Randy Knight
California Polytechnic State University
San Luis Obispo, CA

• Students enter with a large number of misconceptions. These are little changed by “traditional” lecture instruction.
• The “knowledge structure” of intro students differs markedly from that of experts.
• Students lack a structured approach to problem solving. Few students acquire higher-order problem-solving skills simply by attempting large numbers of standard problems.
BUT. . .
• Significant learning cans can be achieved using activeengagement (peer-instruction, tutorials, interactive lecture demonstrations, etc.) that focus on conceptual understanding.
• Problem solving can be improved by explicitly teaching expertlike problem-solving skills.

Richard Steinberg : Photoelectric effect with sophomore physics majors. On the final exam, less than 50% could
• explain why the current was never negative
• explain why the current is not zero when V = 0.
Most thought that
• the currentvoltage relation should be Ohm’s law
• the battery was the cause of electrons ejected from the cathode, not mentioning the light.

Shown a situation with no current because the light frequency was below threshold, 80% predicted that current would flow if the numerical value of the phototube’s potential difference V (in volts) was increased to be larger than the numerical value (in eV) of the work function.
I’ve found that very few students, on the final exam, can explain what it is about the photoelectric effect that violates classical physics or how Einstein’s postulates make predictions that match observation.

University of Washington, and I’ve confirmed:
A B
5 µm
Light of wavelength 1 µm is emitted from A and detected at B. Draw on the figure the trajectory a photon follows from A to B.”
More than half of answers, on the final exam, are a sinusoidal wave with 5 oscillations or a wave packet.

The majority of students think that a double-slit electron interference pattern is due either to Coulomb interactions between electrons or to the electrons somehow interacting with (“bouncing off”) the edges of the slits.
Most predict the pattern would disappear if electrons were fired one at a time.

Most of these students have little trouble solving standard textbook problems, such as calculating a stopping voltage.
Few are building any kind of mental model of photons, quantization, or how quantum physics differs from classical physics.

David Meltzer: Heat, entropy, and pV diagrams.
Published work is with intro students, but in AAPT talks he says juniors do little better. I confirm.
For an ideal gas, is the heat Q
A required for process A greater than, less than, or equal to the heat Q
B
Explain.
required for process B?
Most common answer: Q
A
= Q
B
.
Explanations based on pV = nRT.

A hot solid object is placed inside a sealed, thermally insulated box filled with cold air. After a long time, the object and the air reach the same temperature. During this time, the total entropy of the object and the air
A. Increases
B. Decreases
C. Is unchanged
D.
Can’t say without more information.

A hot solid object is placed inside a sealed, thermally insulated box filled with cold air. After a long time, the object and the air reach the same temperature. During this time, the total entropy of the object and the air
A. Increases
B. Decreases
C. Is unchanged
Most common answer. Strong belief in “conservation of entropy.”
D.
Can’t say without more information.

Chandralekha Singh: Test of basic ideas from quantum mechanics to entering grad students at several selective universities. These are your best undergrad majors!
1.
“By definition, the Hamiltonian acting on any allowed state of the system
 will give the same state back. That is, H

= E
 .” Explain why you agree or disagree with this statement.
2.
Which of the following wave functions are allowed for an electron in a one-dimensional infinite square well of width a : (a sketch of the potential well was included)
A. Csin 3 (
 x/a) B. C [ 2/5 sin(
 x/a) + 3/5 sin(2
 x/a) ]
C. Cexp[-(x - a/2)/a) 2 ]
3.
What is the most fundamental equation of quantum mechanics?

Correct response rate ≈30% for nearly all questions. The majority of your best, grad-school-bound students leave QM thinking
1.
The most important equation is the time independent Schrodinger equation.
2.
All states are energy eigenstates.
Further, they have no real working concept of
1.
What it means to be in a stationary state.
2.
Superposition of states.
3.
What it means in QM to make a measurement or how measurements change wave functions.
4.
How to interpret expectation values except in the most basic situations.

