Transcript PER and the Undergraduate Curriculum Randy Knight California Polytechnic State University San Luis Obispo, CA.

PER and the Undergraduate Curriculum
Randy Knight
California Polytechnic State University
San Luis Obispo, CA
30 Years of PER in Intro Classes
• 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.
What About Physics Majors?
Sophomores in Modern Physics
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 current-voltage relation should be Ohm’s law
• the battery was the cause of electrons ejected
from the cathode, not mentioning the light.
Sophomores in Modern Physics
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.
Sophomores in Modern Physics
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.
Sophomores in Modern Physics
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.
Sophomores in Modern Physics
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.
Juniors in Thermodynamics
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 QA
required for process A greater
than, less than, or equal to the
heat QB required for process B?
Explain.
Most common answer: QA = QB.
Explanations based on pV = nRT.
Juniors in Thermodynamics
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.
Juniors in Thermodynamics
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
Most common answer. Strong belief
C. Is unchanged
in “conservation of entropy.”
D. Can’t say without more information.
Quantum Mechanics: Grad Students
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. Csin3(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?
Quantum Mechanics: Grad Students
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.
Knowledge Structures
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.
Knowledge Structures
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.
Teaching and Learning
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.
The Van Heuvelen Educational Transformer
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
Can We Do Better?
What Does Research Tell Us?
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!
Expert-Like Knowledge Structures
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.
Metacognition
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.
Beware Cognitive Overload
Well studied. The idea that you’ve
got only so much working memory.
Lectures FAR exceed the cognitive
capacity even of experts.
GARY LARSON
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.
Constructing Knowledge
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.
How?
• 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!
Example: Concept Question in
Thermodynamics
Two identical monatomic gases expand. In these expansions:
A. ∆SA > ∆SB
B. ∆SA = ∆SB
C. ∆SA < ∆SB
D. The two processes can’t be compared.
Adapted from U. Colorado PER Group
The Five Lessons
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