Scientia et Technica Año XXVIII, Vol. 28, No. 03, julio-septiembre de 2023. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214
144
Evaluation of Newton's Law Learning:
Application of the Force Concept Inventory
Evaluación del aprendizaje de las leyes de Newton: Aplicación del Inventario del
Concepto de Fuerza
C. A. Hernández-Suárez ; R. Prada-Núñez ; F. Álvarez-Macea
DOI: https://doi.org/10.22517/23447214.24530
Scientific and technological research article
Abstract—The Force Concept Inventory is a test to determine the
level of conceptual knowledge of students about mechanical
physics and to evaluate the effectiveness of different teaching
strategies on the conceptual component of learning. The test was
applied with the purpose of knowing the level of conceptualization
of the students who study the subject of Physics in a basic and
medium educational institution. The results of the pre-test gave to
know the students' level of conceptualization and offered
information for the elaboration of workshops based on real
physical situations to elaborate force diagrams. The results of the
post-test allowed estimating Hake's learning gain and showed
evidence about the students' conceptual evolution and information
to develop future teaching activities about Newton's laws.
Index Terms— Dynamics, Force Physics education, Law, Pre-
college programs.
Resumen—El Inventario de Conceptos de Fuerzas es una
prueba para determinar el nivel de conocimiento conceptual de los
estudiantes sobre física mecánica y para evaluar la efectividad de
las diferentes estrategias de enseñanza sobre el componente
conceptual del aprendizaje. La prueba se aplicó con el propósito
de conocer el nivel de conceptualización de los estudiantes que
estudian la asignatura de Física en una institución educativa
básica y media. Los resultados del pretest permitieron conocer el
nivel de conceptualización de los estudiantes y ofrecieron
información para la elaboración de talleres basados en situaciones
físicas reales para elaborar diagramas de fuerza. Los resultados
del postest permitieron estimar el aprendizaje de Hake y
mostraron evidencias sobre la evolución conceptual de los
estudiantes e información para desarrollar futuras actividades de
enseñanza sobre las leyes de Newton.
Palabras claves— Dinámica, Educación en Física, Fuerza, Leyes,
Programas preuniversitarios.
I.
INTRODUCTION
N mechanical physics, the concept of force is fundamental in
academic programs in Science and Engineering, so students
(who come from pre-university education), need to
conceptualize it to apply Newton's laws in the resolution of
different concrete problem situations.
One of the curricular orientations for the teaching of Natural
Sciences in secondary education (by the Ministry of National
Education of Colombia), is related to the theoretical and
practical foundations of classical mechanics, from the
movement of bodies and their interactions, the concept of force,
work and energy, supported by mathematical modelling, for the
explanation of situations in nature [1, 2].
Therefore, the students' learning, before focusing on
algorithmic and algebraic procedures, must be oriented towards
a conceptual domain that allows them to understand the laws
and the explanation of physical phenomena, since, when
approaching the solution of a problem, it is decontextualized
from the conceptual arguments of Physics. This adds to the
inherent difficulty of concepts and their relationships to be
understood; acceleration and force, equivalence between rest
state and movement with constant speed, inertial and non-
inertial systems, among others [3].
One of the difficulties that hinder the learning of Mechanical
Physics is related to the erroneous preconceptions of the
students [4], that are born from the daily experience that lead to
internalize incorrect relations between different physical
magnitudes, for example, to use the term force in a variety of
contexts, using vague and ambiguous associations [5], which
are difficult to modify in structural terms.
The personal construct of students' previous ideas are
representational schemes that do not model adequate scientific
conceptions, thus becoming an obstacle that does not favor
2023.
This manuscript was sent on June 20, 2021 and accepted on June 20, Universidad Experimental del Táchira, Venezuela. Urbanization Altos del
Tamarindo Casa 9, Villa del Rosario, Colombia. Professor at Universidad
C. A. Hernández-Suárez, Bachelor's degree in Mathematics and Computer
Science from Universidad Francisco de Paula Santander, Master's degree in
Science Education from Universidad Experimental del Táchira, Venezuela.
Calle 14 # 3-23 Urbanización Garcíaherreros, Cúcuta, Colombia. Professor at
Universidad Francisco de Paula Santander, Cúcuta, Colombia (e-mail:
cesaraugusto@ufps.edu.co).
R. Prada-Núñez, B.Sc. in Mathematics and Computer Science, Universidad
Francisco de Paula Santander, M.Sc. in Mathematics, mention in Education,
Francisco de Paula Santander, Cúcuta, Colombia (e-mail:
raulprada@ufps.edu.co).
