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? Jay exerts a force on Bob, but Bob doesn’t exert a force on Jay. Bob exerts a force on Jay, but Jay doesn’t 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.

Student Response - Mass They found consistent wrong model used.

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.

Student Response - Velocity They found consistent wrong model used.

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.

Student Response Velocity They found consistent wrong model used.

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.

Student Response 4 They found consistent wrong model used.

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.

Student Response They found consistent correct model used.

Compare/Contrast Results Velocity  They found – consistent wrong model We found agreement Mass  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