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Uso de GeoGebra en el aprendizaj= e de secciones cónicas de geometría analítica y su incidencia en rendimiento académico de los estudiantes de nivelación universitaria

Use of GeoGebra in learning conic sections of analytical geometry and its impact on academic performance of university level students

&nb= sp;

¹

Luis Fabian Brito Mancero

https://orcid.org/0009-0008-2108-1715

Universidad Estatal de Bolívar (UEB)

luis.brito@ueb.edu.ec

2

Marcela Yolanda Brito Mancero<= o:p>

https://orcid.org/0000-0003-26= 89-3516

Escuela Superior Politécnica de Chimborazo (ESPOCH)

mybrito@espoch.edu.ec

Artículo de Investigación Científica y Tecnológica

Enviado: 11/11/2024

Revisado: 15/12/2024

Aceptado: 02/01/2025

Publicado: 30/01/2025

DOI: https://doi.org/10.33262/ap.v7i1.576 =

<= span lang=3DEN-US style=3D'font-size:8.0pt;line-height:115%;font-family:"Times= New Roman",serif; mso-fareast-font-family:"Times New Roman";color:blue;mso-ansi-language:EN= -US'>

&= nbsp;

Cítese: <= /b>

Brito Mancero, L. F., & Br= ito Mancero, M. Y. (2025). Uso de GeoGebra en el aprendizaje de secciones cón= icas de geometría analítica y su incidencia en rendimiento académico de los estudiantes de nivelación universitaria. AlfaPublicaciones, 7(1), 88–99. = https://doi.org/10.33262/ap= .v7i1.576

ALFA PUBLICACIONES, es una revista multidisciplinar= , trimestral, que se publicará en soporte electrónico tiene como misión contribu= ir a la   formación de profesionales competentes con visión humaníst= ica y crítica que sean capaces de exponer sus resultados investigativos y científicos en la misma medida que se promueva mediante su intervención cambios positivos en la sociedad. https://alfapublicaciones.com

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Palabras claves:

Aprendizaje, estrategia didáctica, rendimiento académico, secciones cónicas.

Resumen:

Introducción. El rendimiento de la matemática en el bachillerato en el Ecuador es bajo ya = que las metodologías enseńanza aprendizaje se centran en métodos tradicionale= s, en caso de la geometría analítica suele centrarse en un tratamiento algebraico de las figuras lo que contribuye a que los estudiantes present= en dificultades en la adquisición de nuevos conocimientos durante la universidad. Objetivo. Anal= izar comparativamente el rendimiento académico que alcanzan los estudiantes de nivelación universitaria en la asignatura de Geometría analítica en el te= ma cónicas, cuando en el proceso enseńanza-aprendizaje se hace uso de una herramienta didáctica tecnológica como el software libre GeoGebra frente = a la enseńanza-aprendizaje tradicional. Metodología. Se partió de la hipótesis que el aprendizaje de cónicas con el uso del progr= ama GeoGebra incide de manera significativa en el rendimiento académico. Para= lo cual se identificó un grupo control y un grupo experimental de los estudiantes de Geometría analítica, se realizó la descripción del desenvolvimiento en los subtemas circunferencia, parábola, elipse e hipér= bola con el método tradicional y con el uso de GeoGebra; finalmente se correlaciona los rendimientos académicos alcanzados por cada grupo; para = la recolección de datos se utilizó aplicó una prueba diagnóstica, cuatro talleres uno por cada subtema trabajado y una prueba global final. Resultados. En la evaluación diagnostica = se encontró que los rendimientos de los estudiantes provenientes del bachillerato se encuentran por debajo del 70%; el aprendizaje de las secciones circunferencia, parábola y elipse se demostró que existe difere= ncia significativa a favor del aprendizaje con el uso de GeoGebra. Conclusión. El introducir metodologías tecnológicas en el proceso enseńanza apr= endizaje mediante el uso de GeoGebra en el estudio de secciones cónicas incide de forma positiva en la adquisición de conocimientos. Área de estudio general: Educac= ión. Área de estudio específica: Sec= ciones cónicas. Tipo de estudio:<= /b> Artículos originales.

