Incorrect reasoning is context dependent

1
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

2
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

3
A personal example

• Students can correctly answer
• Is a net force acting on an object traveling at
  constant velocity?
• What is Newtons 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!

4
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

5
Contextual features

• Velocity
• Acceleration
• Pushing
• Mass

6
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?

7
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

8
THE DATA

• Number of Students ? 280
• Abilities gt 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
9
Concentration Factor?

• C gt 0.5 ? High concentration factor
• 0.2 ltClt 0.5 ? Medium concentration factor
• C lt 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.

10
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?
• Jay exerts a force on Bob, but Bob doesnt exert
  a force on Jay.
• Bob exerts a force on Jay, but Jay doesnt exert
  a force on Bob.
• Each student exerts a force on the other, but Jay
  exerts the larger force.
• Each student exerts a force on the other, but Bob
  exerts the larger force.
• Each student exerts the same amount of force on
  the other.
• None of the above is appropriate. Write in your
  response.

11
Student Response - Mass
They found consistent wrong model used.
12
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?
• The stationary car exerts a larger force on the
  moving car.
• The moving car exerts a larger force on the
  stationary car.
• Both cars will feel the same force.
• Only the stationary car will feel a force.
• You cannot tell from the given information.

13
Student Response - Velocity
They found consistent wrong model used.
14
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?
• 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.

15
Student Response Velocity
They found consistent wrong model used.
16
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?
• 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.

17
Student Response 4
They found consistent wrong model used.
18
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?
• 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.

19
Student Response
They found consistent correct model used.
20
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
  dont address this model.
• Acceleration ?
• They found consistent correct response
• We found very erratic data. Lowest correct