Transcript Common Sense Concepts about Motion

Common Sense Concepts
About Motion
By Ibrahim Abou Halloun and David
Hestenes
Presented by
Jonathan McLaughlin and Keith Magni
Overview
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Common Sense Beliefs
Categories of Alternative Conceptions
Aristotelian
Impetus
Common Sense Concepts of College Students
Taxonomy of Common Sense Concepts about
Motion
Common Sense Beliefs
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“…every one of the misconceptions about
motion common among students today was
seriously advocated by leading intellectuals in
pre-Newtonian times.”
Common Sense Beliefs
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“…common sense beliefs should be treated with
genuine respect by instructors. They should be
regarded as serous alternative hypotheses to be
evaluated by scientific procedures.”
Aristotelian Physics
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The speed of an object is proportional to its
weight.
v=W/R
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Quantitative physics was impossible.
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Only living things can apply a force. Non-living
things can only stop or guide motion.
Aristotelian Physics
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Forces only move an object when they
overcome an object’s resistance (related to
inertia/weight).
V=F/R
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Without a force, an object comes to rest
immediately.
Free-falling objects increase their weight as they
get closer to their natural place on earth.
Mediums can both resist motion and propel an
object.
Impetus Physics
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“…the active agent imparts to the
object a certain immaterial motive power which
sustains the body’s motion until it has been
dissipated due to resistance.”
Impetus Physics
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Allows for the explanation of
circular impetus: persistent
motion of the planets and
the grinder’s wheel.
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Allows for motion in a vacuum
Impetus Physics
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The Historical Precursor of momentum and
Kinetic Energy.
Impetus Physics
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Albert of Saxony uses Impetus
to explain projectile motion.
Impetus Physics
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A of S on Projectile Motion
Compromise between:
Impetus
 Gravity
 Air resistance
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Impetus Physics
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A of S on Projectile Motion
Three Stage Trajectory:
Initial Stage: impetus suppresses the effect of
gravity.
 Intermediate Stage: shows compromise between
impetus and gravity.
 Final Stage: the projectile falls vertically in “natural
Motion.”
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Impetus Physics
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Kinematical Ideas also developed in the14th
century along w/ Impetus theory.
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Distinctions made between uniform velocity
uniform acceleration, and non-uniform
acceleration.
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Resulting in birth of concepts of instantaneous
velocity and acceleration.
Impetus Physics
Kinematical Ideas developed in 14th Century
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Oresme develops graphical method of
representing variable quantities.
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Used to derive “Mertonian” “Mean Speed Rule.”
Impetus Physics
Kinematical Ideas developed in the 14th century
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“… in a given time interval, the distance
traveled w/ uniform acceleration is equal to the
distance traveled w/ uniform speed equal to the
instantaneous speed in the accelerated motion at
the middle instant of the time interval.”
Impetus Physics
Kinematical Ideas developed in the 14th century
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These developments were essential prerequisites
for Galileo’s kinematical analysis of projectile
motion.
Common Sense Concepts of
College Students
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478 Students given a multiple choice diagnostic
pre/post-test used to assess common sense
concepts.
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Alternative answers on test correspond with
Aristotelian and Impetus theories.
22 students were further interviewed to gain
further insight into conceptions.
Pre/Post-Test Results
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18 % of students’ answers were predominantly
Aristotelian.
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65 % of students’ answers were predominantly
Impetus type.
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17% of students’ answers were predominantly
Newtonian.
Pre/Post-Test Highlights
Students demonstrated a belief that:
 an object slows down if no net force is applied
(47%/20%).
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an object under constant force moves at
constant speed (66% /54%).
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an impetus is required to keep an object moving
(65%/44%).
Student Interviews
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Students were asked questions about their
conceptions of:
General concepts of motion
 Free particle motion
 One-dimensional motion under a constant force
 Two-dimensional motion under a constant force
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General Concepts of Motion
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Students had difficulty distinguishing between
kinematical concepts.
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Students believed that inanimate objects may
stop or redirect objects but cannot generate
force.
General Concepts of Motion
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Students believed that gravity is an impetus
force.
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Students accepted the existence of a vacuum,
but insisted that motion could not occur outside
of a material medium.
Free-Particle Motion
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Students with Aristotelian beliefs had bizarre
arguments.
Ex) A block sliding on a surface would come to rest because “you
need wheels to keep it going.”
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Students with impetus beliefs varied in their
explanations. Some believed that objects begin
losing impetus immediately, while other believed
that objects lose impetus when they encounter
resistance.
One-Dimensional Motion Under
A Constant Force
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Some students believed that objects under
constant force would speed up but eventually a
speed limit would be reached.
Two-Dimensional Motion Under
A Constant Force
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Students had a concept of projectile motion and
that the path of a projectile was parabolic, but
had trouble identifying that projectile motion
was the result of a constant force.
Consistency of Ideas
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Students were inconsistent in their responses,
however, students with quasi-Newtonian beliefs
were much more consistent in their beliefs.
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Students who showed common-sense ideas used
a mix of Aristotelian and Impetus type
explanations for physical events.
Consistency of Ideas
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“…much of the incoherence in the student CS
[common sense] systems is the result of vague
and undifferentiated concepts.”
Persistence of Alternative
Concepts
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“As a rule, students held firm to mistaken beliefs
even when confronted with phenomena that
contradicted those beliefs.”
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Students tended not to contradict their own
beliefs but to attribute the contradiction to some
other principle.
Persistence of Alternative
Concepts
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“We doubt that a demonstration can be effective
unless it is performed in a context that elicits
and helps to resolve conflicts between common
sense and specific scientific concepts.”
Persistence of Alternative
Concepts
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“…students who showed obstinate beliefs were
able to come to adequate justifications, mostly
not because they have seen something in
conflict with their beliefs, but because they came
to realize the inconsistency of their thinking
when asked to reflect on their own arguments.”
Taxonomy of Common Sense
Concepts About Motion
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Principles of Motion
Correspond to Newton’s Laws
Influences on Motion
Correspond to Force influences