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Pre-University
Mathematics
(Case: Core University Alberto
Adriani)
Authors: Isaac Guerrero Mora
Universidad
de los Andes, NUAA-ULA
Mérida,
Venezuela
Milagro
Yesenia Montilla Davila
Universidad
de los Andes, NUAA-ULA
Mérida,
Venezuela
Domingo
Alberto Alarcón
Universidad
de los Andes, NUAA-ULA
Mérida,
Venezuela
Abstract
In this work an approach to a
written didactic guide was made to leverage the training of our pre-university
students of the Alberto Adriani University Nucleus of the Universidad de los
Andes. It starts with a diagnosis about the competences in basic mathematics of
young people who are studying to study engineering at Universidad de los Andes.
6 independent modules are proposed in a written guide and validated with their
respective application in a group of students enrolled in the pre-university
course. This work follows in general terms a methodology based on the
structured survey. With the results obtained we can conclude that its
development has been successful, this despite the fact that the general average
did not exceed 50%, taking into account that more than 40% managed to
assimilate the information and exceed 10 points.
Keywords:
formation; guide; learning.
|
Date Received: 08-07-2017 |
Date Acceptance: 30-09-2017 |
Matemática Preuniversitaria
(Caso: Núcleo
Universitario Alberto Adriani)
Resumen
En este trabajo se realizó una aproximación a una guía didáctica escrita
para apalancar la formación de nuestros estudiantes preuniversitarios del
Núcleo Universitario Alberto Adriani de la Universidad de los Andes. Se inicia
con un diagnóstico sobre las competencias en matemáticas básicas de los jóvenes
optantes a estudiar una carrera de Ingeniería en la Universidad de los Andes.
Se proponen 6 módulos independientes en una guía escrita y se valida con su
respectiva aplicación en un grupo de estudiantes inscritos en el curso
preuniversitarios. Este trabajo sigue en líneas generales una metodología
basada en la encuesta estructurada. Con los
resultados obtenidos podemos concluir que su desarrollo ha sido acertado, esto
pese a que la media general no superó el 50%, tomando en cuenta que más del 40%
logró asimilar la información y superar los 10 puntos.
Palabras clave: formación; guía; aprendizaje.
|
Fecha de Recepción: 08-07-2017 |
Fecha de Aceptación: 30-09-2017 |
1.
Introduction
This document proposes a
research that aims to develop and apply a basic mathematics guide for
pre-university training, aimed at the acquisition and refinement of skills
needed to start a university career, particularly in Engineering, these young
pre-university students includes young people from the past years of high school
and young people enrolled in the pre-university admission course of the Alberto
Adriani University Nucleus of the Universidad de los Andes.
It is based on a
fundamental question as to whether it is sufficient or is necessary to improve
the performance of mathematics students at the baccalaureate level as to
whether they are mathematically competent.
In this sense, there is
important evidence to be specified. The precarious performance of high school
students in tests of Mathematical Olympiad (Guerrero and Porras, 2012a),
possibly associated to: an inadequate performance of the teacher of mathematics
to properly train students or a cultural change in the vision of education
perceived by students , they constitute a scenario, where it is fundamental to
propose actions aimed at improving the training of high school students or
those who are already high school graduates. Specifically, it is considered
necessary for the student to have tools that allow him to incorporate the use
of problem solving as part of the process of teaching and learning mathematics.
For this, it is required
to provide in a timely manner knowledge about problem solving, its theoretical
foundations and adequate strategies in the analysis.
Another important cause
is the low performance, the high dropout rate, of university students in the
first semesters of the different careers.
In this sense, it is
considered necessary to develop and validate a mathematics guide, which
provides theoretical and methodological information on solving problems of
mathematical problems.