Keywords:

Learning, teaching strategy, academic performance, conical sections

&= nbsp;

Abstract

Introd= uction. The performance of mathematics in high school in Ecuador is low s= ince teaching-learning methodologies focus on traditional methods; in the case= of analytical geometry, it usually focuses on an algebraic treatment of figu= res, which contributes to students presenting difficulties in the acquisition = of new knowledge during university. Object= ive. Comparatively analyze the academic performance achieved by univer= sity level students in the subject of Analytical Geometry in the topic of coni= cs, when in the teaching-learning process a technological didactic tool such = as the free software GeoGebra is used compared to traditional teaching-learn= ing. Method= ology. The hypothesis was that learning conics with the use of the GeoGe= bra program significantly affects academic performance. For which a control g= roup and an experimental group of Analytical Geometry students were identified, the description of the development in the subtopics circumference, parabo= la, ellipse and hyperbola was carried out with the traditional method and with the use of GeoGebra; Finally, the academic performance achieved by each g= roup is correlated; To collect data, a diagnostic test was applied, four workshops, one for each subtopic worked on, and a final global test. Results. In the diagnostic evaluation, it was found that the performance of students from high school is below 70%; The learning of the circumference, parabola and ellipse sections showed that there is a significant differen= ce in favor of learning with the use of GeoGebra. Conclusion. In= troducing technological methodologies in the teaching-learning process using GeoGeb= ra in the study of conic sections has a positive impact on the acquisition of knowledge. Gener= al Study Area: Education. Specific study area: conic sections. Type of study: Original articles.

1.&n= bsp;     Introducción<= /o:p>

El estudio de geometría analític= a, ayuda al desarrollo de destrezas, tanto para la asimilación como para la compresión de la matemática (Vargas & Gam= boa, 2013). Para <= span style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",se= rif; color:windowtext;text-decoration:none;text-underline:none'>Murillo (2020), la enseńanza de la geometría analítica generalmente se la realiza con un enfoque tradicional para el análisis de las figuras lo que repercute en un insuficiente conocimiento en= los estudiantes. Garzón (2020) establece que el estudio de cóni= cas en el bachillerato se centra en un tratamiento algebraico de las figuras y = que el tipo de metodologías simples y tradicionales empleadas en la enseńanza contribuye a que los estudiantes presenten dificultades. Dávila-Ornelas et al. (2013) mencion= an que cuando se necesita emplear los conocimientos de geometría en las carrer= as universitarias aparecen las dificultades para los estudiantes. Por esta raz= ón la presente investigación se desarrolló con los estudiantes de los cursos de nivelación de la Escuela Superior Politécnica de Chimborazo.

En Ecuador el rendimiento en las áreas de conocimiento relacionadas = a la matemática es bajo incluyendo la Geometría Analítica. Según Bravo (2019) esto se debe a que las herramientas metodológicas y recursos didácticos no son adecuados. Se ha demostrado que los métodos pedagógicos tradicionales teóri= cos expositivos utilizados por algunos docentes no se encuentran en concordancia con los avances tecnológicos (Wampash, 2018), lo que afecta negativamente ta= nto a estudiantes como a docentes ya que se ha demostrado que la motivación doc= ente depende en alto grado a los resultados positivos (Grisales-Aguirre, 2018). Ante esta realidad se evidencia la necesidad de utilizar herramientas novedosas, acordes a los avances tecnológicos que facilite la comprensión de conceptos abstractos como los geométricos que resultan complicados para los estudiantes y así lograr resolver situaciones problémicas de manera sencilla mediante el uso de la gráfica y el análisis (Ibarra, 2019).<= /span>

El software gratuito matemático GeoGebra permite resolver complicados problemas mediante la asociación de objetos geométricos y algebraicos conectando estas dos áreas de conocimient= o de forma creativa, lo que motiva a mejorar el aprendizaje de matemáticas (Saldańa, 2017), el software permite operar funciones y proporciona una gran gama de comandos, las ventanas interactivas ayudan a visualizar el trabajo con gráficas claras y precisas generando un agradable entorno de trabajo. Bello (2013) afirma que el conocimiento de GeoGebra en docentes y estudiantes es limitado lo que incluye el tema de secciones cónicas.<= /span>

2.&n= bsp;     Metodología

La investigación se realizó con enfoque cuantitativo, el estudio fue de tipo correlacional descriptivo, se utilizó un diseńo cuasiexperimental donde se trabajó con un grupo control en el que se aplicó un modelo de enseńanza aprendizaje con el uso de cálculos algebraicos tradicionales con graficas de forma manual y un grupo experimental en el que se utilizó como herramienta didáctica tecnológica el software GeoGebra.

