Research in the Teaching and Learning of Physics

Part II: Physics Education Research

Prof. #S’s Pretest Posttest <G>

A 97 51% 64.5% 0.28

B 192 51% 64.3% 0.27

C 70 50% 63.6% 0.27

D 119 53% 63.6% 0.23

E (n.c) 82 37% 53% 0.15

F (hs.h) 24 30% 52% 0.31

G (hs.g) 25 30% 44% 0.20

(Halloun and Hestenes, 1985)

A series circuit consists of three identical light bulbs connected to a battery as shown here. When the switch S is closed, do the following increase, decrease, or stay the same?

(a) The intensities of bulbs A and B(b) The intensity of bulb C(c) The current drawn from the battery(d) The voltage drop across each bulb(e) The power dissipated in the circuit

a

ABC

a

12 V4 Ω2 Ω6 Ω8 VPQ

For the circuit shown, calculate (a) the current in the 2 W resistor and (b) the potential difference between points P and Q.

ABCDE

• Find the direction of the acceleration of the pendulum bob at each position.

Why so bad?

• Constructivism–students build their own knowledge– Students not blank slates – Lectures filtered by initial conceptions– Unreliability of memory

• Lectures– Passive learning (no deep processing)

Conceptual change theory

• Disequilibrium

• Exploration of alternatives

• Choice of alternative

• Bottom line: – Deep processing– Formation of links

Applications of the theory

• Physics by Inquiry– Students perform experiments and discuss

results with peers to develop their own theories

• Workshop Physics– Students perform experiments and discuss

consistency with different theories

• Interactive Lecture Demos– Designed for deep processing of demonstrations

Six thousand students

Problem Solving

Expert-novice studies

• Knowledge organization

• Strategies

Knowledge organization

• A comparison of novice and expert behavior on tasks involving introductory physics problems (Chi 1981)

• Study 1: Sort 24 problems into categories– Novices grouped problems (1, 4), (2, 7)– Categories: Inclined planes, springs, pulleys– Experts grouped problems (6, 2), (3, 5, 8)– Categories: Energy principles, Momentum

principles, [Newton’s] Second law

Knowledge organization

• Study 2: Repeat with specially designed problems– e.g., problem 3a vs. changing last sentence to

“With what speed does the man hit the ground?”

– categorizations the same for novices and experts

Knowledge organization

• Study 3: Say as much as possible about the problems in a given category (e.g., inclined plane or energy principles) and how they might be solved– Novices talked about surface features of the problem:

angle of incline, length, friction/no friction, block, mass of block, forces on block, pulley, normal force

– Experts talked about possible solution paths, such as conservation of energy or Newton’s laws and their applicability conditions first before describing other factors like the ones mentioned by novices

Knowledge organization

• Study 4: Give a basic approach for solving a problem – Experts immediately descibed the physics

principles relevant to solving the problem– Novices either made very genral statements

about how to proceed (“First figure out what is going on, then see how different things are related to each other…”), or described the equations they would use in solving the problem.

Knowledge organization

• Timing information from novice and expert attempts to solve a problem (Larkin 1979)

• Bursts versus random separation (chunks)

0

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0 10 20 30 40 50 60

Δ ( )T seconds

Novice

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0 10 20 30 40 50 60

Δ ( )T seconds

Expert

Problem-solving procedures

Analyzing protocols of solutions

• Experts– Qualitative analysis– Multiple representations– Self-monitoring

• Novices– Single representations

Problem-solving procedures

Give experts a problem.

Ignore air resistance. A rigid wheel spins with angular velocity 0 about a frictionless axis. The wheel drops on a horizontal floor, slips for some time, and then rolls without slipping. After the wheel starts rolling without slipping, the center of mass speed if vf. How does vf depend on the kinetic coefficient of friction between the floor and the wheel?

Problem-solving procedures

• Similarities between experts and novices– Had trouble planning a solution

– Had difficulty thinking about both effects (friction and slipping time)

• Differences– Experts visualized the problem and considered

applicable basic physics principles first

– Experts considered analogies and limiting cases

– Novices confused slipping/rolling cases

– Novices confused linear/angular and horizontal/vertical velocities (failed to visualize)

Curricular implications

• Knowledge organization– Use of HAT (Mestre, 1993)– Explicit teaching of structure (Reif and Eylon,

1984)

• Strategies– Explicit teaching of strategies and use of

computers (Heller, 1992; Reif and Allen, 1992)– Use of different problems (vs. exercises) to

force more expert-like problem analyses

Standard problem

A block with a mass of 5 kg is given a shove and travels 4 m up a ramp that makes an angle of 20° with the horizontal. If the kinetic coefficient of friction between the block and the ramp is 0.6, what was the initial speed of the block?

