Presentation on theme: "TEAL at MIT: Teaching Pedagogy ISTITUTO "E.Fermi” Cristina Bonaglia Dirigente Scolastico Feb 18, 2015 Dr. Peter Dourmashkin Physics Department MIT"— Presentation transcript:
TEAL at MIT: Teaching Pedagogy ISTITUTO "E.Fermi” Cristina Bonaglia Dirigente Scolastico Feb 18, 2015 Dr. Peter Dourmashkin Physics Department MIT email@example.com
MIT Experiment in Active Learning (Technology Enabled Active Learning) TEAL Fourteen Year Ongoing Experiment at MIT: A merger of presentations, tutorials, and hands-on laboratory experience into a technologically and collaboratively rich environment
(Some) Elements of Active Learning How can you encourage student participation in class? 1.Peer Instruction and Concept Tests 2.Group Problem Solving 3.Discovery Activities 4.Discussion Questions 1.Simulations and Visualizations
ConcepTests / Peer Instruction Model: Eric Mazur’s Peer Instruction based on ConcepTests using “Clicker” Technology Methodology: Concept Test Thinking Individual answer Feedback: Just in Time Teaching Peer discussion Revised group answer Explanation
Concept Question: Contact Force Consider a person standing in an elevator that is accelerating upward. The magnitude of the upward contact force on the person is 1.greater than 2.equal to 3.less than the magnitude of the downward force of gravity on the person.
Concept Q.: Contact Force Ans. Answer 1. System: person. The contact force, N, on the person due to the interaction between the person’s feet and the elevator is greater than the gravitational force, mg, on the person due to the interaction between the Earth and the person because the contact force must also accelerate the person, as well as oppose the gravitational force. Thus N – mg = ma implies that N > mg. So the magnitude of the upward contact force is greater than the magnitude of the downward gravitational force. Acceleration diagram Force diagram
Students work in small teams at the white boards solving problems with instructor feedback Problem Solving
Expert Problem Solving MIT students will solve approximately 10,000 problems in four years Students learn to become expert problem solvers through practice Develop confidence based on experience Necessary for innovation and creative thinking Problem solving requires factual and procedural knowledge, knowledge of numerous schema, plus skill in overall problem solving.
Beginner Problem Solvers Unable to represent physical concepts Unable to combine multiple ideas Unable to apply mathematical reasoning Engage in symbol manipulation Unable to estimate and make ‘back of the envelope’ calculations
Pólya: How to Solve it! 1.Getting Started – identify assumptions and givens, identify what information is needed and what should be neglected 2.Plan the Approach – articulate a strategy that may involve multiple concepts and problem solving methodologies, 3.Carry out the plan – use multiple types of representations, equations, graphs, visualizations 4.Reflection and Modification: Ability to modify plan in a constructive manner. 5.Review - does the answer make sense? Reflect on the limits of the model.
At the start, teachers can give some guidance During problem solving teachers circulate and give guidance At the end of the problem solving, teachers provide closure Enabling Problem Solving
Circular Motion: Force Diagram Newton’s Second Law becomes System: satellite
Group Problem: Circular Motion A racing car is rounding a turn. Draw a free-body diagram showing all the forces you think are acting on the car. Estimate the magnitude of the acceleration of the car. What is the direction of the acceleration?
Momentum Diagrams 1) Identify all objects in system. 2) Choose a reference frame. 3) Draw a momentum diagram for i)state of the system before interaction ii)state of system after collision. Diagram should include 1.Choice of unit vectors 2.Show each mass element. Show the speed and arrow for direction of velocity of each mass element.
Momentum Principle: Integral Version Momentum Principle: equate two sides (vector equality)
Group Problem: Heading Estimate the acceleration of the head due to the heading of a soccer ball. Could this cause brain injury? In your groups: discuss what models and concepts may apply. What information is needed and what can be neglected?
