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These slides were used in Daveid Hestenes’
General Interest Seminar at Edinburgh
University’s School of Physics and
Astronomy on 28th April 2009.
Slides 1–25 were presented during the
lecture. Slides 26–41 are supplemental.
http://www.ph.ed.ac.uk/seminars
Naïve Beliefs
about Physics
and Education
David Hestenes
Arizona State University
UK 2009
Why is physics so difficult?
Stock answer: – few have the talent for it!
Science Education Research has a different answer,
from thorough investigation of personal beliefs about how
the world works uninformed by science (hence naïve!)
Definitive conclusions:
• naïve beliefs dominate student performance in
introductory physics!
• conventional instruction is almost totally
ineffective in changing them!
• this result is independent of the instructor and
his/her mode of teaching!
How can this be? Can’t we do better?
Major result: A detailed taxonomy of naïve beliefs
about mechanics – the science of motion
• very stable and expressed with confidence – deep seated!?
• incompatible with Newtonian physics
– misconceptions vs. alternative hypotheses
• universal – everyone has them!
• independent of intelligence
– Aristotle  Jean Buridan  Galileo  Newton!
• retrograde amnesia of physicists
• implications for structure and development of cognition
– perceiving the world as Newtonian!
• reliable instruments
– to detect the presence and change of naïve beliefs
• large body of data
– for comparisons from high school to grad school
Naïve Physics  a system of common sense beliefs
about the physical world
Research problem:
– Develop simple and reliable instruments to
distinguish systematically between naïve and
Newtonian beliefs about motion and force.
– Evaluate the effectiveness of physics instruction
in changing naïve beliefs.
Instruments:
– Mechanics Diagnostic: AJP 53, 1985
– Force Concept Inventory: Physics Teacher, 1992
– Mechanics Baseline: Physics Teacher, 1992
Collaborators: I. Halloun, M. Wells, G. Swackhamer
Will discuss: instrument design, extensive data, implications
Major beliefs about forces
Newtonian
vs.
Naive
university physics
post instruction
Results
• First Law
 “Force implies motion”
(Impetus Principle)
~ 60%
• Second Law
 “Force is action”
(No Passive forces)
~ 40%
• Third Law
 “Force is war”
(Dominance Principle)
~ 90%
still maintain
naïve view!!
Effects of conventional instruction (> 1,000 univ. students)
• small (< 15% improvement)
• independent of instructor & mode of instruction
• reproducible and universal (across the U. S.)
• persistence to graduate school
Discriminating power of the FCI – from saliency of its distractors
12. A book is at rest on a table top. Which of the foll owing force(s) is (are)
acting on the book?
1. A downwa rd force due to gravit y.
2. The upw ard fo rce by the table.
3. A ne t downw ard fo rce due to air pressure.
4. A ne t upwa rd force due to air pressure.
What the answers tell us:
(A) 1 only – No “passive forces” – table just gets in the way!
(B) 1 and 2
(C) 1, 2, and 3_ – “under pressure”
(D) 1, 2, and _4 – “bouyancy” – correct answer
(E) none of these; since the book is at rest there are no forces acting on it .
Most informative – Force requires an active agent!
“Force is Action” metaphor
vs. Newtonian “universality of force”
as the only causal mechanism!
Metaphors dominate common sense reasoning!
22. A go lf ball driven down a fairway is observed to trave l through the air wit h a trajectory
(fli ght path) simil ar to that depicted below.
Which of the foll owing force(s) is (are) acting on the go lf ball whil e it i s in flight?
“Container metaphor”
“go power”
(A) 1 only
(B) 1 and 2
(C) 1, 2, and 3
}
1. the force of gravit y
2. the force of the "hit " = medieval concept of “impetus”
3. the force of air resist ance
Missed by 42% of
junior & senior science majors
in a physics class at Harvard (1991)
(D) 1 and 3
(E) 2 and 3
Refer to the following statement and diagram w hile answering the next two questions
A large truck b reaks down ou t on the road and receives a push back into town by a sma ll
compact car.
13. Whil e the c ar, still push ing the truck, is speeding up to ge t up to cruis ing speed
(A) the force by the car pushing ag ainst the truck is equa l i n a mount to that of t he truck
push ing back aga inst the car.
20% of
physics
graduate
students
(B) the force by the c ar push ing aga inst the truck is le ss than that of the truck push ing back
aga inst the car.
(C) the force by the c ar push ing aga inst the truck is greater than that of the truck push ing
back aga inst the car.
“Conflict (or war) metaphor” & “dominance principle”
(D) the car's engine is runn ing so it a pplie s a force as it pushe s aga inst the truck but the
truck's eng ine is n't runn ing so it can' t push back with a force against the car.
(E) neither the c ar nor the truck exe rt any force on the other , the truck is push ed forward
sim ply because it is in the way of the car.
How common are these naïve beliefs?
Clerk Maxwell’s commentary on
Herbert Spenser’s appearance before Section A
of the British association (Belfast 1874):
“Mr. Spenser in the course of his remarks regretted that so
many members of the Section were in the habit of
employing the word Force in a sense too limited and definite
to be of any use in a complete theory of evolution.
“He had himself always been careful to preserve that
largeness of meaning which was too often lost sight of in
elementary works. This was best done by using the word
sometimes in one sense and sometimes in another –– and in
this way he trusted that he made the word occupy a
sufficiently large field of thought.”
Implications
• Since students ascribe different meanings to basic terms
like force, they systematically misunderstand most of
what they hear and read in introductory physics!