F. R. Álvarez-Macea, B.Sc. in Mathematics and Physics, Universidad de
Antioquia, M.Sc. in Natural Sciences Teaching, Universidad Nacional de
Colombia, Medellín, Colombia. Calle 67 # 53-108 Medellín, Colombia.
Professor at the University of Antioquia (e-mail: fermin.alvarez@udea.edu.co).
I
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conceptual change [6] despite teaching attempts.
Therefore, helping a conceptual change requires teaching
activities that start from what the student knows, in a social
teaching context [7, 8], that favor the clear, stable and organized
reconstruction of knowledge with which they can face and solve
diverse situations and, at the same time, acquire knowledge that
demands a higher level of abstraction within the same field.
The intervention developed in this study that has as its axis
of analysis the consistent representation of the interactions
between systems through the so-called force diagrams (free
body diagrams) [9], is based on the perspective of collaborative
learning that is based on the psychological theory the
sociocultural theory [7] and of cognitive development [10].
On the other hand, the Force Concept Inventory (FCI) [11,
12] evaluates the degree of understanding of concepts in
Mechanical Physics. It is usually used as a pre-test/post-test
(Hake's factor [13]) to determine the effectiveness of some
teaching strategies used during students' conceptual learning.
There are studies on the application of FCI in university
students in the United States, Spain and some Latin American
countries [3, 14] but no studies are recorded in basic education
students, which is where students are beginning to build their
ideas of the physical concepts that will be used later in
secondary and university education.
In accordance with the above, from the framework of the
implementation of this strategy in the Physics subject in an
educational institution of basic and secondary education, the
hypothesis raised consists in whether the teaching of Newton's
laws from the perspective of collaborative learning through the
use of force diagrams allowed a conceptual evolution of their
learning. For this purpose, the FCI and Hake's factor were
applied to know the students' conceptual level in relation to the
concepts of Mechanical Physics.
II.
METHOD
A.
Approach and design
The research was done under the quantitative paradigm, with
intentional sampling, because the target groups are formed
through entry mechanisms outside of teachers' control. The
design was quasi-experimental, in which the Force Concept
Inventory [11] was applied as a pre-test, to explore the
preconceptions of Newtonian mechanics that students had,
followed by an teaching intervention [7, 10] with the following
activities: design, implementation and application of
workshops based on real physical situations and where the
elaboration of force diagrams is the central axis. At the end of
the intervention, the FCI was applied again as a post-test
allowing to estimate the so-called Hake's learning gain [13].
B.
Population and sample
The implementation of the proposal was developed in 40
10th grade students divided into two groups belonging to an
educational institution located in Norte de Santander,
Colombia. The ages of the students are between 14 and 16 years
course in their academic training. All the young people who
participated in the implementation of the experience were
informed orally about the nature and purposes of the
experience; their response was of unanimous acceptance of
wanting to participate actively in the process. In addition, they
were informed of the commitment made with the institutional
directives to deliver a copy of the project and its results, which
will be available for any type of consultation.
C.
Instruments
Force Concept Inventory (FCI). Is a test designed by
Hestenes, Wells and Swackhammer in 1992 that measures the
understanding of the basic concepts of Newtonian mechanics,
the didactic efficiency of the teaching-learning process of the
latter, and allows to detect the preconceptions that it has he
evaluated on this subject [11, 12]. The FCI is composed of 30
questions. The advantage of the FCI is that it allows to
determine the level of knowledge of mechanics, to evaluate the
didactic efficiency of the teaching-learning process, the degree
of comprehension, to detect and to classify the conceptual
errors incurred by the students and their preconceptions and
their evolution in time [16, 17]. The FCI was used in its Spanish
version [18] with questions with 5 answer options, grouped into
the following categories [11]: Cinematics; Newton's First Law
(Inertia); Newton's Second Law (Force and Acceleration);
Newton's Third Law (Action and reaction); Principle of
overlap; Types of force; This instrument was used because it
measures (in a certain sense) the ability of Newtonian thought
[19]. A high score on the FCI does not indicate a unified
knowledge of the concept of force, however, a low score
indicates a lack of knowledge of basic Newtonian concepts.
Free-Body diagram (FBD). Also called force diagram [5] of
a body or a group of bodies (or a part of a body) which is called
a system and is represented in isolation from its environment,
where all the external forces acting on it are shown, allowing
the modelling of a body and its interactions with its
surroundings. The modelling process allows to solve problems
by simplifying the situations to be studied, therefore, it will be
incomplete and inaccurate, but it will serve to explain and
predict the behavior of an object or system; the model will be
valid if the analytical results are experimentally verified.