La población se constituye con 169 estudiantes distribuidos en cuatro paralelo= s de la signatura de Geometría plana, analítica y trigonometría de nivelación de= la Escuela Superior Politécnica de Chimborazo en el Período académico octubre = 2021 – marzo 2022, dos paralelos GC1 y GC2 con 44 y 41 estudiantes respectivamen= te corresponden al grupo control con metodología de enseńanza tradicional y los paralelos GE1 y GE2 con 42 y 44 estudiantes respectivamente que corresponde= n al grupo experimental donde se utilizó la herramienta tecnológica del uso de software libre GeoGebra:

Se utilizó el método de investigación hipotético deductivo partiendo de la hipótesis de que el empleo del programa GeoGebra = en la enseńanza de cónicas incide de manera significativa en el rendimiento acadé= mico de los estudiantes, las variables analizadas fueron: Uso de GeoGebra en= la enseńanza de secciones cónicas circunferencia, parábola, elipse e hipérbola= con la variable rendimiento académico.

Previo a realizar el análisis estadístico se efectuó una depuración de la base de datos, mediante la cual se eliminó valores perdidos resultantes de activida= des no realizadas por los estudiantes. La investigación se realizó con 85 estudiantes en el grupo control sin GeoGebra y 86 estudiantes en el grupo experimental con GeoGebra, a excepción de la prueba de diagnóstico se valoró más del 80% de estudiantes evaluados en cada una de las actividades.

La recolección de datos se realizó mediante la aplicación de pruebas objetivas= ex ante o diagnostica, durante y ex post o final la enseńanza de secciones cónicas, los instrumentos utilizados para la evaluación de conocimiento se establecieron de la siguiente manera; la prueba diagnóstica se contenía 10 interrogantes, cuatro talleres de cinco preguntas uno por sección circunferencia, parábola, elipse e hipérbola y finalmente prueba objetiva f= inal con 10 interrogantes.

Se aseguró la confiabilidad de los instrumentos mediante la validación de las pruebas objetivas y talleres utilizando el método de juicio de expertos, do= nde cinco docentes con experiencia en la enseńanza de geometría analítica valor= aron compresión, claridad y facilidad de la interrogante; opciones de respuestas= y congruencia de la interrogante; para cada instrumento utilizado. (ver tabla 1)

Tabla1

Validación por expertos de los instrumentos aplica= dos pruebas objetivas y talleres

Instrumento

Las preguntas son comprensibles, fáciles= y claras, para el evaluado

Las opciones de respuesta son adecuadas<= o:p>

Las preguntas son congruentes
para poder validar la misma

Prueba de diagnóstico

92P%

93%

93%

Taller circunferencia

92%

91%

91%

Taller parábola

92%

91%

92%

Taller elipse

92%

91%

92%

Taller hipérbola

91%

89%

91%

Prueba final

90%

91%

91%

Nota: resumen de las tablas de valoración de los instrumentos, la valoración total se encuentra = en los anexos del trabajo de titulación citado.

Fuente: Brito (2022)

3.&n= bsp;     Resultados

Para evaluar si el uso del programa GeoGebra en = la enseńanza de las cónicas influye significativamente en el rendimiento acadé= mico de los estudiantes, se llevó a cabo un análisis comparativo de los conocimientos previos mediante pruebas de diagnóstico. Posteriormente, se realizó un análisis estadístico para comparar los puntajes obtenidos por los grupos con y sin el uso de GeoGebra en cuatro áreas de la geometría analíti= ca: circunferencia, parábola, elipse e hipérbola. Esto permitió determinar si existen diferencias significativas en el rendimiento académico entre ambos grupos y si el empleo de GeoGebra mejora el aprendizaje.<= /p>
3.1 Análisis del diagnóstico