2. Problem statement.
The teaching
of mathematics has occupied an important place within the different curricular
designs that have been implemented in the country. Particularly, in the
National Basic Curriculum (Ministry of Education, 1997, p.119), as well as
recent documentation from the national government on education (MPPE, 2015, p.161),
it is proposed, for the area of Mathematical Knowledge, the problem solving,
as a tool for the teaching-learning of mathematics. Also, in specialized
literature, special emphasis is placed on the use of problem solving as a tool
in the development of mathematical learning. Therefore, it is advisable to
develop strategies to get the student to learn to solve mathematical logic
problems (other sciences, concrete reality, intra-mathematical).
On the other
hand, one of the notorious characteristics of the teaching of mathematics is
the low performance of Venezuelan students in the subject (Gallo and Pichardo,
2008a), which is a problem recognized not only nationally but also globally.
In this
order of ideas, the Mathematical Olympiad carried out in our country by the
National Association of Mathematical Competences (ACM) specifically in the
Regional Final Test (PFR) applied in 2011 (PRF-2011), whose resolution requires
that the student is able to solve mathematical problems using notions of school
mathematics, shows worrisome results. Out of 15,652 students who started the
respective selections organized by the ACM to determine who would participate
in the PFR-2011, only 3.9% of the participants managed to advance. Of the
latter, 84% did not respond to the problems posed in said test (Guerrero and
Porras, 2012b).
This
precedent, together with the fact that the participants constituted an
important representation of the young students of secondary mathematics of the
State of Mérida, reveals a situation of precariousness in the mathematical
formation of said young people, in the resolution of problems such as those
posed by the ACM in the Mathematical Olympiad (Idem). Where it is perceived
that this action may be linked to the performance of teachers.
In this
sense, the central question of this research is the following: Is it enough or
is it necessary to improve the performance of young pre-university students at
present? If it is necessary to improve such performance, would it be enough
with the implementation of a Basic Mathematics guide or would it be convenient
to involve the university with propaedeutic programs that help the young university
student to face a long career such as science, engineering, among others?
3. Record
Gallo and
Pichardo (2008b), in their work entitled "Strategies to promote meaningful
learning of the clearing of mathematical formulas in the Liceo Bolivariano
Ignacio Carrasquero" propose a research where they elaborate strategies in
the search of meaningful learning on the subject in question. This research was
of the Project Feasible type, it was developed as a non-experimental field
design for the development of strategies mainly in mental and conceptual maps,
where the sample consisted of three science teachers in the 2007-2008 school
period. They conclude by pointing out the importance of creating strategies
that leverage meaningful learning in mathematics, particularly in the field of
teacher training.
Hernández
and Velasco (2010), present a work whose main objective was to develop a
computerized educational material for the learning of fractions, aimed at
students of fourth, fifth and sixth grade of Primary Education of the
Bolivarian National Educational Unit El Vigía de los Teques, Miranda State.
This investigation was carried out with a projective type methodology, because
it seeks to propose an alternative of change (computerized educational
material) for the learning of mathematics. The results of this work indicate,
in general terms, that the application of the developed material contributes to
the improvement of the ability to learn concepts, use of rules and application
of discriminations to carry out operations with fractions.
Lozada and
Ruiz (2011a), present a paper entitled "Teaching Strategies for the
teaching-learning of multiplication and division in 1st-year students".
This was a feasible project with a descriptive field design, the population
considered was defined by the teachers of seven secondary schools, the students
of the Bolivarian High School "Ciudad de Valera" and two teachers in
charge of the CBIT, of the Valera municipality, Trujillo state. This research
allowed to evaluate the use of didactic strategies and to use them as a support
tool for the teaching-learning of Mathematics.
These works reveal part of the real problem about the
teaching-learning of mathematics, proposing alternatives for change. The work
that is proposed in this document coincides with those previously discussed in
terms of its line of research; agree on the search for meaningful learning by
designing teaching strategies that improve the acquisition of mathematical
knowledge in high school students.
