What are Your Students Really
Thinking?
Using diagrams, white boards, and Socratic questioning to
reveal your student’s innermost thoughts … about physics
 Modeling Physics
David Hestenes, Malcolm Wells, Greg Swackhamer, and 100’s of others
Arizona State University http://modeling.asu.edu/
Extended Physics Community at UNC Greensboro, http://epc.uncg.edu
 CASTLE (Capacitor Aided System for Teaching
and Learning about Electricity)
Dr. Melvin Steinberg, Smith College
Available from PASCO, EM-8624A CASTLE Kit - PASCO scientific .
The Modeling Method of
Physics Teaching
Recognized by the U.S.
Department of Education
one of the seven best K-12 educational
technology programs out of 134 programs
evaluated (2000).
one of two exemplary programs in science
education (2001).
Why use whiteboards, diagrams
and Socratic Questioning?
Unaware that their own ideas … differ drastically from those
of the teacher, most students systematically misunderstand
Symbolic
what they hear
and readRepresentations
in traditional introductory physics.
Verbal
Physical
System
Algebraic
Diagrammatic
Graphical
Mental
Model
Why is this so?
• Before physics instruction, students hold naïve
beliefs about mechanics which are incompatible
with Newtonian concepts in most respects.
• Such beliefs are a major determinant of student
performance in introductory physics.
• These beliefs are strongly held and often
unconscious.
• Students do not change their deeply held beliefs
until they are conscious of those beliefs, are aware
that those beliefs do not effectively explain the
world, and have a viable alternative.
A Taxonomy of Naïve Beliefs
A.
Principles of motion
1. Description of motion:
2. In the absence of forces, every object remains at rest (with respect to the earth).
3. The causal principle of motion: Every motion has a cause.
4. The greater mass exerts the greater force.
5. the object which causes motion of the other exerts the greater force, because it overcomes the
other’s opposition.
6. Dominance: Motion is determined by the larger of two competing forces.
7. Compromise: Motion is determined by a compromise among competing forces.
B.
Influences on Motion
1. Inertial Resistance
2. A constant force produces a constant velocity
3. Acceleration is due to increasing force.
4. A constant force has a limited effect depending on its magnitude.
5. long-range forces cannot act on an object in a vacuum.
6. An Internal force (or impetus) maintains motion of an object
7. Resistance opposes an applied force or consumes the impetus of a moving object.
8. Obstacles may redirect or stop motion, but they cannot be agents of an applied force.
9. Gravity is a tendency of objects to fall down, but is not a force.
10. Heavier objects fall faster.
Research Backs up These
Conclusions
Mean Score (%)
Comparison of Force Concept Scores
90
80
70
60
50
40
30
20
10
0
traditional
novice modelers
Cary Academy
non-honors
past years
Cary Academy
non-honors
2005
Course
Expert Modelers
Cary Academy
advanced
Advantages of Diagrams, Graphs
and Socratic Approach
• Multiple modes of expression appeal to each student’s
strengths and give the teacher a more complete picture of
what is happening inside student’s brains.
• Students learn more thoroughly by having to explain their
own thoughts well enough for other students to understand.
• Diagrams and graph serve as a bridge between
experiments, fundamental principles and specific
equations.
• Students can develop their own equations using the
structure provided by diagrams and graphs.
• Provides frequent opportunity for students to articulate,
defend and test their own beliefs.
Advantages Re-inforced by other
aspects of modeling
• Uses principles and equations
developed in discovery-based labs.
• Encourages student creativity – more
interesting for teacher
• Part of a learning cycle that truly
changes student's beliefs
Disadvantages of Socratic
Approach
• takes time
• takes a year-long investment to develop student skills
• takes great teacher skill to lead students through confusion
and teach them how to think for themselves
• more difficult and time consuming to plan lessons and
classes
• Learning curve for teacher
• Resistance from some students, colleagues, parents and
administrators
What do I hope you will learn
from this presentation?
• How to use pie charts, bar graphs, vector addition
diagrams, circuit diagrams, and motion graphs and
diagrams to promote understanding and develop equations.
• How to direct students through problem-solving
Socratically without examples.
• Diagrams, graphs and Socratic questioning are more
successful when combined with a full modeling cycle
• You want to work with other teachers to bring a modeling
workshop to your district. (NCLB, funded through district,
bring workshop to teachers)
The Modeling Approach to Energy
• Starts with the first law of thermodynamics.
• Energy storage and transfer are more
fundamental concepts than potential energy,
kinetic energy and work.
• There are not different forms of energy.
• Energy is the ability to cause change.
How can energy be stored?
• In moving objects – kinetic energy
• In stretching objects – elastic potential energy
• In gravitational fields – gravitational potential
energy
• In hot objects – thermal energy
• In electric fields– electrical potential energy
• In chemical bonds – chemical potential energy
• In electrons orbiting atoms – atomic energy
• In the nucleus of an atom – nuclear energy
Energy Bar Graphs and System
Schemas
Energy bar graphs and system schemas build on the
conceptual foundation established by energy pie charts,
but organize the information in a way that strongly
suggests the conservation of energy equation.
Example: A person exerts a constant force on a box
initially at rest on a horizontal, frictionless surface and
pushes it for a distance of several meters. NOTE:
consider that it starts from rest and is still being pushed
even in the last pie.