Frustration and humiliation when they can’t
understand why they can’t perform better.
S: “I understand the theory, I just can’t work the problems!

Student turnoff!
• Why have physics teachers and professors so long
remained insensitive to this problem?
Because
• They are satisfied with their own system of
naïve beliefs about education !!
Conventional physics instruction
• is tacitly based on a system of naïve beliefs about
knowing, thinking and learning.
• These beliefs are implicit in the way the subject is taught!
• Thus, they are transferred tacitly to students,
influencing the way they study!
To examine and evaluate these beliefs
• they must be explicated from their tacit state, and
• compared with alternatives
To that end, we need to characterize and compare
the following Belief Systems:
Naïve psychology
& epistemology
vs.
Cognitive Science
& Learning Theory
A comparison of
Belief Systems
Naïve
Scientific
• grounded in
folklore, hearsay,
casual observation
• grounded in
systematic empirical
investigation
• fragmented and
compartmentalized
• highly integrated
and systematic
• uncritically accepted
• critically evaluated
From naïve physics to naïve epistemology
• Caloric Theory of heat: heat is a substance
– transferable from one body to another.
• Caloric Theory of knowledge:
– knowledge (caloric) is substance-like
– facts and ideas are things that can be packaged
in words and distributed to students
– “a fact is a hard thing!” – Ronald Reagan
• Implication: A Transmissionist Theory of Instruction
– to know is to possess knowledge stuff (caloric)
– to learn is to collect knowledge
– to think is to manipulate knowledge
– to teach is to distribute knowledge
Transmissionist theory is the foundation for the
Marketing Model of Education
Scientific knowledge
Produced
Packaged
Retailed
Consumed
Implications:
is a commodity (caloric)
by scientists
in universities and laboratories
in textbooks, software, films, . . .
by professors and educators
by teachers (clerks) in schools (local stores)
& universities (supermarkets)
by students, business and industry
• Teacher-retailers and student-consumers are seen
(and see themselves) as outsiders to science
• Education is evaluated by the quality of transmission
from scientist-producer to student-consumer
Let us examine
Transmissionist Theory
in practice:
WWII Army
Instructor’s
Manual
Dedicated educational researchers have probed beyond
this crude model of transmissionist instruction to discover
the operative principles of a deep-seated theory!
Principles of Transmissionist Learning Theory
Oth Law: Knowledge (caloric) is quantized,
2 kinds of quanta identified so far:
• factons – items emitted by teachers
to be recorded on exams!
• factinos – items of profound insight and
significance emitted by professors!
1st Law: Students are heavy absorbers of factons!
factinos (being of zero conceptual mass)
pass through with little detectible effect!
2nd Law: Factons can seldom be retrieved
in their original form!
Among the many deep implications of this theory:
Kelvins Theorem: Instruction always increases
the entropy of the universe!
Critique (essential to science)
Socrates: “the unexamined _______ is not worth _____!”
Transmissionism:
• Reifies concepts into things (concrete thing metaphor)
• Transmits concepts as messages (conduit metaphor)
• Fails to
ideas
& words
differentiate:
messages & signals
knowledge & information
Communication involves more than transmission!
“One _____’s message is another _____’s noise!”
– foreign language
Messages must be reconstructed from signals with a codebook!
{