Context-rich problemWhile visiting a friend in San Francisco you decide to drive around the city. You turn a corner and are driving up a steep hill. Suddenly, a small boy runs out on the street chasing a ball. You slam on the brakes and skid to a stop leaving a 50 foot long skid mark on the street. The boy calmly walks away but a policeman watching from the sidewalk walks over and gives you a ticket for speeding. You are still shaking from the experience when he points out that the speed limit on this street is 25 mph. After you recover your wits, you examine the situation more closely. You determine that the street makes an angle of 20° with the horizontal and that the coefficient of static friction between your tires and the street is 0.80. You also find that the coefficient of kinetic friction between your tires and the street is 0.60. Your car's information book tells you that the mass of your car is 1570 kg. You weigh 130 lbs. Witnesses say that the boy had a weight of about 60 lbs and took 3.0 seconds to cross the 15 foot wide street. Will you fight the ticket in court?

You have an internship in an exobiology laboratory investigating the possible types of life that might occur on other planets. Your team is testing possible mechanisms that a swimming organism might use to stabilize its temperature. One of your team suggests that this hypothetical animal could remove excess heat generated by its metabolic processes by using a sac of gas similar to a fish’s swim bladder. The sac would be within the body of the animal near the surface of its skin. The process would work as follows: First the sac would be isolated from the outside and gas inside the sac would be in thermal contact with many small blood vessels in the sac wall. The sac would slowly expand to its maximum volume but be kept at constant pressure by muscles around the sac. While the volume was held at its maximum, the pressure of the gas would rise until a maximum pressure was sensed by the muscles. At that time, blood would be cut off from the vessels and gill like slits would open in the animal’s skin bringing the sac into thermal contact with the outside fluid that it is swimming in. The muscles around the sac would then cause the sac to contract to its minimum volume while keeping the pressure of the gas inside constant. Finally, when the sac reached its minimum size, the muscles would allow the gas pressure to drop while not changing the volume of the sac. Then the slits would close, isolating the sac from the outside fluid and the process would repeat. Throughout this process no gas would enter or leave the sac. To determine if this animal could survive, you decide to calculate the ratio of the heat output by this process to the work input necessary to manipulate the sac. To get some reasonable numbers, you assume that both the volume of the sac and the pressure of the gas in the sac double during the process. You also assume an ideal gas with a molar specific heat of (3/2)R.

Experiment problems

Magnetic Field Measured by U-Loop with Current: An inventor claims that he can lift objects using a magnetic field and the current

through a wire. You have a model of her apparatus at your lab table. A U-shaped loop hangs down from a horizontal support. The bottom of the loop is between a U-shaped magnet. You are to evaluate this device for the company for which you work to see if it has any promise. Run some current through the loop and note the behavior of the loop.

(a) As a starter, based on your observations, other measurements with the apparatus, and the concepts of physics, estimate the strength of the magnetic field in the region of the bottom of the U loop.

(b) Having learned more about how the device operates, indicate any deficiencies that may limit the ability of this device to be used to lift objects.

Jeopardy problems

Q = (8.0 mol) (8.31 J/mol K) (361 K) ln(34.3 L/60 L)

FF

N

W

x

y

f

push

26.5°

Ranking tasks

Rank these situations from greatest to smallest on the basis of the pressure on the cork by the water.

Computer coaches

• One obstacle to students’ acquisition of effective problem-solving skills is the difficulty in providing them with sufficient individualized coaching.

• Computers may be a practical means of providing individualized coaching.

• Role of coach is to provide students with guidance and feedback while they practice making decisions based on effective strategies for solving problems.

Effective strategies1. Focus the problem • Draw a picture illustrating the situation • Determine the question to be answered • Choose which physics principle(s) to use

2. Describe the physics • Draw physics diagrams • Determine target quantity(ies) • Write down quantitative relationships

3. Plan the solution • Select equation containing the target quantity • Identify other unknowns in equation • Solve a sub-problem to find each unknown • Check units

4. Execute the plan • Calculate value of target quantity(ies)

5. Evaluate the answer • Check if answer is properly stated • Check if answer is unreasonable • Check if answer is complete

Minnesota problem-solving frameworkDraw a picture

• important objects • perspective

kinematics quantities • position • velocity • acceleration • time

dynamics quantities • force

• other parameters

Polya (1945)Heller and Reif (1984)Heller, Keith & Anderson (1992)Van Heuvelen (1991)

Needed cognitive functions

• Students usually focused on implementing

• Inadequate decision-making:

– recall of incorrect information

– failure to recall useful information

– non-proceeding procedures

• Inadequate assessment:

– incorrect implementations

– failure to learn from mistakes

DecidingImplementing

Assessing

Heller and Reif (1984)Reif and Larkin (1991)Reif and Scott (1999)

Computer coaches

• Collection of computer programs, each assisting students in

solving a single physics problem.

