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Sinergias educativas
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Didactic situations mediated by tic for
the representation of numerical sets
Situaciones didácticas mediadas por tic para la
representación de conjuntos numéricos
Jorge Washington Encalada Huayamave
*
Jorge Wilson Flores Rodríguez*
Jomayra Lisbeth Zhune Chila*
Jennifer Daniela Esmeraldas Rodriguez*
Abstract
The present research seeks to determine the importance of the use of
ICT in the representation of numerical sets, for which a sample of
eighth grade students in parallel A and B of the Minerva School of
Basic Education was considered, in order to verify the proposed
objectives, a test was applied to both groups of students and it was
possible to conclude that: within the Control Group, to whom a
traditional class was given, more than 50% did not master the subject
in its entirety; while the Experimental Group with a class mediated
by ICT and didactic situations, was able to prove that this tool allows
learners to master the content, specifically in rational numbers.
Therefore, the design of the guide was carried out, which will benefit
students and in turn will be a working tool for teachers in the area of
mathematics.
* Master's Degree in Logistics Management, University
of Guayaquil, jorge.encaladah@ug.edu.ec
https://orcid.org/0000-0002-7675-404X
* Master's Degree in Higher Education, Universidad de
Guayaquil, wilson.floresr@ug.edu.ec
https://orcid.org/0000-0002-7436-7441
* Bachelor of Science in Education, mention in Physics
and Mathematics, Unidad Educativa Particular Dr.
Agustín Cueva Tamariz, zjomayra@uepact.edu.ec
https://orcid.org/0009-0005-7532-2375
* Bachelor's Degree in Education Sciences, mention in
Physics and Mathematics, Universidad de Guayaquil,
jennifer.esmeraldasr@ug.edu.ec
https://orcid.org/0009-0004-9725-840X
Article
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Keywords: Didactic Situations, ICT, Numerical Sets, Didactic
Guide.
Resumen
En la presente investigación se trata de determinar la importancia del
uso de las TIC en la representación de conjuntos numéricos, para lo
cual se consideró como muestra a Octavo año de básico paralelos A
y B de la Escuela de Educación Básica Minerva, en busca de
verificar los objetivos planteados se aplicó un test a ambos grupos
de estudiantes y con ellos se pudo concluir que: dentro del Grupo de
Control, a quienes se les impartió una clase tradicional, más del 50%
no dominaban el tema en su totalidad; mientras que el Grupo
experimental con una clase mediada por TIC y situaciones
didácticas, logró comprobar que esta herramienta permite a los
aprendices dominar el contenido, específicamente en números
racionales. Por ello, se llevó a cabo el diseño de la guía, misma que
beneficiará a los estudiantes y a su vez será una herramienta de
trabajo para los docentes del área de matemáticas.
Palabras clave: Situaciones didácticas, TIC, Conjuntos Numéricos,
Guía Didáctica.
Introduction
The different online methodological strategies applied by teachers
have varied during this time. The teaching of didactics in
Mathematics has been in constant innovation, as well as its learning
methodology, which at the same time suggests a series of rules for
the resolution or representation of exercises, such as numerical sets.
Undoubtedly, during the last five years we have been able to
appreciate a great amount of technological advances worldwide in
the educational field, although they are little used in our country;
because in these 18 months of pandemic, the whole planet has been
forced to adopt and implement the online modality in the educational
classrooms, but not all educators were prepared for it.
According to reports of the United Nations Children's Fund
(UNICEF, 2021), one year after the health emergency, progress in
education has unfortunately regressed in most of the world and this
is also evident in Ecuador, since a survey conducted by the same
entity reveals that 7 out of 10 students in seventh grade of basic
education had an unsatisfactory or elementary level in the subjects
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of Language and Literature and Mathematics; while, since the
beginning of the pandemic, 6 out of 10 students consider that they
are learning less. Meanwhile, around 15% of students stated that they
have not had regular contact with their teachers.
For this reason, it is relevant that educators, as main guides, can use
different methodological strategies in the teaching/learning process
of mathematics and that they are closely related to ICT. In addition,
educational curriculum strategies such as problem-based learning,
collaborative learning and project-based learning should be taken
into account, since they pursue a single objective, that is, that
students build knowledge with the help of a mediator.
For his part Cabanillas, 2017, in his thesis mentions that: "The
student learns by adapting to an environment that is a factor of
contradictions, difficulties and imbalances, a bit like human society
does. This knowledge, the fruit of the student's adaptation, manifests
itself through new responses, which are the mark of learning".