a scientific alternative :
CONSTRUCTIVIST
Learning Theory
Constructivist Learning Theory (one version)
Physical
World
is known by
construction
Mental models &
conceptual systems
• Facts exist only as part of a conceptual system.
• Information is meaningful only to the extent that
it can be represented within the system.
• Radically new information can be incorporated only by
restructuring the conceptual system.
Implications of Constructivist Theory


• Understanding a new idea is a creative act
– comparable to the original creation! – Piaget
• To learn physics is to reinvent it
– only with bigger hints and better tools!
The conceptual transition:
Naïve
Physics
Newtonian
Physics
recapitulates one of the great scientific revolutions
– rewriting the codebook of the students experience!
The wonder is ______?
Instructional implications of transmissionist theory
• Clear lectures
Ineffective
• Impressive demonstrations
instructional
• Worked examples
methods
• Lots of homework
• Passive students
Constructivist
• Hidden knowledge
critique
• Conceptual filtering
Example: formula-centered problem solving:
– see “the answer” comes from a formula.
– homework practice confirms this.
– discount as irrelevant: “if not required on exams”
“theory” as “not practical”
“diagrams” as “ not essential”
}
}
Consequences of conventional problem-solving instruction
According to Don Woods – Editor, Problem-solving News:
“We at McMaster University found that our students solved
over 3000 homework problems over a four year engineering
program; they saw professors solve on the board over 1000
example problems. We could detect no improvement in
problem-solving ability . . . Students still made the same
mistakes. Something needs to be done!
Clue:  20% elect to draw free-body diagrams on exams!
Constructivist moral:
– Drill and practice is not effective at eliminating
misconceptions and developing understanding.
– Practice makes permanent!!
Implications for instructional design
Transmissionism
teacher-centered
knowledge transfer
passive reception
teacher presentation
teacher authority
spectator’s of science
“seeing is believing”
Constructivism
student-centered
cognitive skill development
active engagement
student articulation
student evaluation
participation in science
“If I hadn’t believed it,
I wouldn’t have seen it!”
Constructivist Implementation
• The teacher creates and maintains a learning environment
• “No quick fixes” – no substitute for technical knowhow & skill
• “The devil is in the details” – Malcolm Wells,
a documented existence proof!
Richard Feynman: A Teacher’s Responsibility
Each generation that discovers something from its experience must
pass that on, but it must pass that on with a delicate balance of respect
and disrespect, so that [it] … does not inflict is errors too rigidly on its
youth, but it does pass on the accumulated wisdom, plus the wisdom
that it may not be wisdom.
It is necessary to teach both to accept and to reject the past with a kind
of balance that takes considerable skill. Science alone of all the subjects
contains within itself the lesson of the danger of belief in the infallibility
of the greatest teachers of the preceding generation.
“What is Science?” Physics Teacher 7, 313-320 (1969)
Summary
Student initial beliefs
– about the physical world,
– about knowing and learning,
are major determinants of what they learn in intro physics
Conventional physics instruction is highly inefficient, because
– it fails to take student beliefs into account, and
– it is itself based on naïve beliefs about learning!
This problem cannot be resolved without
– a strong program of educational research
and curriculum development,
– together with continued development of scientific
learning theory, broadly based in cognitive science!
The bottom line!
“It ain’t what you don’t
know that hurts you,
It’s what you know
that ain’t so!”
Mark Twain
Brief taxonomy of (naïve) alternatives to Newtonian force laws
(1) Force applied by a (living) agent in contact
(a) No motion unless F > m or W
Threshold
(internal resistance)
principle
(b) Constant F  constant v
(c) Acceleration due to increasing F
(d) F has limited effect
Finite effect
(i) Wears out
principle
(ii) Accelerates object to critical speed v = F/m
(e) Long-range force requires a medium
Cannot act in a vacuum
(2) Motive power (impetus)  called “force”
(a) Imparted by contact
(b)  mv
(c) may wear out or build up like an applied force
(3) Resistance opposes or consumes “force”
(4) Obstacles just get in the way!
(5) Gravity: “Heavier objects fall faster”
Conceptual Calibration of the FCI
3 Stages of Conceptual Evolution in Newtonian mechanics
FCI
scores
I. Develop universal force concept
 Recognize agents of force (active & passive)
 Differentiated concept of motion
velocity vs. acceleration
60%: Newtonian Threshold
II. Develop (vectorial) dynamical concepts
Discriminate 1st and 2nd Laws
80%: Mastery Threshold
III. Develop complete interaction concept
 universal, reciprocal, binary
>90%
Essential to the 3rd Law & conservation laws
What is a typical FCI score?  comparative statistics
F CI mean score / 100
80
Traditional
University physics
Posttest mean: 63%
60
Newtonian
Threshold: 60%
73
Postt est
65
51
40
31
Random score:
H.S. courses before modeling
31
30
Pretest
20
0
t
y
Instruction
Traditional
Ref orm
Modeling
For 62 H.S. & college courses (Hake, AJP, 1998)
For 696 students of teachers who tried to implement all aspects of the modeling method.
FCI has high validity and reliability on every measure
 False negatives rare (“these questions too trivial for my students!”)
 Misses are highly informative!
+ strong correlation with problem solving ( Graduate Record Exam)