• Problems use kinematics, Newton’s laws, conservation of

energy

• Context-rich problems Heller and Hollabaugh (1992)

Reciprocal teaching

Features:

• Student is always actively engaged

• Cognitive functions are practiced in a relevant context

• Cognitive functions are modeled by tutor and performed by student

• Cognitive demands are higher in second mode

Tutor coaches studentStudent coaches tutorTutor decidesStudent implementsTutor assesses

Student decidesTutor implementsStudent assesses

Palincsar & Brown (1984)

PAL coaches student

QuickTime™ and aGIF decompressor

are needed to see this picture.

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QuickTime™ and aGIF decompressor

are needed to see this picture.

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Student coaches PAL

Student performs independently

Assessment

• Recruited a small number (~20) of volunteers to test usability

• Students uniformly enthusiastic about being coached (interaction mode 1)

• Students not as enthusiastic about coaching PAL (interaction mode 2)– Students don’t feel like they’re solving a problem

– This mode is more difficult for students

– Mode of interaction may not be helpful for true novices

Coordination classes

• Elements of a CC– Causal net

• Reasoning pathways for making inferences

– Readout strategies• Filters that direct attention to meaningful elements

• Performance criteria– Integration

• Coordination within a single situation

– Invariance• Coordination between multiple situations

Ball on V-track demo

Results

Anim 1 Anim 2 Anim 3 Anim 4 Anim 5

one-ball (physics)

8% 42% 0% 0% 50%

two-ball (physics)

0% 17% 63% 17% 4%

one-ball (psych)

23% 35% 0% 4% 38%

two-ball (psych)

15% 42% 0% 8% 35%

Causal netsExpectations Description and comments

DECEL-UP Speed decreases when rolling uphill (very common)

ACCEL-DOWN Speed increases when rolling downhill (very common)

SAME-SPEED Ball B has same velocity before and after valley (physics-cons. of energy, psych-rare)

NO-GAIN Speed does not increase without cause (ANIM 3)

TIE Balls reach end of track at same time (physics-cons. of energy, speed, psych-low confidence)

Read-out strategiesExpectations Fixed-referent Relative-motion

DECEL-UP good sensitivity good sensitivity

ACCEL-DOWN poor sensitivity in 5 systematic error in 5

SAME-SPEED poor sensitivity systematic error in 5

NO-GAIN good sensitivity in 3 poor sensitivity in 3

TIE N/A good sensitivity

• Speed and position often confused in relative motion readouts• NO-GAIN insensitivity because no change in relative position?

Decision making• Common successful process: Making read

out and comparing to expectation

• Identifying an animation as realistic despite incompatibility with expectation:Process Effect

Incorrect readouts Limit choices

Extend choices

Feedback Change expectations to match readouts

Change readouts to match expectations

Decision making

• Incorrect readouts– ANIM 5 ruled out for violation of DECEL-UP– ANIM 2 not ruled out despite violation of

SAME-SPEED

• Feedback– Psych students expressing TIE eventually

dropped it in favor of other expectations– Physics students expressing TIE used rel.

motion readouts to choose ANIM 3 (consistently failed to report NO-GAIN)

Integration and invariance

• Physics students lacked invariance in ANIM 3

• Physics students failed to integrate NO-GAIN related readout in final decision

• Psych students did not integrate TIE expectation

Conclusion and implications

• Coordination classes are adaptable and can be modified based on external data, often without a person’s awareness

• Students’ cognition in a particular situation may depend on different factors than those in a seemingly closely related situation

• Instruction should consider whether errors are due to incorrect readouts or incorrect causal nets

Epistemology and expectations

• Dimensions– Structure of knowledge (coherence)– Nature of knowing and learning (absorption vs.

constructivism)– Real-life applicability (lab/class vs. real world)– Evolving knowledge (absolutism vs. extreme relativism)– Source of ability to learn (talent vs. effort)

• Diana study– Pass-fail, understand physics more deeply (Diana)– Get a good grade

The most serious criticism which can be urged against modern laboratory work in Physics is that it often degenerates into a servile following of directions, and thus loses all save a purely manipulative value. Important as is dexterity in the handling and adjustment of apparatus, it can not be too strongly emphasized that it is grasp of principles, not skill in manipulation which should be the primary object of General Physics courses.

Robert Millikan (1903) Mechanics Molecular Physics and Heat

Learning physics is about as difficult for me as it is for the average high school student.