En la Figura 1 se presenta los resultados de las calificaciones obtenidas en la prueba objetiva diagnóstica aplicada a los dos grupos de estudio, está prueba se la realizó con el fin de determinar el nivel de conocimientos con los que provienen del bachillerato, el rango de calificaciones se normalizo de 0 a = 10 puntos. Se estableció el puntaje para todos los grupos estuvo por debajo de= 6.99 lo que afianza lo afirmado por y Murillo (2020), que el conocimiento de las temáticas de cónicas en el bachillerato es limitado, lo que atribuyen a uso de metodologías tradicionales en la enseńa= nza de algebra; el mayor porcentaje de calificaciones del grupo control se ubic= aron en el rango de 4,01 a 6,99 y en el grupo experimental el mayor porcentaje de calificaciones se ubican en el rango de menor o igual a 4.

Figura 1

Puntajes obtenidos e= n las evaluaciones diagnóstico de la asignatura de Geometría Analítica=

Fuente: Brito (2022)

3.2&= nbsp; Análisis de las calificaciones de los talleres de secciones cónicas
Se realizó un análisis comparativo de los puntajes alcanzado por los grupos control y gru= po experimentales en cada uno de los talleres: circunferencia, parábola, elips= e e hipérbola. Los diagramas muestran el rango de datos, con las medias de calificaciones obtenidas.

Figura 2

Diagrama comparativo calificaciones por actividad y grupo

Fuente: Brito (2022)

En la figura 2 se visualiza = el análisis descriptivo que identifica las características generales de las calificaciones alcanzadas por los estudiantes en cada una de las actividades analizadas. En los talleres que corresponden a las secciones circunferencia, parábola y elipse, se puede determinar que el grupo experimental presentan mejores calificaciones lo que reafirma lo establecido por Vera & Sabino (2018), y que la utilización de GeoGebra beneficia el desarrollo del pensamiento geométrico de los estudiantes; mien= tras que en el taller de hipérbola y examen final no se observa diferencia en las calificaciones alcanzadas por cada uno de los grupos de estudio.

3.3 Análisis de la diferencia en el rendimiento académico =

En el reglamento del régimen académico de la Escuela Superior Politécnica de Chimborazo (<= span style=3D'mso-bookmark:_Hlk99202632'>ESPOCH, 2020) se establece que, para aprobar una asignatura el mínimo a obtener es el 70% del puntaje máximo, con base en esta referencia para el análisis del rendimient= o se toma en cuenta el número de estudiantes con puntuación mayor o igual de 7 s= obre 10 equivalente al 70% de la calificación máxima. <= /span>

Tabla 2

Rendimiento académico sobre 70%

Curso

Estudiantes matriculados

Prueba Diagnóstico

Taller Circunferencia

Taller Parábola

Taller Elipse

Taller Hipérbola<= span style=3D'mso-bookmark:_Hlk99202632'>

Examen final

N° estudiantes rendimientos sobre 70%<= /span>

%

N° estudiantes rendimientos sobre 70%<= /span>

%

N° estudiantes rendimientos sobre el 70%

%

N° estudiantes rendimientos sobre 70%<= /span>

%

N° estudiantes rendimientos sobre70%

%

N° estudiantes rendimientos sobre 70%<= /span>

%

GC1

42

4

10%

9

21%

14

33%

16

38%

22

52%

14

33%

GC2

41

2

5%

14

34%

15

37%

0

0%

12

29%

16

39%

GE1

42

1

2%

19

45%

16

38%

16

38%

25

60%

17

40%

GE2

44

0

0%

9

20%

23

52%

13

30%

18

41%

16

36%

Promedio GC

7%

28%

35%

19%

41%

36%

Promedio GE

1%

33%

45%

34%

50%

38%

Fuente: Brito (2022)

En la tabla 2 se puede observar que en la prueba diagnóstica = el grupo experimental presenta menor número de estudiantes con rendimiento sob= re el 70% en relación con el grupo control. También se puede notar que tanto en los talleres como en la prueba final el promedio de estudiantes con rendimientos iguales o mayores al 70% del grupo experimental siempre estuvo= por sobre el grupo control, siendo el examen final el presenta menor diferencia= con un 2% y mayor diferencia la se ubica en el taller de la parábola con un 10%.

