#### Transcript Incorrect Reasoning

```Incorrect reasoning is context dependent
• Incorrect reasoning may be called a
misconception, preconception, alternative
concept, etc.
• Application of incorrect reasoning depends
on how a topic is presented (rck at const.
Speed ex.)
– I.E. the contextual features
People make sense of the world by using models
• A model is a functional mental construct
associated with a concept that can be applied in
context settings relevant to explanatory results (Bao
and others, 766)
• Correct model = expert model
• Incorrect/partially correct model = common
model
• Students’ ability to apply models correctly can
vary by context
A personal example
• Students can correctly answer:
– Is a net force acting on an object traveling at constant velocity?
– What is Newton’s First Law?
– Draw a free body diagram for an object falling at terminal
velocity
• But most got the following test question wrong:
– Suppose that a 10,000 kg jet is cruising at a constant velocity
when the force of the thrust from its engines is a constant
80,000N. What is the acceleration of the jet? What is the force
of air resistance acting on the jet?
• There is something about the context that is
confusing students!
Common model usage varies
• May be consistently used for all problems
• May be used inconsistently used
– Dependent upon the number of contextual
features embedded in the presentation of the
problem or question
Contextual features
• Velocity
• Acceleration
• Pushing
• Mass
Multiple contextual features limit
common modeling analysis
• Difficult to tell which contextual feature is
activating common model usage.
• Bob/Jay Example #1
• Is it the contextual feature of mass or of
pushing that is confusing students?
Isolating contextual features is
more useful
• Allows assessment of common model
• Bob/Jay Example #2
• Strong suggestion that a student who
answered incorrectly is using an incorrect
model based on the physical feature of
mass
THE DATA
Number of Students  280
Abilities => wide range.
Table Summarizing the data
Vel.
Mass
Push
Accel.
Score
0.20
0.18
0.27
0.71
Concentration
factor
0.63
0.64
0.42
0.58
Concentration Factor?
• C > 0.5  High concentration factor
• 0.2 <C< 0.5  Medium concentration factor
• C < 0.2  Low concentration factor
• Velocity, mass, and acceleration high
concentration
• Push  low concentration
• All scores are poor except Acceleration – students
use wrong model for those.
•
What
did
we
find
out?
Two students, Bob and Jay, sit in identical office chairs facing each
other. Bob has a mass of 100 kg and Jay has a mass of 70 kg. Both
Bob and Jay place their feet against the other. They then both
suddenly push outward with their feet at the same time, causing
both chairs to move. In this situation, while their feet are still in
contact, which of the following choices describes the force?
a. Jay exerts a force on Bob, but Bob doesn’t exert a force on Jay.
b. Bob exerts a force on Jay, but Jay doesn’t exert a force on Bob.
c. Each student exerts a force on the other, but Jay exerts the larger
force.
d. Each student exerts a force on the other, but Bob exerts the larger
force.
e. Each student exerts the same amount of force on the other.
f. None of the above is appropriate. Write in your response.
Student Response - Mass
They found
consistent wrong
model used.
Question 1
3%
8%
Smaller
38%
Bigger
Same *
None
51%
•
Question 2
Car 1 traveling along the street and collides
with a stationary car. Both cars are the same
mass. Which statements describe the forces
involved?
a. The stationary car exerts a larger force on the
moving car.
b. The moving car exerts a larger force on the
stationary car.
c. Both cars will feel the same force.
d. Only the stationary car will feel a force.
e. You cannot tell from the given information.
Student Response - Velocity
They found
consistent wrong
model used.
Question 2
4%
1%
Stationary
Moving
44%
51%
Same *
Can't tell
Question 3
•
Two cars are traveling towards each other. One
car is going at 40 mph while the other car is
traveling at 60 mph. Which statements describe
the forces involved during the collision?
a.
b.
c.
d.
The faster car feels a larger force than the slower car.
The slower car feels a larger force than the faster car.
Both cars will feel the same force.
Only the slower car will feel a force.
Student Response Velocity
They found
consistent wrong
model used.
Question 3
2% 7%
Faster
35%
Slower
Same *
56%
Only slower
Question 4
•
Two cars traveling in the same direction collide.
One car is traveling at 40 mph while the other
car is traveling at 60 mph. Which statements
describe the forces involved during the
collision?
a.
b.
c.
d.
The faster car feels a larger force than the slower car.
The slower car feels a larger force than the faster car.
Both cars will feel the same force.
Only the slower car will feel a force.
Student Response 4
Question 4
They found
consistent wrong
model used.
3%
8%
Faster
33%
Slower
Same *
56%
Only slower
Question 5
•
Car 1 traveling along the street and collides with
a stationary car 2. Both cars are the same mass.
Which statements below describe the magnitude
of the acceleration on the cars?
a.
b.
c.
d.
e.
Car 1 will have a larger acceleration than car 2.
Car 2 will have a larger acceleration than car 1.
Both cars will have the same acceleration.
Only the stationary car will feel acceleration.
You cannot tell from the given information.
Student Response
They found
consistent correct
model used.
Question 5
12%
14%
Car 1
18%
Car 2
Same *
27%
Only car 2
Can't tell
29%
Compare/Contrast Results
• Velocity 
– They found – consistent wrong model
– We found agreement
• Mass 
– They found – consistent wrong model
– We found agreement
• Pushing 
– They found – inconsistent wrong response
– We found – Now that I look at it my questions don’t
address this model.
• Acceleration 
– They found – consistent correct response
– We found – very erratic data. Lowest % correct
```