Then, seeing each of the characteristics and surprising factors that
the teacher must present in his activities, a wide range of cognitivist
theories of mathematics opens up, such as the one proposed by Guy
Brousseau, who postulates the Didactic Situations as a means to be
raised within the methodology and that consequently will produce
that students achieve meaningful learning.
Thus, the following question arises: How do ICT-mediated didactic
situations affect the representation of numerical sets in students in
the eighth year of higher basic education at the Minerva School of
Basic Education, school year 2021 - 2022?
In view of the above, we propose to analyze the application of
didactic situations mediated by ICT for the representation of
numerical sets.
Materials and methods
Within this work we made use of bibliographic research, since
through it we were able to analyze the variables, on the one hand we
obtained the characteristics of Guy Brousseau's theory and on the
other hand each one of the sets of numbers that we intended to
represent; because once the information was registered and
understood, we would proceed to the elaboration of the didactic
situations.
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The didactic situations are presented below with reference to their
phases:
Table 1. Didactic Situations
DIDACTIC SITUATION
Integers
Imagine that you are traveling in space and suddenly in the galaxy you
see floating a series of positive and negative major numbers.
- These numbers do not know where to be located and just float and
float all over the galaxy.
- In the following table we are asked to order them from smallest to
largest, and then represent them in the Geogebra program by plotting
them on a number line.
- Use the numbers shown in the images and proceed to solve, as
mentioned in the previous item above.
Link to access the Geogebra program:
https://www.geogebra.org/classic?lang=es
Natural Numbers
Open the following link, in which you will find a liveworksheets tab
of integers:
https://es.liveworksheets.com/worksheets/es/Matem%C3%A1ticas/N
%C3%BAmeros_naturales/N%C3%BAmeros_de_cinco_cifras_sz12373
18kb
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1. Now we are asked to represent all the ordered numbers of the
third activity of the liveworksheets sheet, using the Geogebra
program. https://www.geogebra.org/classic?lang=es
2. And if we now use our imagination... Imagine you want to
reach the top floor of a large building and you are standing on step 1
of the stairs, about to climb to the top floor, first you climbed 20
steps, rested a few seconds and continued climbing 25 more steps,
you rested again and continued climbing 50 more steps, you rested
again and finally you climbed 35 more steps. How many steps did you
manage to climb in the end?
- Use Paint and then paste the screenshot here:
Rational Numbers
1. Download the file provided in the following link:
https://docs.google.com/presentation/d/1D3KkefNBDkPbGrWKo9_3D
IEoi5apmkGg/edit?usp=sharing&ouid=105244651347006951304&rtp
of=true&sd=true
2. You are asked to solve the following problems and point out
the alternative you consider correct, for them work on the slides using
the equation tool.
3. Take a screenshot when you solve the whole exercise and
come up with the result and paste it here.
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4. And if once the problems have been solved, we order the
fractions of the income used in the two problems, how will we order
from smallest to largest?
5. Using the Geogebra program:
https://www.geogebra.org/classic?lang=es represent the fractions of
the two problems, and then take a screenshot of the program and
paste it here.
Rational Numbers
1. Teaching strategy
a. On the google website, download the Geoenzo program:
https://geoenzo.softonic.com/descargar
b. Once the program is installed, you will be asked to draw 6
cardboard formats (it can be of different colors), with the virtual
geometric game you will have to measure the length and width of
each cardboard.
c. For the length each format should be 50cm and for the width
30cm. As shown in the following example:
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2. On the blackboard, once the first cardboard format is drawn, write
on it the number 1 (which will represent a unit) and draw a number line
on it.
Solution: It will be as follows.
3. Now on the digital whiteboard, let's divide the second cardboard in
1⁄2, taking as a reference that it should measure 25cm when split in
half, in the first part we will write ½ and in the second half 2/2.
Now it's your turn.
4. The third cardboard we divide into 4 equal parts, of 12.50 cm each,
in the first part we write 1/4, in the second 2/4, in the third ¾ and in
the fourth 4/4. How would you do it?
Set Screenshot:
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5. Divide the fourth piece of cardboard into 5 equal parts, 10 cm each,
in the
first part we write 1/5, in the second part 2/5, in the third part 3/5, in
the fourth part 4/5, and
in the fifth 5/5. How would you do it?
6. Take all the cardboard formats as a reference and in work teams
discuss and draw your own conclusions.