Para probar si = el rendimiento académico de los estudiantes que recibieron los conocimientos de cónicas mediante el método de enseńanza aprendizaje con el uso de GeoGebra presenta una diferencia significativa en comparación con el método tradicio= nal, se realizó las pruebas de hipótesis para cada actividad realizada mediante = el test Mann Whitney comparando las medianas de las dos muestras independiente= s ya que estas no se cumplen el supuesto de normalidad.

3.4 Verificació= n de hipótesis<= /h4>
En la tabla 4 = se muestra el resumen de las pruebas de hipótesis y el intervalo de confianza = para cada sección cónica, se utiliza la notación:

η₁: mediana Grupo control Sin GeoGebra

η₂: mediana Grupo experimental Con GeoGebra. =

Tabla 3

Pruebas de hipótesis= como intervalos de confianza realizados

Acti= vidad

Inte= rvalo al 95% de confianza para las diferencias de las medianas

_= 1;₁ - η₂

Prue= ba de hipótesis

Hipó= tesis alterna

Valo= r p

Prueba Diagnóstico

(1,0 ; 1,8)<= o:p>

H₁: η₁ - η₂ ≠ 0

0,000

T. Circunfer= encia

(-1,= 3 ; -0,0)

H= 321;: η₁ - η₂ < 0

0,034

T. Parábola<= o:p>

(-1,1 ; -0,0= )

H₁: η₁ - η₂ < 0

0,02= 2

T. Elipse

(-1,= 5 ; -0,0)

H= 321;: η₁ - η₂ < 0

0,017

T. Hipérbola=

(-1,0 ; 0,5)=

H₁: η₁ - η₂ < 0

0,122

Examen =

(-0,= 7 ; 0,5)

H= 321;: η₁ - η₂ < 0

0,41= 1

Fuente: Brito (2022)

En la tabla 3 se demuestra que existe diferencia altamente significativa con un nivel de confianza del 95% en la mediana de las evaluaciones diagnóstica con un (val= or p =3D 0,000), donde las calificaciones obtenidas por el grupo control son superiores a las calificaciones del grupo experimental con una diferencia d= e 1 a 1,8 puntos. Los talleres de las secciones circunferencia, parábola y elip= se se presentaron diferencia significativa en las medianas con un p valor meno= r a 0,05 demostrando que las calificaciones de los estudiantes del grupo control fue menor en un rango de 1,1 a 1,5 en comparación a las calificaciones de l= os estudiantes del grupo experimental, resultados que concuerdan con lo establecido por Montańo & Valarezo (2023), que determinaron que el uso de GeoGebra tuvo un impacto significativo en los aprendizajes de las secciones cónicas en los estudiantes del Instituto Supe= rior Tecnológico Loja. El taller de la sección hipérbola y el examen final no presentan diferencia significativa ya que los valores p en superan el nivel= de significancia de 0,10. Estos resultados resaltan la efectividad de GeoGebra= en el aprendizaje significativo del algebra en la temática de secciones cónica= s.

4.      Conclusiones<= /o:p>

·&nb= sp;        El análisis de la prueba diagnóstica concuer= da con lo aseverado en estudios previos donde se afirma que la asimilación de = los conocimientos de las secciones cónicas es limitada en el bachillerato ecuatoriano, ya que se obtuvo el mayor porcentaje de calificaciones con un = 52% se ubicó en el rango de 4,01 a 6,99 puntos, seguido por el 47% en el rango menor o igual a 4 puntos, y solo el 1% alcanzó una calificación de 9 a 10. = La hipótesis de que aprendizaje de secciones cónicas con el uso del programa GeoGebra incide de manera significativa en el rendimiento académico se comprueba, puesto que se puede verificar que existe una diferencia significativa a favor del grupo que aprendió mediante el uso de GeoGebra en tres de las cuatro secciones analizadas en el presente estudio.<= /span>

5.      Conflicto de intereses<= /o:p>

Los autores declaran que no existe conflicto de intereses en relación con el artículo presentado.

