My active teaching at The Engineering School has mostly followed a modified "Socratic dialogue" method -- short discussion periods interspersed with active writing, experimentation, and small group discussion. TES also seeks to integrate engineering design considerations into all classes, so every instructional unit was capped by a design project.

To illustrate the style of my teaching, I have included below a sample lesson script for a lesson on Momentum from early in the year. Each numbered point represents a question or prompt that I gave the students, or an activitity that they were asked to do. The comments following each number represent some of the expected responses from the students, the correct answers, or discussion of the subtleties.

Goals:

To introduce the numeric quantity "Momentum", which is equal to the product of mass and velocity

To use the concept of momentum to explain how a rocket moves in space

Script:

1. Q: How do rockets move in space?

Their answer will be: They push against something.

2. Q: But there’s no air up there – there’s nothing to push against…

They will be stumped.

3. Q: What’s Newton’s Second Law?

F = ma -- the sum of the external forces on an object equals mass*acceleration, they know this one already.

4. Q: What is a ?

a = acceleration = Rate of change of (velocity)

so F = m * Rate of change (velocity)

or F = Rate of change (mass * velocity)

5. So if F = 0, the rate of change of (MV) is 0 ---- and if the rate of change of (MV) is zero, then force is zero.

They should now be sold on the idea that force is intimately related to the rate of change of this quantity (MV), whatever it is.

6. Q: Now suppose you have a rocket, sitting motionless in space with the engines turned off. The we turn the engines on, and the rocket accelerates, gaining a speed of 23 meters per second. The rocket has a mass of 10,000kg. How could this happen?

7. Q: There are no external forces. So the rate of change of M*V should be zero – which means that the rocket shouldn’t move, right?

They get this -- the rocket shouldn't be able to move, because there's no force.

8. Q: But since the rocket _is_ moving, it does have an M*V -- its 23 * 10,000 = 230,000 kg m/s.  Are we missing something?

Some of them start to have the idea that something else must be moving the opposite direction of the rocket. One or two of them will suggest considering the fuel exhaust.

9.  Do demo -- skateboard and medicine ball.   Make sure they see that the ball is like the fuel, and the person on the skateboard is the rocket.

Note: The skateboard wasn't very effective because it had too high a friction for the recoil to be noticeable. What I did in class was to call out the most gregarious, athletic student to stand across the room from me, and then I threw the medicine ball at him from about 10 feet. He caught the ball, but stepped back noticeabley to maintain his balance. When he threw the ball at me, I made an exaggerated step back on impact, and then made a _very_ exaggerated step back when I threw the ball back to him. We repeated this several times until the students all had clearly seen that throwing the ball one way caused the thrower to move the opposite way. At this point we stopped to confirm that the medicine ball is like the rocket fuel, thrown backward at high speed in order to push the rocket (me) in the direction we want to go.

10.  Have them write-up an explanation of how the rocket moves.

11.  So what is this (MV) thing?   It's such a useful quantity that it gets its own special name -- momentum, p = mv, and it is the best way to deal with figuring out what will happen in collisons, rockets, and a lot of other situations.

12.  Q: Which is bigger, the momentum of an 18-wheeler, or a tennis ball?

13.  Q: Suppose the truck has a mass of 10,000 kg, and a speed of 1 m/s.  How fast would the tennis ball (.10kg)have to be going to have the same momentum?

14.  Practice finding momentum of different objects -- have them estimate masses and speeds.