17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA ENSEÑANDO A LOS ESTUDIANTES A PENSAR COMO FÍSICOS Tevian Dray & Corinne Manogue

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA TEACHING STUDENTS TO THINK LIKE PHYSICISTS Tevian Dray & Corinne Manogue

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17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Support National Science Foundation (DUE) – , , , – , , Oregon State University Oregon Collaborative for Excellence in the Preparation of Teachers Grinnell College Mount Holyoke College Utah State University

17 mayo 2011V CONGRESO NACIONAL DE 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

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA A Question for the Audience

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA A: B:

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Mathematics vs. Physics Math: Physics: Two disciplines separated by a common language!

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Mathematics vs. Physics Mathematicians teach students to be precise => pay attention to language (good) => be afraid (bad) Physicists teach students to solve problems they’ve never seen before => must coordinate many strategies => jump in even if you can’t see the end

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Physics is about things Teach geometric reasoning. Main Message #1

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Visualization—Table

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Visualization—Level Curves

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Visualization—Graph

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Curvilinear Coordinates

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Curvilinear Basis Vectors Imagine you are on a ________. Close your eyes and point in the direction of increasing ___.

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Curvilinear Basis Vectors

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Look for a unifying idea that allows students to see the coherence of the subject. Main Message #2

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA The Vector Differential

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA The Vector Differential

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA The Vector Differential One idea — all of vector calculus!

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA The Geometry of Change

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA The Master Formula where

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA The Hill Imagine you are standing on this hill. Close your eyes and point in the direction of the gradient where you are standing.

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Visualization—Gradient

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Main Message #3 Plan for a concept to build over time. Vibrant juxtapositions within a single class. Important concepts across several classes.

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Cross Product Think of something you know about the cross product.

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Cross Product

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Area Elements Find the area elements on the surface of a cylinder.

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Area Elements On top:On side:

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Main Message #4 Understand ALL the different skills that students need to solve a problem. Help them break a complex problem into smaller pieces.

17 mayo 2011V CONGRESO NACIONAL DE 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.

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Potential Due to Charged Disk What is the electrostatic potential at a point, on axis, above a uniformly charged disk?

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA One Physics Concept Coulomb’s Law:

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Superposition Superposition for solutions of linear differential equations:

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Chopping and Adding Integrals involve chopping up a part of space and adding up a physical quantity on each piece.

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Computational Skill Can the students set-up and do the integral?

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Constants vs. Variables Which of these symbols are constants and which are variables?

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Limits (Far Away)

Active Engagement

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Small Whiteboard Questions

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Large-enrollment Classrooms

17 mayo 2011V CONGRESO NACIONAL DE 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.

17 mayo 2011V CONGRESO NACIONAL DE ENSENANZA DE LA FISICA Lecture vs. Activities Rule of thumb: –If the can get it from lecture—then lecture!! –If they can’t get it from lecture—then make them fall in the trap when you are there to help them out.

17 mayo 2011V CONGRESO NACIONAL DE 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

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