+

Elements of Modeling Instruction
Impediments to learning physics:
(a) Misconceptions about common physical phenomena.
(b) Misconceptions about scientific method.
(c) A view of science as a fragmented collection of facts,
rules and formulas.
Instructional objectives include:
(a) a clear concept of "physical model,” including
both qualitative and quantitative aspects,
(b) familiarity with a basic set of models as the core of
introductory physics,
(c) skills in the techniques of modeling, especially interplay
between diagrammatic and symbolic representations,
(d) experience in the deployment of models to understand
the physical world--to interpret and analyze data,
to explain, to predict and to plan.
Managing Classroom Discourse (talk is not enough!)
 Aim: raise level to scientific discourse
 Establishing the subject of discourse
Demos
Problems
}
Issues
Questions
}
Claims to be
investigated
 Communication requires shared meaning
students get common access with whiteboards, etc.
 Meaning (of words, equations, diagrams)
 is constructed from situated use
 must be negotiated

Quality of discourse depends on
 Representational tools and how they are used
 Structure of arguments
 Standards – set by teacher
 Scientific argumentation arises spontaneously when
students have the discursive resources
Modeling Instruction
 Instructional design:
The instructional modeling cycle
engages students in all aspects of scientific inquiry:
• Empirical: Design and conduct experiments to investigate
structure in physical systems and processes.
• Theoretical: Construct, analyze and apply scientific
models and theories.
• Technical: Use scientific instruments and modeling tools
to sharpen scientific investigation and inference.
• Social:
Scientific discourse and argumentation
to negotiate mutual understanding of models
and implications of experimental results.
 Teachers guide student inquiry by
• organizing activities and discourse around scientific models
• informed by research on student conceptual learning
Assessing the energy concept




