important underlying structures of the whole nonnormative answer network. Alternative reasoning procedures that involve student alternative conceptions are
represented in Modules including high correlations among nonnormative answers
to different questions, and some interesting interpretations are supplied. However, it
is worth to note that the analysis provides information about patterns of
nonnormative answers, but “the drawback is that we cannot investigate how these
patterns relate to normative responses”, as the authors state (Brewe et al. 2016).
In the literature some studies using Cluster Analysis (ClA) methods and
concerning research in education are found. ClA methods can separate a sample of
students into subgroups so that students belonging to the same subgroup are more
similar to each other than those are not belonging in the same ones. These subgroups
can be studied to characterise students’ answers of open-ended questionnaires
(Springuel et al. 2007; Fazio et al. 2013; Battaglia and Di Paola 2015; Di Paola
et al. 2016; Battaglia et al. 2017a, b; Battaglia et al. 2019) or multiple-choice tests
(Stewart et al. 2012). All these papers show that the use of ClA leads to individuate
groups of students whose characterisation makes sense to researchers. In a recent
paper, Stewart et al. (2012) analyse the student answers to seven questions by using
Model Analysis. They study the state of student’s knowledge and ClA methods to
characterise the distribution of students’ answers. They show that ClA is an effective
method to inquiry the student understanding and to discover subgroups of a data set
mathematically well-defined and meaningful for the researcher.
15.3 The Research Question
Hestenes et al. (1992) as well as successive researchers have divided the FCI test in
different conceptual dimensions (Hestenes and Halloun 1995). We want to investigate the student understanding of two of such dimensions, and making diagnostic
inferences about student knowledge. The research question that guided our study is:
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?
15.4 Methodology and Sample
15.4.1 The Sample
We administered the FCI test just at the beginning of an activity that the authors
proposed as an optional course about Newtonian Mechanics. The sample was
composed of 148 freshman engineering students. We analysed all the students
who answered to more than 80% of the questions. For this reason, we analysed a
subsample composed of 116 students (73.3% male and 26.7% female).
15 Freshman Engineering’ Reasoning Strategies When Answering FCI. . .
191
represented in Modules including high correlations among nonnormative answers
to different questions, and some interesting interpretations are supplied. However, it
is worth to note that the analysis provides information about patterns of
nonnormative answers, but “the drawback is that we cannot investigate how these
patterns relate to normative responses”, as the authors state (Brewe et al. 2016).
In the literature some studies using Cluster Analysis (ClA) methods and
concerning research in education are found. ClA methods can separate a sample of
students into subgroups so that students belonging to the same subgroup are more
similar to each other than those are not belonging in the same ones. These subgroups
can be studied to characterise students’ answers of open-ended questionnaires
(Springuel et al. 2007; Fazio et al. 2013; Battaglia and Di Paola 2015; Di Paola
et al. 2016; Battaglia et al. 2017a, b; Battaglia et al. 2019) or multiple-choice tests
(Stewart et al. 2012). All these papers show that the use of ClA leads to individuate
groups of students whose characterisation makes sense to researchers. In a recent
paper, Stewart et al. (2012) analyse the student answers to seven questions by using
Model Analysis. They study the state of student’s knowledge and ClA methods to
characterise the distribution of students’ answers. They show that ClA is an effective
method to inquiry the student understanding and to discover subgroups of a data set
mathematically well-defined and meaningful for the researcher.
15.3 The Research Question
Hestenes et al. (1992) as well as successive researchers have divided the FCI test in
different conceptual dimensions (Hestenes and Halloun 1995). We want to investigate the student understanding of two of such dimensions, and making diagnostic
inferences about student knowledge. The research question that guided our study is:
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?
15.4 Methodology and Sample
15.4.1 The Sample
We administered the FCI test just at the beginning of an activity that the authors
proposed as an optional course about Newtonian Mechanics. The sample was
composed of 148 freshman engineering students. We analysed all the students
who answered to more than 80% of the questions. For this reason, we analysed a
subsample composed of 116 students (73.3% male and 26.7% female).
15 Freshman Engineering’ Reasoning Strategies When Answering FCI. . .
191