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T= aptana kañari como recurso didáctico, para desarrollar razonamiento lógico matemát= ico en quinto año de básica

Taptana kañari as a didactic resource, to develop mathematical logic= al reasoning in the fifth year of elementary school.

 

 


1

Elias Vaquilema Inguillay.                            https://orcid.org/0000-0002-5914-8486

Universidad Católica de Cuenca, Azogues, Ecuador

elias.vaquilema.78@est.= ucacue.edu.ec

 

2

Roxana Auccahuallpa Fern= ández                 https://orcid.org/0000= -0002-5242-2083

Universidad Católica de Cuenca, Azogues, Ecuador

roxana.auccahuallpa@uca= cue.edu.ec

 

3

Sergio Constantino Ochoa Encalada             https://orcid.org/0000-000= 3-3067-3719

Universidad Católica de Cuenca, Azogues, Ecuador<= /o:p>

scochoae@ucacue.edu.ec

 

 

 

 

 

 =

 

Artículo de Investigación Científica y Tecnológica

Enviado: 09/07/2022

Revisado: 24/08/2022

Aceptado: 19/09/2022

Publicado:05/10/2022

DOI: https://doi.org/= 10.33262/ap.v4i4.286

<= span lang=3DEN-US style=3D'font-size:12.0pt;line-height:115%;font-family:"Time= s New Roman",serif; mso-fareast-font-family:Calibri;color:blue;mso-ansi-language:EN-US'>=  

 

 

Cítese:

 

 

Vaquilema Inguillay, E., Auccahuallpa Fernández , R. . . . . . . . . . . . . . . ., & Ochoa Encalada, S. C. (2022). Taptana kañari como recurso didáctico, para desarrollar razonamiento lógico matemático en quinto año de básica. AlfaPublicaciones, 4(4), 83–102. https://doi.org/10.33262/ap= .v4i4.286

 

 

 

ALFA PUBLICACIONES, es una Revista Multidisciplinar, Trimestral, que se public= ará en soporte electrónico tiene como misión contribuir a la &nbs= p; formación de profesionales competentes con visión humanística y crít= ica 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  

La revista es editada por la Editorial Ciencia Digital (Editorial de prestigio registrada en la Cámara Ecuatoria= na de Libro con No de Afiliación 663) www.celibro.org.ec<= /a>

 

 

 

Esta revista está protegida bajo una licencia Creative Commons AttributionNonCommercialNoDerivatives 4.0 International. Copia de la licencia: http://creativecommons.org= /licenses/by-nc-nd/4.0/

 

Palabras claves:

Innovación educacional, aprendizaje activo, enseñanza primaria, Matemática, estrateg= ias de enseñanza <= /p>

 

 

Resumen

Este trabajo investigativo fue con el objetivo de fortalecer el razonamiento lógico matemático en los estudiantes de qui= nto año de básica del CECIB “Daniel Clavijo Iglesias” en la resolución de problemas, mediante el uso de la Taptana, para de esta manera mejorar el nivel de razonamiento matemático. Para lo cual, se trabajó mediante la metodología cuasi experimental, con un enfoque epistemológico mixto, de muestreo aleatorio estratificado y de cohorte longitudinal. Como población de estudio en la presente investigación tuvo una participación directa y volunta= ria de 12 estudiantes de quinto de básica del CECIB “Daniel Clavijo Iglesias”= que está ubicada a 3200 m.s.n.m en la jurisdicción de la comunidad de Cebadas, como instrumento de investigación se aplicó fichas de observación pretest= y post-test evidenciando como resultado que el material didáctico utilizado en los niños permitió lograr un cambio significativo, ya que la significación bilateral es menor a 0,05 en todas= las variables, de esa manera logrando un razonamiento lógico matemático.=

 

 

Keywords: Educational innovation, active learning, primary education, Mathematics, teaching strategies

 

Abstract

This investigative work was with the objective of strengthening the mathematic= al logical reasoning in the students of fifth year of basic of the CECIB "Daniel Clavijo Iglesias" in the resolution of problems, with t= he Taptana, in order to improve the level of reasoning. Mathematical. For which, we worked through the quasi-experimental methodology, with a mixed epistemological approach, stratified random sampling and longitudinal coh= ort. As a study population in the present investigation, 12 fifth-year students from the CECIB "Daniel Clavijo Iglesias" had a direct and volun= tary participation, which is located at 3200 m.a.s.l. in the jurisdiction of t= he community of Cebadas, as a research instrument, cards were applied. of pre-test and post-test observation, showing as a result that the didactic material used in the children allowed to achieve a significant change, si= nce the bilateral significance is less than 0.05 in all the variables, thus achieving a mathematical logical reasoning.

 = ;

 

<= o:p> 

 

Introducción.

La Educación = del siglo XXI exige que los estudiantes desarrollen habilidades, competencias y destrezas que permitan resolver situaciones en su diario vivir, pero lamentablemente en nuestra práctica educativa evidenciamos dificultades en = el proceso de la enseñanza de las matemáticas ya que los estudiantes no han desarrollado un pensamiento crítico, analítico y reflexivo que permita a el= los resolver situaciones en su vida cotidiana, Socas (2011) en sus estudios realizados en la Universi= dad de La Laguna al informe PISA menciona que “el análisis de los resultados obtenidos en estas evaluaciones nos muestran unos resultados insuficientes = en las matemáticas” (p. 200). 