_________________________________________________________
_________________________________________________________
_________________________________________________________
____________________________________
Source: Revised bibliography
Prepared by: Jennifer Daniela Esmeraldas Rodríguez and Jomayra
Lisbeth Zhune Chila
Thus, the research design becomes quasi-experimental with two
groups belonging to the eighth year of the Minerva School of Basic
Education, specifying that parallel "A" would become the control
group made up of 22 students who will be taught a traditional class,
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while "B" would be established as the experimental group, also with
22 members, who will receive the content through didactic
situations. Table 2.
Table 2. Variables Scheme
Experi
mental
group
x
O
1
Control
group
-
-
-
O
2
x: Didactic situations mediated by ICTs
O1: Representation of numerical sets
O2: Representation of numerical sets
On the other hand, since the data recording is in numerical form, the
study takes a quantitative approach, with which descriptive statistics
will be used for the tabulation and graphic representation of results,
as well as inferential statistics, since the Student's t-test for
independent samples will be used.
It is important to mention that the results were based on the tests
applied directly to the sample, which consisted of a 10-question
questionnaire.
Based on the objective of this quasi-experimental study, it is
estimated that:
• Null hypothesis (H0): the use of ICT and didactic situations
do not influence the representation of numerical sets.
• Alternative hypothesis (H1): the use of ICT and didactic
situations influence the representation of numerical sets.
Results
Calculation of Test Validity - Cronbach's Alpha
A non-standardized test was applied to the research sample, and
because of this it will be subjected to validation by means of
Cronbach's alpha coefficient. Table 3.
Table No. 3: Cronbach's Alpha
A
l
p
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54
h
a
0
.
9
3
1
3
7
3
3
3
Source: Test applied to students
Prepared by: Jennifer Daniela Esmeraldas Rodríguez and Jomayra
Lisbeth Zhune Chila
Since the value obtained is greater than (0.7), it is concluded that the
test is correctly structured.
Comparison between the control group without didactic situation
and the experimental group with didactic situation
The results obtained in the test performed on the Control and
Experimental Groups are detailed below:
Figure 1. GC and GE Test Results
Source: Student test
Prepared by: Jennifer Daniela Esmeraldas Rodríguez and Jomayra
Lisbeth Zhune Chila
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The students in the control group obtained 63.18% of correct
answers in general, showing that they still do not manage to
represent the numerical sets. On the other hand, the students in the
experimental group obtained a percentage of 80.00% of correct
answers, which shows that by correctly applying didactic situations
with the help of ICT, students can be guided to the indicated scope
of the skill.
Analysis of the test results by means of the T-test
Due to the fact that we will apply a t-test for independent samples,
we resort to the calculation of data normality, which is shown below.
Normality of the data Control and Experimental Group
Within the calculation it is possible to verify a p-value greater than
the significance in both samples, therefore it is concluded normality
of data in both parallels. Table 4.
Table 4. Normality of data
8th "A" grade
8th "B".
p-value>0 .100
p-value>0 .100
Source: Test applied to students
Prepared by: Jennifer Daniela Esmeraldas Rodríguez and Jomayra
Lisbeth Zhune Chila
Equal Variances
Once the normality of the data was verified, they were subjected to
the calculation of the F statistic, which obtained a value of 0.56 and,
being greater than the significance value (0.05), an equality of
variances was established. Table 5
Table 5. Equality of Variances Test
Method
Test statistics
GL1
GL2
p-value
F
0,56
21
21
0,186
Source: Test applied to students
Prepared by: Jennifer Daniela Esmeraldas Rodríguez and Jomayra
Lisbeth Zhune Chila
T-test
Finally, due to the research design used, the independent samples T-
test was applied; within this test "p" reached a value of "0" and with
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it we conclude that the means of the ratings of the parallels "A" and
"B" are different.
Discussion
The study variables were examined bibliographically to elaborate
didactic situations mediated by ICT that facilitate the representation
of numerical sets and to be evaluated in the test, which measured the
acquisition of the mathematical theme, obtaining 80% in the general
average of correct answers for the group to which the didactic
situation was applied, thus reflecting an improvement in comparison
to the control group that showed only 63.18% of correct answers.
With the T-test, the results obtained in the test applied to the eighth
grade students were analyzed and with it the alternative hypothesis
is accepted, which indicates that the use of ICT and didactic
situations influence the representation of numerical sets. Thus, the
use and correct application of didactic actions and activities facilitate
the acquisition of the desired mathematical skill.
In view of the results provided by the test, it is verified that students
and teachers need a tool that allows them to optimize mathematics
classes; therefore, it is assured that the elaboration of a pedagogical
document for the application of didactic situations mediated by ICT
in the representation of numerical sets will be of help.
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