4. Marco Teórico
Teaching-learning
process of mathematics
It has been
considered that the teaching of mathematics taught in the different school
institutions should be part of the integral formation of the human being, which
should be taught from an early age. An essential purpose of the teaching of
mathematics is to allow the student to appropriate mathematical knowledge, as
well as to think more frequently mathematically, especially in real life
situations. The complexity of the teaching of mathematics necessarily requires
the didactic training and methodology of the teachers. In this sense, according
to Mora (2003a), the teaching of mathematics has to take into account aspects
such as: (a) the meaning of the teaching of mathematics, (b) basic stages of
the process of teaching mathematics and (c) the teaching of specific
mathematical methods and contents.
The teaching
of mathematics can be characterized, according to Godino (2009), as a process
that requires on the one hand the domain of the discipline, in this case the
mathematical knowledge and rigorous concepts that are necessary for the
understanding of them , and on the other side of the mastery of a set of skills
for the correct performance in the work of mathematics teachers.
In Venezuela, a teaching model prevails in the
mathematics classes, from definitions and theorems to examples or applications
and not to proposing a mathematical situation where solutions are sought and
finally formalized in definitions and theorems (Mora, 2003b). This model has
been shown as deficient for the achievement of mathematical learning by students.
In this sense, the need to generate didactic-methodological strategies aimed at
overcoming the tradition of teaching mathematics based on the model described.
4.1. Teaching strategies
Saavedra
(2001) defines teaching strategies as the criterion from which the use of
teaching procedures appropriate to the circumstances in which the learning
process occurs is determined.
As
previously mentioned, the design, development and implementation of
mathematical teaching strategies are urgently needed, aimed at overcoming the
obvious difficulties in learning this science.
Starting
from assumptions in which it is considered that the teaching of mathematics
aims to incorporate values and develop attitudes in students, so that they
obtain concepts in a clear and comprehensive manner, which allows them to solve
mathematical problems, apply them to reality, It is then necessary to put into
play strategies that allow the development of capacities to perceive,
understand, associate, analyze and interpret the knowledge acquired to confront
their environment (Lozada and Ruiz, 2011b).
Díaz and Hernández (2002), argue that instructional
strategies are a set of procedures that students assimilate and then use
intentionally, with the purpose of solving problems. In this regard, the development
of teaching strategies by the teacher should be aimed at the development of
instructional strategies such as those referred by these authors.
5. Methodology
This research is
proposed as a feasible project divided into three parts. The first part consists
of the documentary review of the problem on teaching at the baccalaureate
level, the second a phase of diagnosis in critical areas of mathematics. And
finally a part of development and validation of the teaching material.
Considering as a population all the young graduates of the Alberto Adriani
municipality of the State of Mérida, opting for a university quota in the
Alberto Adriani University Nucleus of the Universidad de los Andes.
For the development of this research, it has been considered pertinent
to put into play a mixed model of research in which both qualitative and
quantitative methodological aspects are combined (Mertens, 2005). Specifically,
the methodology that is proposed to follow is a structured survey, whose
procedures are registered in an action research. Based on the structured survey
as a methodology and the questionnaire as an instrument.
6. Population Sample
The population considered for this research is made up
of all the young pre-university students of the Alberto Adriani University Nucleus,
these young pre-university students are young high school students or students
in the last year of high school and diversified from high school with the
intention of pursuing a university degree. The sample consisted of the 53 young
people enrolled in the pre-university admission course of the Alberto Adriani
University Core section 01 of the semester A-2016.
7. Needs Study
An
instrument was applied, with a problem for each unit proposed, in order to
explore the knowledge of the pre-university students of the Alberto Adriani
University Nucleus in the respective areas.
The validity
of these questions in terms of their correlation with the proposed objectives
was made through the trial of three experts in the area, belonging to the
Alberto Adriani University Nucleus of the Universidad de los Andes.
The six
questions asked focused on the basic aspects of each area. Next, the applied instrument was
shown:
Figure 1. Dispersion of the results of the
Instrument.
SEE IN THE ORIGINAL VERSION
Source: Guerrero (2017).