6.      Declaración de contribución de los autores

Todos autores contribuyeron significativamente en la elaboración del artículo.

7.&n= bsp;     Costos de financiamiento

La presente investigación fue financiada en su totalidad con fondos propios de= los autores.

8.&n= bsp;     Referencias bibliográficas

Bello Durand, J. B. (2013). Mediación del Software GeoGebra en el aprendizaje = de programación lineal en alumnos de quinto grado de educación secundaria = [Tesis de maestría, Pontificia Universidad Católica de Perú, Lima, Perú]. <= /span>https://tesis.pucp.ed= u.pe/items/83b9e7ce-4be2-4be7-9f9e-59bcaaae305a

Bravo Guerrero, F. (2019). Las nuevas clases de geometría= . RECUS, 4(3), 14-21. http= s://dialnet.unirioja.es/descarga/articulo/7368627.pdf

Brito Mancero, L. F. (2022). GeoGebra como herramienta didáctica para el aprendizaje de las cónicas y su incidencia en el rendimiento académico de l= os estudiantes de nivelación de la Escuela Superior Politécnica de Chimborazo = 2021 [Tesis de maestría, Escuela Superior Politécnica de Chimborazo, Riobamb= a, Ecuador]. http://dspace.espoch.edu.ec/handle/123456789/17275

Dávila-Ornelas, M. Y., Gaspar de Alba, A. G., Hernández Sánchez, P., & Fonseca, A. (201= 3). Secuencia didáctica para el aprendizaje de las figuras cónicas y sus difere= ntes representaciones. CULCyT/Eduación, 10(50.1), 27-36 https://dialnet.unirioja.es/descarga/articulo/7067277.pdf=

Escuela Superior Politécnica de Chimborazo [ESPOCH]. (2020). Reglamento de Regim= én acedémico. http://admision.espoch.edu.ec/wp-content/uploads/2017/09/Reglamento-de-Regi= men-Academico-ESPOCH-RRA2014.pdf

Garzón Zipa, C. J. (2020). Situaciones didácticas para el aprendizaje de las cónicas desde el concepto de métrica [Tesis de maestría, Universidad Pedagógica y Tecnológica de Colombia, Tunja, Colombia]. http://repositorio.uptc.edu.co/handle/001/3720

Grisales-Aguirre, A. (2018). Uso de recursos TIC en la enseńanza de las matemáticas: retos y perspectivas. Entramado, 4(2), 198 - 214. http://dx.doi.org/10.18041/1900-3803/entramado.2.4751=

Ibarra Núńez, M. (2019). GeoGebra movil en la enseńanza de las matemáticas. Mem= orias de la I Jornada ecuatoriana de GeoGebra, 37 - 49. https://www.researchgate.net/publication/346547499_Geogebra_Movil

Montańo, P., & Valarezo, O. (2023). Uso de GeoGebra para generar aprendizajes significativos de las secciones cónicas. LATAM Revista Latinoamericana de Ciencias Sociales y Humanidades, 4(5), 65-85. https://doi.org/10.56712/latam.v4i5.1302

Murillo Quińones, N. C. (2020). Objeto de aprendizaje para la enseńanza de las secciones cónicas incorporando los conceptos matemáticos, la teoría de representaciones y las aplicaciones [Tesis de maestría, Universidad Nacional de Colombia, Manizales, Colombia]. https://repositorio.unal= .edu.co/handle/unal/77611

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El artículo que se publica es de exclusiva responsabilidad de los autores y no necesariamente reflejan el pensamiento de la Revista Alfa Publicaciones.

El artículo queda en propiedad d= e la revista y, por tanto, su publicación parcial y/o total en otro medio tiene = que ser autorizado por el director de la Revista Alfa Publicaciones.