The Hake factor. Also called relative gain of conceptual
learning, indicates the average real gain of standardized
conceptual learning [13]. It is used to determine the level of
conceptual learning achievements in the implementation of a
didactic strategy, that is, with the results of an evaluation (pre-
test and post-test) the impact on the assimilation of type
knowledge is determined conceptual. In the case of this
proposal, the g factor allows to establish the changes achieved
in the different dimensions of the FCI when implementing a
didactic strategy, since the low, medium and high levels of
achievement in the g factor are related to the level of conceptual
mastery of the phases of the FCI. For the calculation of the
Hake's factor � the Equation (1) is used [13]:
𝐹𝐶𝐼
𝑝𝑜𝑠𝑡
(
%
)
−𝐹𝐶𝐼
𝑝𝑟𝑒
(%)
old. It should be noted that this is the first introductory physics
�
=
100−𝐹𝐶𝐼
𝑝𝑟𝑒
(1)
(%)
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Scientia et Technica Año XXVIII, Vol. 28, No. 03, julio-septiembre de 2023. Universidad Tecnológica de Pereira
This factor can take values between 0 and 1, where 0
represents no learning, while 1 corresponds to the maximum
possible learning. Establishing with the relative learning gain
it is possible to classify three levels of achievement, these are:
High: � > 0.7
Medium: 0.3 < 𝑔 ≤ 0.7
Low: 0 ≤ 𝑔 ≤ 0.3
D.
Data collection procedure
Application of the FCI pre-test. To analyze the initial state
(preconceptions and diagnosis) that the students of mechanical
TABLE II
AVERAGE PERCENTAGE OF SUCCESS IN THE PRE-TEST AND POST-TEST AND GAIN OF
THE HAKE INDEX OF THE TARGET GROUP
Topic
First law
% Pretest
27.25
%Postest
58.00
Hak
0.42
e Index
medium
Second law
31.92
57.85
0.38
medium
Third law
56.00
83.50
0.63
medium
Force classes
32.15
58.71
0.39
medium
Cinematics
39.45
68.21
0.47
medium
physics had, the modified FCI in their numbering was applied
as a pre-test (only 20 items were taken: 1, 2, 3, 4, 7, 13, 14 , 15,
16, 17, 18, 21, 22, 23, 24, 25, 26, 27, 28, 29). The selected
questions were directed to reach the conceptual levels of the
students proposed in their area plan related to the concepts of
force and proper Newton's laws. To perform the analysis, it was
divided into fundamental aspects defined by groups of topics
(TABLE I).
Didactic interventions. The classes were of a theoretical-
experimental type where inclined planes, wooden blocks,
laboratory pulleys, dynamometer, chronometers, pita ropes and
power table were used. These activities were carried out in 20
hours of class attendance. For the didactic interventions related
to the subject of cinematics (5 exercises) it was analyzed if the
students have clear concepts of position, speed, and
acceleration; as well as if they recognize these physical
magnitudes as vector magnitudes.
For the topic of Newton's Laws (10 exercises), it was
identified if the students understand the approach of the law of
inertia (movement does not imply presence of external force.
TABLE I
CLASSIFICATION OF FCI QUESTIONS BY TOPIC
Topic Grouping of questions
Cinematics 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15.
Newton's first law 5, 7, 9, 10, 12, 13, 14, 15, 16 and 20.
Newton's Second 1, 2, 3, 5, 6, 7,8, 11, 12, 13, 14, 15, 17 and 18.
Newton's third law 4, 8, 9, 10 and 19.
Force classes 1, 2, 3, 5, 6, 7, 11 and 20.
We also analyzed the ideas they have about the cause of
movement and its implications in speed and acceleration.
Finally, the understanding of the interaction between two
bodies was investigated, due to the fact that it is common to
consider a dominance principle in which "the strongest exerts
the greatest force"; the strongest is usually the object with the
greatest dimension, the most activity and/or the greatest amount
of mass. This conflict leads to erroneous interpretations of this
law. For the analysis of the subject each exercise consists of
construction of force diagrams; decomposition of forces into
rectangular components, if necessary; presentation of the
equations of Newton's laws, and solution of the equations to
find the physical variable requested in each statement,
considering the data from each exercise.
