The Concept of Force and the Mechanics Curriculum

Terry ScottAndrew Gray

Daniel Schumayer

StatisticianNot a Statistician

Minion

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

The Force Concept Inventory

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.

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.

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?

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

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.

Factor 1 – Identification of Forces.

Factor 2 – Newton’s First

Factor 3 – Newton’s Second

Factor 4 – Newton’s First Again

Third Law/First Law conflation – Qu.16

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.

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.