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Sinergias educativas
January - March Vol. 9 - 1 - 2024
http://sinergiaseducativas.mx/index.php/revista/
eISSN: 2661-6661
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Page 47-51
Received: July 12 , 2023
Approved: December 30 , 2023
Proposal for the implementation of
methodological strategies for the
development of mathematical logical
reasoning in third year high school
students
Propuesta de implementación de estrategias
metodológicas para el desarrollo del razonamiento
lógico matemático en los estudiantes de Tercer Año de
Bachillerato
Fernando Procel
*
Abstract
Logical mathematical reasoning is a powerful tool that can be
applied in various areas of life, from solving everyday problems to
making important decisions. Its application helps us develop
fundamental cognitive skills and face challenges more efficiently.
The objective is for students to recognize that numbers, operations
and figures are interrelated contents and processes that are present in
everyday life and that it is necessary to develop skills to expand their
reasoning capacity. The present research is of a descriptive
documentary type, and is based on the strategies of the constructivist
theory of learning, where Piaget states that the individual acquires
his knowledge from the preliminary information he already
possesses and from the interaction with the environment in which he
develops. The results of the qualitative diagnostic evaluation of the
students at the beginning of the 2023-2024 school year are
discouraging. We can conclude that the students show difficulties,
lack of interest and lack of motivation in solving the exercises.
*
D. in Mathematics, Magister in Educational Sciences,
Mathematics teacher at the Isabel de Godin Educational
Unit, secretariaisabeldegodin@gmail.com,
fernando.procel@yahoo.es, https://orcid.org/0000-
0003-1314-1294
Article
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Keywords: reasoning, strategies, methodology, learning.
.
Resumen
El razonamiento lógico matemático es una herramienta poderosa que
se puede aplicar en diversas áreas de la vida, desde resolver
problemas cotidianos hasta tomar decisiones importantes. Su
aplicación nos ayuda a desarrollar habilidades cognitivas
fundamentales y a enfrentar los desafíos de manera más eficiente. El
objetivo es que los estudiantes reconozcan que los números, las
operaciones y las figuras son contenidos y procesos que se
interrelacionan entre sí y están presentes en el día a día y que es
necesario desarrollar habilidades para ampliar su capacidad de
razonamiento. La presente investigación es de tipo documental
descriptivo, y se basa en las estrategias propias de la teoría
constructivista del aprendizaje, donde Piaget plantea que el
individuo adquiere su conocimiento a partir de la información
preliminar que ya posee y de la interacción con el medio en que se
desenvuelve. Los resultados de la evaluación diagnóstica, de tipo
cualitativa, realizada a los estudiantes al iniciar el periodo lectivo
2023-2024 son desalentadores. Podemos concluir que los estudiantes
demuestran dificultades, desinterés y desmotivación en la resolución
de los ejercicios.
Palabras clave: razonamiento, estrategias, metodología,
aprendizaje.
Introduction
Logical reasoning and mathematical reasoning are two types of
thinking that share some similarities, but also present significant
differences. Logical reasoning refers to the ability to analyze and
evaluate arguments and propositions to determine whether they are
true or false. It is based on principles of logic and is used to solve
problems in different areas of knowledge. On the other hand,
mathematical reasoning focuses on the application of mathematical
concepts and procedures to solve specific problems.
According to (Zurbano, 2014) one of the main differences between
the two types of reasoning is that logical reasoning is used in a wide
variety of areas, while mathematical reasoning is limited to problems
involving mathematical concepts and operations. In addition, logical
reasoning focuses on the evaluation of arguments and propositions,
while mathematical reasoning focuses on the application of
mathematical concepts to solve problems. according to (Accinelli
Gamba & De la Fuente-García, 2013) although both types of reasoning
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share some similarities, there are significant differences in their
application and focus.
For (Rodríguez Cáceres et al., 2021) mathematical logical reasoning
is an important skill that can be improved with practice and
dedication. Among the strategies to improve mathematical logical
reasoning that we have found are:
Have a good understanding of the fundamental concepts and
principles of mathematics. This includes basic operations, algebra,
geometry, probability.
Solve a variety of math problems on a regular basis. Start with simple
problems and gradually increase the difficulty. Problems can be
found in math books, specialized websites or even mobile
applications.
It is important to learn different strategies for solving mathematical
problems, such as decomposing a problem into smaller parts,
identifying patterns, or using diagrams and graphs.
Logical mathematical reasoning leads to critical and analytical
thinking, so it is important to know how to carefully analyze
information and evaluate different possible solutions.
Try to learn from our mistakes, i.e. analyze our mistakes and
understand why we have made a mistake. This will allow us to
identify the areas in which we need to improve and to avoid making
the same mistakes in the future.
Materials and methods
(Puga Peña & Jaramillo Naranjo, 2015). the present research is initial
and exploratory. We consider that it is the first scientific approach to
a real problem that has not yet been addressed or has not been
sufficiently studied and the existing conditions are not yet
determinant. What we are trying to do is to highlight the fundamental
aspects of the problem of the low development of mathematical
logical reasoning and to find the appropriate procedures to elaborate
a subsequent research and to have results that allow us to open lines
of research and to proceed to their consequent verification.
For (Isabel Núñez-Peña et al., 2015) the material available is an
initial qualitative diagnostic assessment. The questions are
structured, i.e., they contain true or false, multiple choice,
completion and problem-solving items. The contents evaluated
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correspond to subjects of the second year of high school, i.e., they
are prerequisite subjects for the next level.
Results
Both the diagnostic evaluation and the obtaining of results were
carried out by the teacher of the subject. Since it is a qualitative test,
the following rubric was used:
• Master the required learning.
• Achieves the required learning.
• Close to reaching apprenticeships
• Does not achieve the required learning.
Seventy-five percent of the students evaluated have major
difficulties in problem solving, whose resolution is based on an
adequate use of mathematical logical reasoning. This warrants an
early intervention to discover the students' strengths and weaknesses.
Discussion
It is necessary to implement appropriate strategies to foster the
ability to understand concepts and establish relationships, stimulate
creativity in the elaboration of mathematical models, construction of
tables from the collection of information. However, the
development of mathematical logical reasoning should begin at an
early age, when the child begins to interrelate with the objects around
him (Piaget). George Polya, a great mathematician of the twentieth
century, proposed the methodology of problem-based learning
(PBL) whose purpose is to guide the search and exploration of
solutions to problems. It is necessary to encourage curiosity and
experimentation in problem solving.
In the short time that we have interacted with the students, we have
noticed a certain lack of interest. It is a priority for students to acquire
skills such as: understanding abstract concepts, the ability to reason,
and establishing relationships between concepts.
Logical mathematical reasoning requires constant practice. The
more we practice, the better our ability to solve mathematical
problems logically and efficiently.
Implementing a new methodology is a challenge for both the teacher
and the students. It may seem more of an obstacle than a challenge,
however, the opinion of the students was very positive, they firmly
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believe that it was an excellent experience, that they would repeat it,
they would recommend it for other courses. In addition, they feel
that they learned more and in a better way.
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