For the topic types of force (20 exercises), we explored the
conception that they have of the term concept force; if they
recognize the force of contact (friction and normal), the forces
present by the action of the strings and the forces at a distance
as the force of gravity. In addition, for the construction of force
diagrams, the student considered the following protocol [20]:
•
Description of the physical situation.
•
Simplified representation of the physical situation.
•
Matrix representation of the interactions between systems.
•
Representation with closed dotted line of the physical
system(s) of interest.
•
Detailed list of the forces acting on the physical system(s)
of interest and assign a notation.
•
Representation of the forces (force diagram) acting on the
system(s) of interest.
•
Representation of forces by simplifying the model to a
particle (if possible).
•
Once the situation of the exercise to be solved has been
described and its simplified representation has been carried out,
it should be done:
o
Choose reference frame.
o
Select a coordinate system that is anchored to the
reference frame.
•
Make the decomposition of forces (rectangular
components) and proceed to apply Newton's laws of motion in
each direction.
•
Solve the equations.
•
Verify the results by performing some usual technique for
this purpose.
Application of the FCI post-test. Finally, the FCI was applied
again and the so-called learning gain was estimated using the
Hake factor of each of the five aspects into which the study was
divided.
III.
RESULTS AND DISCUSSION
A.
Pre-test and post-test results (FCI) and analysis of the
Hake Factor (learning gain)
The presentation and analysis of the results was done
considering the questions of the FCI (Table II). The results are
presented indicating the average percentage of success of the
FCI questions in their pre-test and post-test applications and the
calculation of the Hake factor to numerically visualize the level
of learning achieved (see Table II).
According to Hake's index, the learning gain, for each of the
subjects, is at the middle level, an index very similar to others
obtained in previous studies in the United States and Spain [15].
From the results of the table, it can also be highlighted that
Newton's third law had the highest mean level of gain (0.63),
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which can be attributed to the analysis of physical situations
with the use of force diagrams in association with the matrix
listing of interactions. The above is due to the understanding of
physical concepts rather than the mechanization of
mathematical formulas and the proper construction of force
diagrams.
In addition, for Newton's second law, it was the lowest level
of profit (0.38). This is because some students failed to relate
the acceleration to the resulting force; additionally, they
presented deficiencies in the handling of the equations that in
most of the cases were simultaneous. Here it is necessary to say
TABLE II
AVERAGE PERCENTAGE OF SUCCESS IN THE PRE-TEST AND POST-TEST AND GAIN OF
THE HAKE INDEX OF THE TARGET GROUP
Topic
% Pretest
%Postest
Hake Index
First law
27.25
58.00
0.42 medium
Second law
31.92
57.85
0.38 medium
Third law
56.00
83.50
0.63 medium
Force classes
32.15
58.71
0.39 medium
Cinematics 39.45 68.21 0.47 medium
that the time spent teaching this law was not enough. Some
studies show that the concept with the greatest difficulty is
Newton's second law [3, 14].
Additionally, similar proposals have been implemented
considering a control group (with traditional teaching),
obtaining an average learning gain for the experimental group
of 0.32 (medium) and for the control of 0.01 (low). [21].
Finally, between the application of the pre-test and the post-
test a progress in the students' understanding and correct
application of Newton's laws of motion is observed. The
previous evidence shows that didactic intervention on the use
of force diagrams (mental representations and their
characterization), favored the significant learning of Newton's
laws in basic education students, in comparison with previous
experiences developed in similar contexts [22].
B.
Force diagram analysis
The realization of the force diagrams of the different physical
situations allowed the student to evidence the understanding of
the phenomena studied. In this order of ideas, the following
advances in the learning of the concept of force and Newton's
laws are highlighted:
•
Construction of the interaction matrix, which contributed
to differentiate the action-reaction pairs easily.
•
Understanding sliding friction force.
•
Correct interpretation of the friction coefficient.
•
They adequately represent the external forces acting on the
physical system.
•
Improvements in mathematical procedures applied to the
resolution of physical problems and interpretation of physical
situations related to the environment.
•
The feedback made it easier for the students to construct
force diagrams.
•
Resolution of more complex exercises.
Among the difficulties presented, the following stand out:
•
The reference system or coordinates are not identified, and
the physical variable requested is not found.
•
Deficiencies in the handling of equations.
•
Confusion of the concepts weight and mass, as well as in
the nomenclature of forces.
•
Difficulty in understanding physical situations such as
underestimating friction, weightless pulleys and mass free
ropes that can help simplify a problem.
