longer in contact with the agent applying the impulse” may have been the cause of
the students’ incorrect answers.
The Students in Cl 2 subA cluster supply correct answers to questions Q6, Q8,
Q12, and Q21. These require the description of the motion of dynamic systems or the
prediction of trajectories. However, the same students give incorrect answers in the
case of questions involving explanations of the kinematic variable and the individuation of trajectories. Moreover, they fail to give a correct answer to questions that
mainly require Newtonian explanations about the motions.
The students in by Cl 3 subA cluster supplied correct answers to questions Q6, Q7,
Q12 that require the ability to describe motions and predicting trajectories. Moreover, the same students correctly solved questions Q3, Q9, Q22, Q24 requiring the
ability to use the first and second Newtonian laws to find an explanation. Questions
Q8, Q17, Q25, Q26 show high percentages of incorrect answers indicating in our
students a persistent of naïve conceptions as that “persistence of original impetus”,
“largest force determines motion”, or “motion is possible when forces overcome
resistance” (Hestenes and Halloun 1995). Coherently with the previous description,
the students in Cl 3 subA answer that for an elevator lifting up by a rope at a constant
velocity the rope tension is greater than the force of gravity (17A). The idea that a
constant force makes a body moving with a constant velocity is made explicit by the
students in answers 25D and 26B. Differently, such students use a different model in
answering question Q3 (3C). In this case, they clearly see an increase in the velocity
for a falling object since the force of gravity is constant. Many nonnormative
conceptions above described are strictly connected with the “Impetus Module”
pointed out by Brewe et al. (2016).
As a second step, we performed the same analysis described above to obtain a
partition of our student sample according to their answers to the six questions
classified as SubB. The number, q, of clusters that best partitions our student sample
was obtained through the maximisation of the mean value of S-function, hS(q)i,
calculated for q values from 2 to 4 and their 95% C.I.
We obtained hS(2)i ¼ 0.68 (C.I. ¼ 0.65–0.70), hS(3)i ¼ 0.69 (C.I. ¼ 0.64–0.73),
hS(4)i ¼ 0.62 (C.I. ¼ 0.59–0.64).
As in the analysis of SubA, in this case, we found that the hS(q)i values for q ¼ 2
and q ¼ 3 are comparable. Again, we perform a further analysis by using the VRC
and obtained for the results into three clusters the highest value (VRC(3) ¼ 219 and
VRC(2) ¼ 149).
Figure 15.2 reports the clustering solution into three different groups called
Cl 1 subB, Cl 2 subB, Cl 3 subB. Table 15.3 shows the most frequent answers supplied
by students in different clusters, with correct answers in bold characters
Students in cluster Cl 1 sub correctly interpret the forces as quantities that describe
the interaction between bodies. However, they also cite a kind of force that seems to
be directly connected to the body velocity or to some hit supplied to it as a “force due
to the motion” or “supplied by a hit”). We can conclude that students comprised in
this cluster are characterised by a “hybrid” (Ding and Beichner 2009) or “synthetic”
(Gilbert and Boulter 1998) conception of force. This idea of force unifies different
features of the naïve conceptions (“obstacles exert no force” or “motion implies
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O. R. Battaglia and C. Fazio
the students’ incorrect answers.
The Students in Cl 2 subA cluster supply correct answers to questions Q6, Q8,
Q12, and Q21. These require the description of the motion of dynamic systems or the
prediction of trajectories. However, the same students give incorrect answers in the
case of questions involving explanations of the kinematic variable and the individuation of trajectories. Moreover, they fail to give a correct answer to questions that
mainly require Newtonian explanations about the motions.
The students in by Cl 3 subA cluster supplied correct answers to questions Q6, Q7,
Q12 that require the ability to describe motions and predicting trajectories. Moreover, the same students correctly solved questions Q3, Q9, Q22, Q24 requiring the
ability to use the first and second Newtonian laws to find an explanation. Questions
Q8, Q17, Q25, Q26 show high percentages of incorrect answers indicating in our
students a persistent of naïve conceptions as that “persistence of original impetus”,
“largest force determines motion”, or “motion is possible when forces overcome
resistance” (Hestenes and Halloun 1995). Coherently with the previous description,
the students in Cl 3 subA answer that for an elevator lifting up by a rope at a constant
velocity the rope tension is greater than the force of gravity (17A). The idea that a
constant force makes a body moving with a constant velocity is made explicit by the
students in answers 25D and 26B. Differently, such students use a different model in
answering question Q3 (3C). In this case, they clearly see an increase in the velocity
for a falling object since the force of gravity is constant. Many nonnormative
conceptions above described are strictly connected with the “Impetus Module”
pointed out by Brewe et al. (2016).
As a second step, we performed the same analysis described above to obtain a
partition of our student sample according to their answers to the six questions
classified as SubB. The number, q, of clusters that best partitions our student sample
was obtained through the maximisation of the mean value of S-function, hS(q)i,
calculated for q values from 2 to 4 and their 95% C.I.
We obtained hS(2)i ¼ 0.68 (C.I. ¼ 0.65–0.70), hS(3)i ¼ 0.69 (C.I. ¼ 0.64–0.73),
hS(4)i ¼ 0.62 (C.I. ¼ 0.59–0.64).
As in the analysis of SubA, in this case, we found that the hS(q)i values for q ¼ 2
and q ¼ 3 are comparable. Again, we perform a further analysis by using the VRC
and obtained for the results into three clusters the highest value (VRC(3) ¼ 219 and
VRC(2) ¼ 149).
Figure 15.2 reports the clustering solution into three different groups called
Cl 1 subB, Cl 2 subB, Cl 3 subB. Table 15.3 shows the most frequent answers supplied
by students in different clusters, with correct answers in bold characters
Students in cluster Cl 1 sub correctly interpret the forces as quantities that describe
the interaction between bodies. However, they also cite a kind of force that seems to
be directly connected to the body velocity or to some hit supplied to it as a “force due
to the motion” or “supplied by a hit”). We can conclude that students comprised in
this cluster are characterised by a “hybrid” (Ding and Beichner 2009) or “synthetic”
(Gilbert and Boulter 1998) conception of force. This idea of force unifies different
features of the naïve conceptions (“obstacles exert no force” or “motion implies
196
O. R. Battaglia and C. Fazio