction is not changed by the transformation. 11/19/2016 New Faculty Workshop

Eigenstates on the Ring 11/19/2016 New Faculty Workshop

Socratic vs. Groups How does it feel to teach in these ways? vs. Everyone knows everything 11/19/2016 vs. New Faculty Workshop No one knows anything

We Can Help! • We have developed lots of materials: contact us and check out our wiki and Com. PADRE. physics. oregonstate. edu/portfolioswiki • Try our new online text: physics. oregonstate. edu/Bridge. Book • And published texts: Mc. Intyre (QM), Dray (SR) 11/19/2016 New Faculty Workshop

physics. oregonstate. edu/portfolioswiki 11/19/2016 New Faculty Workshop

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. 11/19/2016 New Faculty Workshop