Workshop for Instructors: Learning to Think About Gravity Concepts of Gravity from Aristotle to Einstein Proving and Disproving Newton Esther Zirbel Claudine Kavanagh Tufts University

Outline Goals for Students and for Workshop Participants Your Interpretations of Motions Abbreviated Power Point Presentation for Students Proving Newton’s Theory – Historical Approach Basics of Einstein – Principle of Equivalence Contrasting Newton to Einstein What do you think Students know? Filling out the A/N/E Matrix Discussion of results of the A/N/E Matrix Further Discussion Questions

1a) Objectives for this Workshop How to teach about gravity to your students? How to make students transition from Aristotelian to Newtonian and Newtonian to Einsteinian Thinking Should all Theories of Gravity be taught, compared, and contrasted? Why/why not? How can the notion of competing explanatory models deepen students’ understanding of the nature of scientific inquiry?

1b) Student’s Goal of this Class Elicit your own Ideas about Gravity Confront you with your own Understanding of Gravity! Learn Scientific Methodology Differentiate between Empirical Models and Theories Discover how Discoveries are made Learn two different Theories of Gravity Which Theory should you chose? When? Why?

2) Motions in the Universe Your interpretations How – Orbits: How and why does the Moon orbit the Earth? How – Free Fall: How and why does the apple fall off the tree? What? What is the nature of Gravity?

3) Power Point Presentation for Students Historical Constructivist Approach “Students not only learn how to justify modern scientific theories, but also how and why older theories were rejected, and how the nature of scientific inquiry changed within the discipline when the scientific community shifted from the old to the new paradigm” Elicit Students to Think Critically Let Students decide which Theory to “Believe” Students get a Flavor of HOW Science is done

Class For details please see attached power point presentation for students. After talking about class continue with workshop…

4) What concepts are children exposed to naturally in the modern day? Space-Time travel? Black Holes? Worm Holes? What is science fact and what is science fiction? Newton? Einstein? Discussion 1

A/N/E Matrix How and why does the apple fall off the tree? How and why does the Earth go around the Sun? How and why of projectile motion?  optional Provide an explanation using Aristotle’s Theory Newtonian Theory of Gravity Einstein’s General Theory of Relativity

Please fill out the A/N/E Matrix What are the Fundamentals of Aristotle’s, Newton’s and Einstein’s Theories of Gravity? What are students’ common, pre-instructional conceptions of gravity? Literature review By Kavanagh & Sneider

Aristotle/Newton/Einstein Matrix Orbits Free Fall Projectile Motion

Sharing of Matrix Results Discussion 2 Sharing of Matrix Results Discussion of leading questions What are the Fundamentals of Aristotle’s, Newton’s and Einstein’s Theories of Gravity? What are students’ common, pre-instructional conceptions of gravity? Are these theories contradictive? How do Aristotle and Einstein compare? How is Newtonian Gravity different?

How & why does Earth orbit Sun? Aristotle: The natural movement of the celestial bodies is circular rather than a movement toward the center of the earth – free motion No Force Newton: The Sun creates a gravitational field that exerts a force upon the Earth, which, in turn, causes it to orbit around the Sun rather than move in a straight line. (Revised Newtonian: N-body problems and motion around the Center of Mass) Gravity is a Force Einstein: The Mass-Energy Distribution of the Sun changes the geometry of space-time. The Earth is in free motion (no forces acting on it!) and travels on a geodesic of space-time. But because space-time is curved around the Sun, the Earth orbits the Sun.

Discussion 3 Open Science Questions What is a force? What is the nature of gravity? What is “free motion” in orbits? Newton’s first law but applied to orbits? Which theory makes the best predictions? Under which conditions? Scale Arguments? Is there a transition between Newton & Einstein? Or are they totally exclusive theories? A problem: Deriving Einstein’s equations using Newton

Discussion 4 Why don’t we teach more Einstein in classrooms, knowing that Newtonian theory has been surpassed? Aristotle: ~380-320 BC Newton: 1678 / 1728 Einstein: 1905 (published) Today: 2007 schools are (still!) teaching 300 yr old theory

Newton versus Einstein Which theory is more intuitive? Is the transition from Aristotle to Einstein more intuitive than the transition from Aristotle to Newton? Which theory is more abstract? Einstein’s theory is pretty abstract, but so is Newton’s Theory of Gravity – which student has actually “seen” two objects attract each other? Which theory is more difficult? The basics of each theory are equally difficult

Open questions for teachers If students have heard about Einstein, why don’t we teach Einstein earlier? (HS/undergrads)? Near universal recognition “Easy fit” with pre-instructional ideas? (Caution…) Newton got us to the Moon Einstein will get us to the Stars

Discussion 5 What and how to teach gravity to your students? Should all Theories of Gravity be taught, compared, and contrasted? How can the notion of competing explanatory models deepen students’ understanding of the nature of scientific inquiry? How can students learn to distinguish between science fiction and science fact? Newton = Fact Einstein = Fiction