Expert’s knowledge structure Novice’s knowledge structure
• Expert’s knowledge structure is hierarchical, based on conceptual understanding and general principles.
• Novice’s knowledge structure consists of loosely connected factoids based around memorized equations.

Much of the pedagogical application of PER to intro physics is based on helping students develop expert-like skills. It is a slow and painful transformation.
The unstated assumption of upper-division instruction is that physics majors somehow undergo a ‘phase transition’ from novice to expert between their freshman and sophomore years!
• Revert to pure lecture format of instruction.
• Emphasis on formalism rather than concepts.
• No demos. Little or no discussion of the experimental basis underlying theories.
• Deductive, ab initio approach rather then concrete, inductive approach.

How we teach is based on unstated and generally unexamined beliefs about how students learn.
As Carl Wieman notes, our traditional approach is to “think very hard about the subject, figure it out clearly, then explain it to students so they understand it with the same clarity.”
Based on assumptions:
• Students are “empty vessels,” tabala rasa, waiting to be filled.
• Students think more or less as we do, only not yet as quickly.
Both are demonstrably wrong.

Historically, we have relied on expository lectures. . . This is a very efficient method to transmit information in terms of the time interval needed. We know the concepts and techniques, and students do not. Why not just tell them? Study after study indicates that this expository method is very inef-fective – the transmission is efficient but the reception is almost negligible.
Alan Van Heuvelen

1. Help students develop expert-like knowledge structures.
2. Help students learn to monitor their own thinking and learning (metacognition).
3. Beware of cognitive overload.
4. Guide students in constructing their own knowledge.
5. Listen to your students!

Explicitly address the following:
1. Why does this make sense?
2.
How does this connect to the real world? What’s the evidence for it?
3. How does this connect to what I already know?
That is, help students build a mesh/network of connected ideas rather than individual factoids.
BUT. . . just telling them won’t have much effect. Need exercises/discussions/activities where they make the connections.

Difficult.
1. Do I understand this?
2.
What don’t I understand?
3. How can I confirm my understanding?
Metacognition is build by reflecting on one’s work and one’s learning.
One idea: Provide exercises in which fictitious students
(Amy, Bill, Carlos, . . .) give various points of view about a physics situation. Students have to write an explanation of who they agree with, and why.

GARY LARSON Well studied. The idea that you’ve got only so much working memory.
Lectures FAR exceed the cognitive capacity even of experts.
Wieman: 15 minutes after giving a non-obvious fact in a physics colloquium, tests the audience of experts with a multiple-choice test.
Typically ≈10% get it right.
Mr. Osborne, may I be excused? My brain is full.

PER + cognitive psychology general conclusion
Students learn by creating or constructing their own knowledge.
• It requires active rather than passive involvement.
• It requires mental effort (ouch!)
• You can’t give it to them.
• But you can guide them in the process.
Goal of teaching: “A guide on the side, not a sage on the stage.” This applies as much to upper-division courses as it does to intro courses.

• Peer instruction: Short ≈10 minute mini-lectures followed by a short student activity.
• Clicker or flashcard questions on concepts.
• Interactive lecture demonstrations.
• Tutorials.
• Class discussions.
• Let class be driven by student question of where they need help.
• Group problem solving.
Students can read derivations in the book – and understand them much better than watching you do it!

Two identical monatomic gases expand. In these expansions:
A.
∆ S
A
> ∆ S
B
B.
∆ S
A
= ∆ S
B
C.
∆ S
A
< ∆ S
B
D.
The two processes can’t be compared.
Adapted from U. Colorado PER Group

1. Keep students actively engaged and provide rapid feedback.
Peer instruction
Interactive lecture demonstrations
2. Focus on phenomena rather than abstractions.
Use experiential labs
From the concrete to the abstract

3. Deal explicitly with students ’ alternative conceptions.
Elicit, confront, resolve
Reiterate!
4. Teach and use explicit problem-solving skills and strategies.
Develop skills in isolation
Help students organize their knowledge

5. Write homework and exam problems that go beyond symbol manipulation to engage students in the qualitative and conceptual analysis of physical phenomena.
You are what you test
Balance qualitative and quantitative