15.4.2 FCI Questionnaire
FCI is a multiple-choice questionnaire and it was presented for the first time in a
paper published in 1995 (Hestenes and Halloun 1995). It is made of 30 multiplechoice questions (each question has five possible answers). The 1995 version
included a classification of the Newtonian force concept investigated in the questionnaire in different dimensions. The FC authors reported a decomposition of the
force concept into six conceptual dimensions by highlighting that all six dimensions
are fundamental for the Newtonian force concept. In another paper (Hestenes and
Jackson 2007) another table with a taxonomy of common-sense misconceptions
related to the Newtonian mechanics, and the corresponding Inventory questions is
proposed.
Here, we define a different categorisation of the 30 FCI questions in four
categories or subtests as listed below.
• SubA includes 15 questions. Each question requires to apply Newton’s first
and/or second laws. Students have to choose among the different five answers
that contains description of trajectories, kinematics quantities and/or
explanations.
1
• SubB includes questions that allow the researcher to evaluate student ability in
identifying interactions between bodies and related forces in different dynamical
or static contexts.
• SubC includes questions involving the Newton’s third law. They require to
identify action and reaction forces acting on bodies in dynamical or static
conditions.
• SubD includes questions requiring student to describe motions by using the
kinematics quantities and laws.
Table 15.1 reports our classification of FCI questions according to the criteria
above described.
15.4.3 Data Coding and k-Means Algorithm
We quantitatively analyse the answers students give to the questionnaire by using
Cluster Analysis (ClA). ClA methods allow us to generate groups of students by
partitioning it and producing a set of non-overlapping clusters. We decided to apply
the k-means algorithm (MacQueen 1967), because of its efficiency and simplicity.
This algorithm requires a coding of the answers. We code the FCI students’
answers by using a binary code and generate a binary matrix, called “matrix of
answering choices”. It is made of N rows and M columns. In this matrix, each row
1 We included questions involving Newton’s first or second law in the same subtest. Such a view can
be also pointed out from the analysis of other interview studies (Brokes and Etkina 2009).
192
O. R. Battaglia and C. Fazio
FCI is a multiple-choice questionnaire and it was presented for the first time in a
paper published in 1995 (Hestenes and Halloun 1995). It is made of 30 multiplechoice questions (each question has five possible answers). The 1995 version
included a classification of the Newtonian force concept investigated in the questionnaire in different dimensions. The FC authors reported a decomposition of the
force concept into six conceptual dimensions by highlighting that all six dimensions
are fundamental for the Newtonian force concept. In another paper (Hestenes and
Jackson 2007) another table with a taxonomy of common-sense misconceptions
related to the Newtonian mechanics, and the corresponding Inventory questions is
proposed.
Here, we define a different categorisation of the 30 FCI questions in four
categories or subtests as listed below.
• SubA includes 15 questions. Each question requires to apply Newton’s first
and/or second laws. Students have to choose among the different five answers
that contains description of trajectories, kinematics quantities and/or
explanations.
1
• SubB includes questions that allow the researcher to evaluate student ability in
identifying interactions between bodies and related forces in different dynamical
or static contexts.
• SubC includes questions involving the Newton’s third law. They require to
identify action and reaction forces acting on bodies in dynamical or static
conditions.
• SubD includes questions requiring student to describe motions by using the
kinematics quantities and laws.
Table 15.1 reports our classification of FCI questions according to the criteria
above described.
15.4.3 Data Coding and k-Means Algorithm
We quantitatively analyse the answers students give to the questionnaire by using
Cluster Analysis (ClA). ClA methods allow us to generate groups of students by
partitioning it and producing a set of non-overlapping clusters. We decided to apply
the k-means algorithm (MacQueen 1967), because of its efficiency and simplicity.
This algorithm requires a coding of the answers. We code the FCI students’
answers by using a binary code and generate a binary matrix, called “matrix of
answering choices”. It is made of N rows and M columns. In this matrix, each row
1 We included questions involving Newton’s first or second law in the same subtest. Such a view can
be also pointed out from the analysis of other interview studies (Brokes and Etkina 2009).
192
O. R. Battaglia and C. Fazio