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¹	Luis Fabian Brito Mancero	https://orcid.org/0009-0008-2108-1715
	Universidad Estatal de Bolívar (UEB) luis.brito@ueb.edu.ec
2	Marcela Yolanda Brito Mancero<= o:p>	https://orcid.org/0000-0003-26= 89-3516
	Escuela Superior Politécnica de Chimborazo (ESPOCH) mybrito@espoch.edu.ec

	Artículo de Investigación Científica y Tecnológica Enviado: 11/11/2024 Revisado: 15/12/2024 Aceptado: 02/01/2025 Publicado: 30/01/2025 DOI: https://doi.org/10.33262/ap.v7i1.576 =
<= span lang=3DEN-US style=3D'font-size:8.0pt;line-height:115%;font-family:"Times= New Roman",serif; mso-fareast-font-family:"Times New Roman";color:blue;mso-ansi-language:EN= -US'>
&= nbsp; Cítese: <= /b>		Brito Mancero, L. F., & Br= ito Mancero, M. Y. (2025). Uso de GeoGebra en el aprendizaje de secciones cón= icas de geometría analítica y su incidencia en rendimiento académico de los estudiantes de nivelación universitaria. AlfaPublicaciones, 7(1), 88–99. = https://doi.org/10.33262/ap= .v7i1.576
		ALFA PUBLICACIONES, es una revista multidisciplinar= , trimestral, que se publicará en soporte electrónico tiene como misión contribu= ir a la formación de profesionales competentes con visión humaníst= ica y crítica que sean capaces de exponer sus resultados investigativos y científicos en la misma medida que se promueva mediante su intervención cambios positivos en la sociedad. https://alfapublicaciones.com <= span style=3D'font-size:8.0pt;line-height:115%;font-family:"Times New Roman",s= erif; mso-fareast-font-family:"Times New Roman"'>La revista es editada por la Editorial Ciencia Digital (Editorial de prestigio registrada en la Cámara Ecuatoriana de Libro con No de Afiliación 663) www.celibro.org.ec
		Esta revista está protegida ba= jo una licencia Creative Commons Attribution Non Commercial No Derivatives 4= .0 International. Copia de la licencia: http://creativecommons.org/licenses/by-nc-sa/4.0/ <= span style=3D'font-size:8.0pt;line-height:115%;font-family:"Times New Roman",s= erif; mso-fareast-font-family:"Times New Roman"'>
Palabras claves: Aprendizaje, estrategia didáctica, rendimiento académico, secciones cónicas.		Resumen: Introducción. El rendimiento de la matemática en el bachillerato en el Ecuador es bajo ya = que las metodologías enseńanza aprendizaje se centran en métodos tradicionale= s, en caso de la geometría analítica suele centrarse en un tratamiento algebraico de las figuras lo que contribuye a que los estudiantes present= en dificultades en la adquisición de nuevos conocimientos durante la universidad. Objetivo. Anal= izar comparativamente el rendimiento académico que alcanzan los estudiantes de nivelación universitaria en la asignatura de Geometría analítica en el te= ma cónicas, cuando en el proceso enseńanza-aprendizaje se hace uso de una herramienta didáctica tecnológica como el software libre GeoGebra frente = a la enseńanza-aprendizaje tradicional. Metodología. Se partió de la hipótesis que el aprendizaje de cónicas con el uso del progr= ama GeoGebra incide de manera significativa en el rendimiento académico. Para= lo cual se identificó un grupo control y un grupo experimental de los estudiantes de Geometría analítica, se realizó la descripción del desenvolvimiento en los subtemas circunferencia, parábola, elipse e hipér= bola con el método tradicional y con el uso de GeoGebra; finalmente se correlaciona los rendimientos académicos alcanzados por cada grupo; para = la recolección de datos se utilizó aplicó una prueba diagnóstica, cuatro talleres uno por cada subtema trabajado y una prueba global final. Resultados. En la evaluación diagnostica = se encontró que los rendimientos de los estudiantes provenientes del bachillerato se encuentran por debajo del 70%; el aprendizaje de las secciones circunferencia, parábola y elipse se demostró que existe difere= ncia significativa a favor del aprendizaje con el uso de GeoGebra. Conclusión. El introducir metodologías tecnológicas en el proceso enseńanza apr= endizaje mediante el uso de GeoGebra en el estudio de secciones cónicas incide de forma positiva en la adquisición de conocimientos. Área de estudio general: Educac= ión. Área de estudio específica: Sec= ciones cónicas. Tipo de estudio:<= /b> Artículos originales.
Keywords: Learning, teaching strategy, academic performance, conical sections	&= nbsp;	Abstract Introd= uction. The performance of mathematics in high school in Ecuador is low s= ince teaching-learning methodologies focus on traditional methods; in the case= of analytical geometry, it usually focuses on an algebraic treatment of figu= res, which contributes to students presenting difficulties in the acquisition = of new knowledge during university. Object= ive. Comparatively analyze the academic performance achieved by univer= sity level students in the subject of Analytical Geometry in the topic of coni= cs, when in the teaching-learning process a technological didactic tool such = as the free software GeoGebra is used compared to traditional teaching-learn= ing. Method= ology. The hypothesis was that learning conics with the use of the GeoGe= bra program significantly affects academic performance. For which a control g= roup and an experimental group of Analytical Geometry students were identified, the description of the development in the subtopics circumference, parabo= la, ellipse and hyperbola was carried out with the traditional method and with the use of GeoGebra; Finally, the academic performance achieved by each g= roup is correlated; To collect data, a diagnostic test was applied, four workshops, one for each subtopic worked on, and a final global test. Results. In the diagnostic evaluation, it was found that the performance of students from high school is below 70%; The learning of the circumference, parabola and ellipse sections showed that there is a significant differen= ce in favor of learning with the use of GeoGebra. Conclusion. In= troducing technological methodologies in the teaching-learning process using GeoGeb= ra in the study of conic sections has a positive impact on the acquisition of knowledge. Gener= al Study Area: Education. Specific study area: conic sections. Type of study: Original articles.