•
Incorrect Decomposition of Vectors into Rectangular
Coordinates
•
It is difficult in physical systems of three blocks to add
masses and unite them into one.
•
Difficulty to apply Newton's laws according to their cases.
•
Difficulties in formalizing force diagrams
•
Although the reference systems and coordinates, the
matrix, and the equations derived from the force schemes are
well posed, they have mathematical difficulties in solving the
problem.
Some of these difficulties in students coincide with those
found in previous studies on physical concepts [23]; and
especially concepts linked to the conception of Newton's laws
[24-28]. Another of the limitations found was the decrease in
the intensity of the weekly hours, due to the development of
various academic activities at the institution.
According to the results obtained from the didactic
implementation, and according to the instruments used, it is
evident that the students have obtained gains with respect to
conceptual learning, in the different components of the FCI.
Hake’s factor does not seek to evaluate the student himself, but
the teaching-learning process and the teacher's didactic
strategies. In relation to the above, it is possible to establish that
the use of force diagrams as a fundamental part in the teaching-
learning of Newton's laws, allowed students to advance towards
a high conceptual level, by improving their reasoning skills,
developing an understanding of concepts and solving more
complex problems [29]. This, together with a better attitude of
the students towards the study of physics.
IV.
CONCLUSION
After the analysis of the pre-test/post-test of the FCI, it is shown
that the didactic intervention that used the force diagrams as a
fundamental element in the teaching-learning of Newton's laws
allowed the systematic use of the interaction matrices of the
forces of the physical systems, the experimentation of Newton's
laws and their application to problematic situations achieving a
significant learning in the students who were the objects of
study.
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César Augusto Hernández Suárez was
born in Villa Caro, Norte de Santander,
Colombia in 1976. He received his
Bachelor's degree in Mathematics and
Computer Science from Universidad
Francisco de Paula Santander, Colombia in
1998. Master in Science Education from
Universidad Nacional Experimental del
Táchira, Venezuela in 2007. He is currently
a research professor at the Faculty of Education, Arts and
Humanities, Universidad Francisco de Paula Santander. His
areas of research include mathematics education and science
education. His production includes the publication of several
articles in indexed journals, and the development of several
books on mathematics education. She is currently pursuing a
PhD in Education Sciences at the Universidad Nacional de la
Plata, Argentina.
ORCID: https://orcid.org/0000-0002-7974-5560.
Raúl Prada Núñez was born in Villa del
Rosario, Colombia in 1976. He received
his Bachelor's degree in Mathematics and
Computer Science from Universidad
Francisco de Paula Santander, Cúcuta -
Colombia, in 1998; Master's degree in
Mathematics mention in Education from
Universidad Nacional Experimental del
Táchira, Venezuela, in 2007 and Master's
degree in Data Optimization from Universidad Politécnica de
Valencia, Spain in 2014. He currently serves as an associate
professor at the Faculty of Education, Arts and Humanities,
Universidad Francisco de Paula Santander. His research areas
include topics in Mathematics Education, Statistics and
Pedagogical Practice. His production includes the publication
of more than 40 articles in indexed journals and the elaboration
of three books on topics such as Teaching Differential Calculus:
an analysis of difficulties in university students, ICT and
Investigative Competences among Basic Education teachers
and Principles of Argumentation and Argumentative Practices
in the training of teachers in Mathematics. He is currently
pursuing a PhD in Humanities, Arts and Education at the
University of Castilla-La Mancha, Spain.
ORCID: https://orcid.org/0000-0001-6145-1786
Fermín Rafael Álvarez Macea was born in
Caucasia, Colombia in 1981. He received
his Bachelor's degree in Mathematics and
Physics from the University of Antioquia
in 2007 and later received his Master's
degree in Teaching of Exact and Natural
Sciences from the National University of
Colombia in 2012. He currently teaches in
the faculties of Education, Pharmaceutical
and Food Sciences at the University of Antioquia, in the faculty
of Exact and Applied Sciences at the Instituto Tecnológico
Metropolitano (ITM) and in the faculty of basic and social
sciences at the Politécnico Jaime Isaza Cadavid. His areas of
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Scientia et Technica Año XXVIII, Vol. 28, No. 03, julio-septiembre de 2023. Universidad Tecnológica de Pereira.
research include mathematical modeling, didactics in the
teaching of mathematics and physics, in the field of education
and engineering. His scientific production includes publications
in national and international indexed journals. He is currently a
doctoral candidate in Educational Sciences at the National
University of La Plata, Argentina.
ORCID: https://orcid.org/0000-0002-2451-9144