Draw a set of four energy pie charts for this
situation.
Example: A person exerts a constant force on a box initially
at rest on a horizontal, frictionless surface and pushes it for a
distance of several meters. NOTE: consider that it starts from
rest and is still being pushed even in the last pie.
EK
Echem
Echem
EK
EK
Echem
Echem
Definition of “Force”
A push or pull
Energy exerted on an object.
Power exerted on an object.
Something that changes the motion of an
object
A resistance.
Example: A person exerts a constant force on a box initially
at rest on a horizontal, frictionless surface and pushes it for a
distance of several meters. NOTE: consider that it starts from
rest and is still being pushed even in the last pie.
EK
Echem
Echem
EK
EK
Echem
Echem
Example: A person exerts a constant force on a box initially
at rest on a horizontal, frictionless surface and pushes it for a
distance of several meters. NOTE: consider that it starts
from rest and is still being pushed even in the last pie.
EK
Echem
Echem
EK
EK
Echem
Echem
Beneath each pie chart, draw a bar graph
representing the same information. Use one bar
for each wedge of your pie.
Example: A person exerts a constant force on a box initially
at rest on a horizontal, frictionless surface and pushes it for a
distance of several meters. NOTE: consider that it starts from
rest and is still being pushed even in the last pie.
EK
Echem
Echem
Echem
EK
Echem
Echem
Echem
EK
EK
EK
Echem
EK
Echem
Example: A person exerts a constant force on a box initially
at rest on a horizontal, frictionless surface and pushes it for a
distance of several meters. NOTE: consider that it starts from
rest and is still being pushed even in the last pie.
With bar graphs, we are concerned principally with
the initial and final energy storage. So erase your
middle two bar graphs and replace them with a
system schema.
Echem
EK
Echem
EK
Echem
EK
Echem
Example: A person exerts a constant force on a box initially
at rest on a horizontal, frictionless surface and pushes it for a
distance of several meters. NOTE: consider that it starts from
rest and is still being pushed even in the last pie.
earth
objec
t
Echem
person
surfac
e
EK
Echem
Example: A person exerts a constant force on a box initially
at rest on a horizontal, frictionless surface and pushes it for a
distance of several meters. NOTE: consider that it starts from
rest and is still being pushed even in the last pie.
Each line in a system schema represents an interaction
between two objects, but only some of those interactions
involve a transfer of energy. If energy is transferred,
add an arrowhead to show which way the energy
flows.
earth
objec
t
Echem
person
surfac
e
EK
Echem
Example: A person exerts a constant force on a box initially
at rest on a horizontal, frictionless surface and pushes it for a
distance of several meters. NOTE: consider that it starts from
rest and is still being pushed even in the last pie.
EK
Echem
Echem
Echem
earth
Echem
person
EK
EK
objec
t
working
Echem
surfac
e
EK
Echem
When a force causes a transfer of energy, that is called
working.
Energy can also be transferred by
conducting.
A piece of hot metal is dropped into a well-insulated glass of
water.
H2O
metal
Etherm-metal E
therm-H2O
conducting
Etherm-metal Etherm-H2O
Energy can also be transferred by
radiating.
A photon of light interacts with an atom, causing its
electron to jump up an energy level.
Uelec + KE = Eelectron
Ephoton
photo
n
electro
n
radiating
Uelec + KE = Eelectron
Ephoton
Color Coding Electric Circuits
 Each wire in an electric circuit is assigned a color
according to the voltage in that wire.
Red = greatest voltage in the circuit
Orange = next greatest
Yellow = medium
Green = next least
Blue = least voltage in the circuit.
 Any wire or connected wires must have the same color
code because wires have too little resistance to sustain a
voltage difference.
 All differences in voltage, and therefore differences in
color must occur across devices such as batteries or light
bulbs.
Bulb Rays and Arrow Tails
 The more rays drawn out of a light bulb, the brighter it
is.
The more tails drawn on an arrow representing electric
current, the greater the current.
Physics Education Research (PER)
shows a real crisis in understanding
• What does it mean when students can readily solve the quantitative
problem at left, yet not answer the conceptual question at right?
B
4
2
P
A
Q
8V
S
C
6
For the circuit above, determine the
current in the 4  resistor and the
potential difference between P and Q.
Bulbs A, B and C are identical. What
happens to the brightness of bulbs A
and B when switch S is closed?
PER shows conclusively that textbooks,
lucid lectures and lots of repetitive
problem-solving are not effective in
remedying the situation.
• Before physics instruction, students hold naïve beliefs about
mechanics which are incompatible with Newtonian concepts
in most respects.
• Such beliefs are a major determinant of student performance
in introductory physics.
• These beliefs are strongly held and often unconscious.
• Students do not change their deeply held beliefs until they
are conscious of those beliefs, are aware that those beliefs
do not effectively explain the world, and have a viable
alternative.
How do you change a mind?
•
•
•
•
•
Become conscious of existing beliefs
Be able to articulate and defend those beliefs
Confront evidence that tests those beliefs
Evaluate alternatives
Learn to catch yourself slipping back into your
pre-conceptions (cycling back to evidence)
Diagrams, graphs and Socratic questioning are components
of an instructional method that produces better results.