Instrumento	Las preguntas son comprensibles, fáciles= y claras, para el evaluado	Las opciones de respuesta son adecuadas<= o:p>	Las preguntas son congruentes para poder validar la misma
Prueba de diagnóstico	92P%	93%	93%
Taller circunferencia	92%	91%	91%
Taller parábola	92%	91%	92%
Taller elipse	92%	91%	92%
Taller hipérbola	91%	89%	91%
Prueba final	90%	91%	91%

Curso	Estudiantes matriculados	Prueba Diagnóstico	Taller Circunferencia	Taller Parábola	Taller Elipse	Taller Hipérbola<= span style=3D'mso-bookmark:_Hlk99202632'>	Examen final
N° estudiantes rendimientos sobre 70%<= /span>	%	N° estudiantes rendimientos sobre 70%<= /span>	%	N° estudiantes rendimientos sobre el 70%	%	N° estudiantes rendimientos sobre 70%<= /span>	%	N° estudiantes rendimientos sobre70%	%	N° estudiantes rendimientos sobre 70%<= /span>	%
GC1	42	4	10%	9	21%	14	33%	16	38%	22	52%	14	33%
GC2	41	2	5%	14	34%	15	37%	0	0%	12	29%	16	39%
GE1	42	1	2%	19	45%	16	38%	16	38%	25	60%	17	40%
GE2	44	0	0%	9	20%	23	52%	13	30%	18	41%	16	36%
Promedio GC	7%	28%	35%	19%	41%	36%
Promedio GE	1%	33%	45%	34%	50%	38%

Acti= vidad	Inte= rvalo al 95% de confianza para las diferencias de las medianas _= 1;₁ - η₂	Prue= ba de hipótesis
Hipó= tesis alterna	Valo= r p
Prueba Diagnóstico	(1,0 ; 1,8)<= o:p>	H₁: η₁ - η₂ ≠ 0	0,000
T. Circunfer= encia	(-1,= 3 ; -0,0)	H= 321;: η₁ - η₂ < 0	0,034
T. Parábola<= o:p>	(-1,1 ; -0,0= )	H₁: η₁ - η₂ < 0	0,02= 2
T. Elipse	(-1,= 5 ; -0,0)	H= 321;: η₁ - η₂ < 0	0,017
T. Hipérbola=	(-1,0 ; 0,5)=	H₁: η₁ - η₂ < 0	0,122
Examen =	(-0,= 7 ; 0,5)	H= 321;: η₁ - η₂ < 0	0,41= 1