15.6 Discussion
The results above described allow us to answer our research question: “To what
extent can a ClA method reveal students’ reasoning profiles of Newtonian mechanics
understanding when they answer FCI questions about the first and second laws and
the concept of force?”
The results above described show that the k-means algorithm can be a useful tool
to discover latent structures within the answers on the FCI test. We highlight a
cluster of students with similar answers and such clusters are characterised by correct
answers as well as by non- correct answers. Moreover, these latter have allowed us to
identify student’s misconceptions/nonnormative conceptions.
The method we used can identify in detail the status of knowledge of the students.
We discover dominant/prevalent behaviours, and these can allow us to infer the
characteristics of models used by students in different contexts.
The main results, obtained by our analysis of FCI answers supplied by our
students characterised by a low level of understanding of the Newtonian dynamics,
allow us to answer our research question, as reported below.
By analysing the student understanding of dynamical characteristics of motions
we note that the majority of our students can’t supply a Newtonian explanation of
such motions (by applying the first and/or second Newtonian laws). They show in
some contexts a correct ability to describe trajectories, but not to explain them in the
theoretical framework of the Newtonian Mechanics. This ability can be attributed
mostly to their common life experience. Only a small number of students are able to
supply correct answers to questions requiring explicative skills, but only in given
contexts.
The majority of students in our sample when is required to identify forces acting
on a moving body only think on the gravitational force and/or “motion force” or
“impetus force”. They almost completely omit the reaction forces. Such students are
characterised by a naïve idea of force, widely discussed in the literature (see Brookes
and Etkina 2009 and included references) and connected with several other misconceptions (“obstacles exert no force” or “motion always implies active force” or
“velocity proportional to active force”) (Hestenes and Jackson 2007). Together with
this naïve idea of force, only a small group of students has a Newtonian concept of
force as a quantity to describe the interaction between objects. In their minds, these
two absolutely different ideas seem to coexist, as several studies also pointed out
(Brookes and Etkina 2009). Finally, it is worth to highlight that, despite such a mixed
idea of force, these students are able to use the first and second Newton laws and to
identify correct relationships between force and motion only in some contexts.
198
O. R. Battaglia and C. Fazio
The results above described allow us to answer our research question: “To what
extent can a ClA method reveal students’ reasoning profiles of Newtonian mechanics
understanding when they answer FCI questions about the first and second laws and
the concept of force?”
The results above described show that the k-means algorithm can be a useful tool
to discover latent structures within the answers on the FCI test. We highlight a
cluster of students with similar answers and such clusters are characterised by correct
answers as well as by non- correct answers. Moreover, these latter have allowed us to
identify student’s misconceptions/nonnormative conceptions.
The method we used can identify in detail the status of knowledge of the students.
We discover dominant/prevalent behaviours, and these can allow us to infer the
characteristics of models used by students in different contexts.
The main results, obtained by our analysis of FCI answers supplied by our
students characterised by a low level of understanding of the Newtonian dynamics,
allow us to answer our research question, as reported below.
By analysing the student understanding of dynamical characteristics of motions
we note that the majority of our students can’t supply a Newtonian explanation of
such motions (by applying the first and/or second Newtonian laws). They show in
some contexts a correct ability to describe trajectories, but not to explain them in the
theoretical framework of the Newtonian Mechanics. This ability can be attributed
mostly to their common life experience. Only a small number of students are able to
supply correct answers to questions requiring explicative skills, but only in given
contexts.
The majority of students in our sample when is required to identify forces acting
on a moving body only think on the gravitational force and/or “motion force” or
“impetus force”. They almost completely omit the reaction forces. Such students are
characterised by a naïve idea of force, widely discussed in the literature (see Brookes
and Etkina 2009 and included references) and connected with several other misconceptions (“obstacles exert no force” or “motion always implies active force” or
“velocity proportional to active force”) (Hestenes and Jackson 2007). Together with
this naïve idea of force, only a small group of students has a Newtonian concept of
force as a quantity to describe the interaction between objects. In their minds, these
two absolutely different ideas seem to coexist, as several studies also pointed out
(Brookes and Etkina 2009). Finally, it is worth to highlight that, despite such a mixed
idea of force, these students are able to use the first and second Newton laws and to
identify correct relationships between force and motion only in some contexts.
198
O. R. Battaglia and C. Fazio