All energy is stored in some physical system.
Energy can be transferred from one thing to another.
This causes changes.
The amount of energy in the universe is constant.
Energy cannot be made, nor can it be destroyed.
Energy tends to disperse to more and more objects.
Entropy can be made, but it cannot be destroyed.
You have a can of soda that you would like to keep cold
and a sandwich to keep warm. You have woolen
blankets and some aluminum foil.
What combination of materials would work best?
9th
HS
UNIV
57%
42%
32%
6%
16%
23%
26%
30%
31%
a. Aluminum foil wrapped around the soda and a
woolen blanket wrapped around the sandwich.
b. A woolen blanket wrapped around the soda and
aluminum foil wrapped around the sandwich
c. Aluminum foil wrapped around each individually.
3%
5%
9%
d. A woolen blanket wrapped around each individually.
5%
6%
4%
e. Wrapping each separately with either material would
work equally well.
A steel ball rolls along a smooth, hard, level surface with a certain speed.
It then smoothly rolls up and over the hill shown below.
How does its speed at point B after it rolls over the hill
compare to its speed at point A before it rolls over the hill?
A
9th
HS
UNIV
4%
6%
6%
10%
30%
44%
23%
24%
20%
56%
35%
26%
4%
4%
4%
B
a. Its speed is significantly less at point B than at point A.
b. Its speed is very nearly the same at point B as at point A.
c. Its speed is slightly greater at point B than at point A.
d. Its speed is much greater at point B than at point A.
e. The information is insufficient to answer the question.
Which of the following statements describe the difference between
a strong chemical bond and a weak chemical bond between two atoms?
i. The strong chemical bond stores more energy than the weak chemical bond.
ii. More energy is needed to separate strongly bonded atoms than
weakly bonded atoms.
iii. More energy is released to the environment when two atoms become
strongly bonded than when two atoms become weakly bonded.
HS
UNIV
a. i only
4%
1%
b. ii only
27%
36%
c. iii only
4%
5%
d. ii and iii only
19%
20%
e. i, ii, and iii
44%
38%
When a candle burns the energy released
9th
HS
UNIV
20%
14%
14%
27%
25%
37%
33%
45%
41%
9%
6%
3%
8%
9%
5%
a. comes mainly from the wax and air
b. comes mainly from the burning wick
c. is produced mainly by the fire
d. comes from the match that lighted the candle
e. Comes mainly from the wax
A living tree in its environment
9th
HS
UNIV
2%
1%
1%
28%
28%
24%
47%
56%
59%
4%
4%
7%
16%
7%
4%
9th
HS
UNIV
59%
29%
21%
12%
27%
31%
7%
13%
13%
9%
19%
25%
10%
9%
9%
a. does not possess energy
b. possesses energy that it has received from the sun
c. possesses energy that it has made as well as
energy that it has received from the sun
d. possesses only energy that it has made
e. possesses energy that it received from the sun
and the energy of its life force.
A dead tree in its environment
a. does not possess energy
b. possesses energy that it has received from the sun
c. possesses energy that it has made as well as
energy that it has received from the sun
d. possesses energy that it has made
e. possesses energy that it received from the sun
and still a little energy of its life force.


Students have an incoherent view of energy.
– Potential energy is often ignored.
• “Just a number”
• “An invented quantity”
• Potential energy is not actual energy.
• It often is thought to have nowhere to exist,
so it cannot really exist.
– Energy can be “produced.”
– Energy conservation only weakly constrains student
thinking. It does not force inferences.
Energy is not useful to students in describing and
explaining natural phenomena.
– They often have to be prompted even to invoke it!