For this instrument the
pre-university students had to give development answers, the questions
intrinsically keep the need to not only understand the process of solving them
but to be familiar with the mathematical language. Regarding the results of the
same, the absence of answers predominated, as well as in some cases in which
the pre-university students explained that they did not understand what they
were being asked. Figure 1: shows the results where you can see a scatter
diagram, being able to observe a range of grades from zero to seven, an average
of 0.28 points measured on a 0-20 scale.
8. Development
of the Guide and Implementation
The guide
developed by (Guerrero, 2017), is available in the library, as a resource for
pre-university courses, at the Alberto Adriani University Nucleus of the
University of Los Andes.
For the
application of the same to the sample an instrument was applied for each unit,
in total 6 instruments, these are not shown in this article, however, they
follow the same trend shown in the first applied instrument, 6 questions in
each test including in one of them the question corresponding to the subject,
made in the diagnostic instrument, after supplying the content of the same.
Table 1
shows the arithmetical means obtained by the pre-university students during the
application of the guide, it is important to appreciate that none of the
subjects managed to exceed 10 points in their average, although 10% of the
participants achieved higher than 18 points, on a scale of 0-20. It is also
important to note that more than 50% of the participants answered the question
asked in the diagnostic instrument.
The average of each participant, as a general balance
of the application of the guide, is shown in figure 1, ordered in an increasing
way, it can be noticed and just under a third of the sample successfully passed
the tests and less than 5% of them managed to maintain an average higher than
15 points on a 0-20 scale, the general average of the sample was 4.89 points.
Table
1. Arithmetic average obtained per unit applied
SEE
IN THE ORIGINAL VERSION
Source: Guerrero (2017).
Figure
1. Increasingly ordered average obtained by each participant in the
application of the 6 units.
SEE
IN THE ORIGINAL VERSION
Source: Guerrero (2017).
9. Conclusions
The low student
performance evidenced in the diagnostic test allows us to identify a possible
problem in the mathematical formation, being this one of vital importance for
the formation in different university careers of our country. On the other
hand, taking into account that the guarantee of said mathematical development
is contemplated in the programmatic contents proposed by the Ministry of the
Popular Power for Education, we can demonstrate the need to implement
strategies that help to minimize the repercussion of such failures in the
different university courses that require competences in the area of
mathematics.
Consequently, a guide on
basic mathematics was developed to reinforce the training of young
pre-university students of the Alberto Adriani University Nucleus of the
University of the Andes, this guide is a resource that is in permanent
adjustment.
The contrast between the
diagnostic test and the results of the tests carried out during the application
of the Basic Mathematical Guide and, we can affirm that its development has
been successful, this despite the fact that the general average did not exceed
50%, taking into account that more of 40% managed to assimilate the information
and overcome the 10 average points of the 6 tests carried out, on a scale of
0-20.
It is proposed as future works, to test the developed guide with
different samples and to elaborate a unit of basic algebra which is required by
the pre-university students at present.
10. References
Díaz, F. & Hernández, G. (2002). Estrategias Docentes para un aprendizaje
Significativo. Una interpretación constructivista. 2da ed. México:
McGraw-Hill.
Gallo, J. & Pichardo, R. (2008a,b). Estrategias para propiciar el aprendizaje
significativo del despeje de fórmulas matemáticas en el Liceo Bolivariano “Ignacio
Carrasquero”. Tesis de pregrado. Mérida: Universidad de los Andes.
Godino, J. (2009). Categorías de análisis de los conocimientos del profesor de
matemáticas. Unión, Revista Iberoamericana de Educación Matemática, 20(4),
págs. 13-31.
Ministerio para el Poder Popular de la
Educación, MPPE (2015). Proceso de
transformación curricular en educación media. [Versión electrónica].