24 Collision Theory https://www.youtube.com/watch?feature=player_embedded&x-yt- ts=1421914688&x-yt-cl=84503534&v=WGTBJHFNywI
Collision Theory: Energy Types of Collisions Elastic: Inelastic: Completely Inelastic: Only one body emerges. Superelastic:
Suppose you are on a cart, initially at rest on a frictionless track. You throw balls at a partition that is rigidly mounted on the cart. After the balls bounce straight back as shown in the figure, is the cart 1. moving to the right? 2. moving to the left? 3. at rest. Concept Question: Recoil
Answer: 2. Because there are no horizontal external forces acting on the system, the momentum of the cart, person and balls must be constant. All the balls bounce back to the right, then in order to keep the momentum constant, the cart must move forward. Concept Question: Collision
Consider two moving objects with velocities in a reference frame fixed to the ground The relative velocity of object 1 with respect to object 2 is defined to be Relative Velocity
Relative Velocity: Elastic Collision Energy/Momentum Law Equation (3): Components of relative velocities: Energy/Momentum Law: x-component of initial relative velocity is equal to the negative of the x-component of the final relative velocity
Demo and Worked Example: Two Ball Bounce A football and tennis ball are dropped from a height h above the ground. The tennis ball on top has mass M 1. The football on the bottom has mass M 2. Assume that the football collides elastically with the ground. Then as the football starts to move upward, it collides elastically with the tennis ball that is still moving downwards. How high will the tennis ball rebound in the air? Assume that M 2 >> M 1. Try this out. Be careful and have fun! M 2 >>M 1
Hands-on: Two Ball Bounce Collision of interest is between the falling tennis ball (labeled 1 in the figure) and the rising football (2) immediately after the football reverses direction due to an elastic collision with the ground. Key model assumption: change in speed of football due to collision is negligible.
Two Ball Bounce Initial velocities: Final velocities: Relative velocities: Energy/Momentum Law: Algebra. Solve Eq. (1) for speed of light ball after collision. Light ball has three times its original speed. Choose positive y-direction upwards.
Two Ball Bounce Energy law for falling: Energy law for rising: Energy and Momentum Law Ratio of heights. Light ball rebounds nine times as high as it fell.
Energy Diagrams Identify system Identify interaction Identify state of system before interaction (initial state) and state of system after interaction (final state) Draw energy diagrams for these states including: 1) Choice of zero point P for potential energy for each interaction in which potential energy difference is well-defined. 2) Draw speed of all objects in system 3) Identify initial and final mechanical energy
Energy Principle Energy Principle: Equate two sides
To every action there is always opposed an equal reaction: or, the mutual action of two bodies upon each other are always equal, and directed to contrary parts. Action-reaction pair of forces cannot act on same body; they act on different bodies.
Concept Question: Interaction Pair A large truck collides head-on with a small car. During the collision 1.the truck exerts a greater force on the car than the car exerts on the truck. 2.the car exerts a greater force on the truck than the truck exerts on the car. 3.the truck exerts the same force on the car as the car exerts on the truck. 4.the truck exerts a force on the car but the car does not exert a force on the truck.
Con. Q. Ans.: Interaction Pair Answer 3. The car and the truck form an interaction pair. By Newton’s Third Law the collision forces on each object have equal magnitude but point in opposite directions.
Group Activity: String Theory Divide up into pairs. Each pair pull on the opposite ends of the provided string.
Group Activity: String Theory 1.Draw three force diagrams on the boards, one for person A, one for person B, and one for the rope. 2.On each diagram draw all the forces acting on the object in your diagram. 3.Identify the action-reaction pairs of forces.
Tug of War Force Diagrams For the rope we have neglected the gravitational force because we are assuming the rope is very light
Torque Diagram 1.Identify System 2.Draw free body diagram. For each force F place the arrow representing the force at the point where the force acts on the rigid body. 3.Identify rotational coordinate system. Choose rotational angle θ and draw curved arrow to represent direction in which angle θ is increasing. 4.Use right hand rule with respect to this direction, to indicate positive direction for angular acceleration. 5.Select point S about which you are calculating torque and draw it on the free-body force diagram. 6.For each force, draw the vector from the point S to where the force F acts.
Experiment: Moment of Inertia of Bicycle Wheel 1. Wrap a string around the rim of a bicycle wheel of radius R = 20 cm and pass it through the valve hole and attach it to a spoke. 2. Attach a weight of mass m = 50 g to the end of the string. 3. Drop the weight from a measured height h f above the ground and allow it to hit the ground. Measure the time, t f, it takes to hit the ground. 4. From these measurement we shall determine the moment of inertia of the wheel about the axle.