1. The Concept of Force and the
Mechanics Curriculum
Terry Scott Statistician
Not a Statistician Andrew Gray
Daniel Schumayer
Minion

2. The Force Concept Inventory
• Concept Inventory rather than a “test”.
• 30 multichoice questions.
• Very good distractors:
– Guessing success very low
– Reliability unusually high
– Pre and post test design seems to work well

3. The Force Concept Inventory

4. FCI - Uses
• Standard uses:
– Evaluate development of conceptual
understanding.
– Evaluate teaching methods.
• Our research:
– Search for conceptual coherence.
– Understand associations in student mind.
– Inform teaching method.
– Suggest future research.

5. Data Collection
• FCI delivered online (Blackboard)
• PHSI191 – Large Health Science service
course.
• 2000 student responses collected over two
years, 2008 and 2009.
• Not obligatory.
• Data checked for disengaged responses
– 50 response sets removed.

6. Data Analysis
• Exploratory Factor Analysis
– Construct correlation matrix (using tetrachoric
correlations)
– Find eigenvalues/eigenvectors.
• What does this mean?
– Factors = latent traits/concepts
– Factors represent student understanding of force.
• How do students group questions, which questions are
about the same thing?
• How does this compare with the way experts group
questions?

7. Interpretation
• 5 factors found in the analysis.
• These factors are not orthogonal
– Correlations between factors – useful
information
• Clear that there is conceptual coherence
in the data.
• Better score = greater conceptual
coherence?
– No evidence, not enough data

8. The Factors
• Factor 1 – Identification of forces.
• Factor 2 – Newton’s first law, linear and
curved paths.
• Factor 3 – Newton’s second law +
necessary concepts
(acceleration, velocity).
• Factor 4 – Newton’s first law with zero net
force.
• Factor 5 – Newton’s third law.

9. Factor 1 – Identification of
Forces.

10. Factor 2 – Newton’s First

11. Factor 3 – Newton’s Second

12. Factor 4 – Newton’s First Again

13. Third Law/First Law conflation –
Qu.16

14. Kinematics?
• Authors of the FCI included a number of
questions solely about kinematics
concepts.
• We find no factor containing only
kinematics questions.
• Kinematics questions are distributed
“where they are needed” in factors about
force laws.

15. Item Response Analysis -
Preliminary
• Preliminary results
• Show third law questions significantly
higher difficulty that other questions
• Marginal analysis
– Assess student ability, predict the questions
they will get right.
– Anomalous numbers of students get 3rd law
questions right but 1st and 2nd law questions
wrong.