Recuperado de: http://www.cerpe.org.ve/tl_files/Cerpe/contenido/documentos/Actualidad%20Educativa/Formacion%20Tecnica/PROCESO%20DE%20CAMBIO%20CURRICULAR%20(PRIMERA%20VERSION)(1).pdf
Guerrero, I. (2017). Matemática básica. Núcleo Universitario Alberto Adriani de la
Universidad de los Andes. trabajo de extensión, Mérida.
Guerrero, I. & Porras, O. (2012a,b). Estudio cuantitativo y cualitativo de los
resultados obtenidos en la prueba final regional de la ACM en el estado Mérida.
Año 2011. Tesis de pregrado. Mérida. Universidad de los Andes.
Hernández, R. & Velasco, G (2010). Material educativo computarizado para el
aprendizaje del contenido de fracciones dirigido a los estudiantes de cuarto,
quinto y sexto grado de Educación Primaria. Tesis de pregrado. Mérida:
Universidad de los Andes.
Lozada, J. & Ruíz, C. (2011a,b). Estrategias Didácticas para la
enseñanza-aprendizaje de la multiplicación y división en alumnos de 1er año. Tesis
de pregrad. Trujillo: Universidad de los Andes.
Mertens, D. (2005). Research
and evaluation in education and psychology: Integrating diversity with
quantitative, qualitative, and mixed methods. Thousand Oaks: Sage.
Ministerio de Educación (1994). Curriculum Básico Nacional. Programa de
estudio Básico. 1era Etapa. Caracas:
Autor.
Mora, D. (2003a,b). Estrategias para la enseñanza y aprendizaje de las matemáticas.
[Versión electrónica] Revista Pedagógica, (24)70. Recuperado de: http://www.scielo.org.ve/scielo.php?script=sci_arttext&pid=S0798-97922003000200002
Saavedra, M. (2001). Diccionario de pedagogía. México: Pax México.
Isaac Guerrero Mora
e-mail: ishaako@ula.ve
Born in Mérida, Mérida State, Venezuela. Graduated
from the Universidad de los Andes (ULA) of the Bachelor of Mathematics,
Magister Scientiae in Modeling and Simulation of Systems; Currently I work as a
Professor in the Núcleo Universitario Alberto Adriani de la Universidad de los
Andes, in the area of Basic Programming.
Milagro Yesenia
Montilla Dávila
e-mail: milagroy@ula.ve
Born in Vigía, Estado Mérida, Venezuela; I currently
do Doctorate studies in Education Sciences at Universidad Fermín Toro,
Barquisimeto Edo. Lara Graduated from the Universidad de los Andes (ULA)
as a Bachelor in Chemistry, Magister in Fundamental and Applied
Electrochemistry (ULA); I am doing teaching tasks in the Chemistry Area for
Engineering careers (ULA); I am currently the Academic Coordinator of the
NUAA-ULA and Active researcher at the Universidad de los Andes, PEI-ULA
Research Stimulus Program and the Ministry of Popular Power for University
Education, Science and Technology PEII-ONCTI; I have participated in the
dictation of workshops, organization of conferences for new university
students, national and international speaker.
Domingo Alberto Alarcón
e-mail: domingoa@ula.ve
Born in Tovar, Mérida State, Venezuela; I currently do
Doctorate studies in Education Sciences at Universidad Fermín Toro,
Barquisimeto Edo. Lara Graduated from the Universidad de los Andes (ULA) as
Bachelor in Chemistry, Master in Fundamental and Applied Electrochemistry
(ULA); I am doing teaching tasks in the Chemistry Area for Engineering careers
(ULA); I am currently Director of the NUAA-ULA, General Coordinator of the
Interdisciplinary Research Group in Engineering and Education GIIIE and Active
Researcher of the Universidad de los Andes, PEI-ULA Research Stimulus Program
and the Ministry of Popular Power for University Education, Science and
Technology PEII-ONCTI; I have participated in the dictation of workshops,
organization of conferences for new university students, national and
international speaker.
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- Original Version in
Spanish -
DOI: https://doi.org/10.29394/Scientific.issn.2542-2987.2018.3.7.10.193-210