De la misma m= anera Larrazolo et al. (2013) mencionan que las matemáticas son planes y programas de mucha importancia e= n el currículo mexicano con el objetivo de desarrollar un pensamiento matemático= en los estudiantes y de esa manera tengan capacidades para resolver diversas situaciones de manera crítica, analítica y reflexiva, pero en los estudios = realizados por el Instituto Nacional para la Evaluación de la Educación (INEE) se evidencia que los estudiantes mexicanos de educación básica logran niveles = de desempeño muy inferiores a los esperado.  

Según Institu= to Nacional de Evaluación (2018= ) en las evaluaciones realizadas en el año lectivo 2017-2018 Ser Estudiante se evidencian bajos puntajes en resultados académicos en el campo de las matemáticas, el mismo constituye un desafío muy importante para el sistema = de educación que a la larga se reflejara de manera directa en la calidad de educación, por lo expuesto, es fundamental desarrollar un pensamiento matemático en nuestros estudiantes con habilidades, destrezas y estrategias= en la resolución de problemas matemáticos y lo más primordial que sean socieda= des con creatividad. 

El desarrollo= de un pensamiento lógico matemático no se ha desarrollado en los estudiantes de quinto año de básica por múltiples factores, uno de ellos es la mala o nula utilización de recursos didácticos en su práctica educativa tales como: Taptana, base 10, círculo de fracciones, triángulo mágico y el uso de las Tecnología de Información y Comunicación, otro de los factores a mencionar es la falta de estrategias innovadoras por parte del docente en el proceso de interaprendi= zaje, como manifiesta Montaluisa (= 2018) que desde un primer momento se debe empezar a trabajar mediante representaciones, la misma se inicia con signos elaborados con materiales concretos sean estas semillas, piedras, palillos y la Taptana elaborada en = madera o cartones y así no caer en los problemas que surgieron en la educación tradicional en una enseñanza repetitiva y memorística. Además, menc= iona que el proceso del interaprendizaje matemático debe ser trabajada en sus tr= es momentos: concreto, gráfico y abstracto.  

El desarrollo= de un pensamiento lógico matemático en el proceso de enseñanza aprendizaje consti= tuye una destreza primordial ya que permitimos a nuestros estudiantes comprender conceptos abstractos partiendo de lo concreto, fomentamos estrategias de ra= zonamiento frente a múltiples realidades, así también desarrollamos la capacidad de creación para que nuestros estudiantes sean individuos cooperativos con la comunidad ante situaciones relacionadas a las matemáticas, como hace énfasi= s Medina (2017) “el desarrollo= de pensamiento lógico matemático se vincula a las vivencias de él y es un elem= ento decisivo para la comprensión de la realidad” (p. 126).

El proceso de= la enseñanza aprendizaje de las matemáticas debe estar enfocada en desarrollar= un pensamiento analítico, reflexivo y crítico trabajando de manera interdisciplinar lo científico con lo andino ya que de esa manera inculcare= mos en los estudiantes la capacidad de resolver diversas situaciones que presen= te en su diario vivir cotidiano, como menciona Barcia et al. (2019)la vinculación de los conocimientos de las matemáticas con las diferentes disciplinas científicas= y saberes ancestrales…contribuye al desarrollo de nuestro medio ya sea en lo social, natural y cultural” (p. 19).

La educación = del siglo XXI exige a todos los docentes fomentar un pensamiento lógico matemát= ico en todos los actores que forman parte del proceso de enseñanza aprendizaje = ya que hoy en día constituye una habilidad fundamental en la formación de los educandos, como hace énfasis Gordon et al. (2022) “El  desarrollo  del  pensamiento  lógico  en  toda  la humanidad,  representa  una   acción importante  dentro  de  su  formación  integral,  pues  dentro  de  las  funciones  básicas  que ejecuta el cerebro, está el saber pensar para resolver los múlti= ples problemas” (p. 4).

La adquisición de habilidades y destrezas= en la resolución de problemas de los educandos demuestran la capacidad de análisi= s, reflexión a las diversas situaciones que se presente en la vida cotidiana d= el educando, con la apropiación de la capacidad de resolución de problemas los educandos resolverán diversas situaciones que surjan en el contexto educati= vo, familiar y social, como menciona Jaime (2021)La resolució= n de problemas mejora la toma de decisiones, la capacidad de análisis, la detecc= ión de necesidades y objetivos por lo que prepara a los educandos para el futur= o, pues adquieren habilidad para identificar, analizar y resolver problemas” (= p. 1).

El proceso de construcción del nuevo conocimiento de las matemáticas en los educandos del siglo XXI debe centrar= en desarrollar habilidades y aptitudes que permitan ser constructores de su pr= opio conocimiento, la misma se logra mediante uso de recurso didáctico como la T= aptana kañari y un trabajo colaborativo en el aula, por lo expuesto Bustamante et al. (2014) hace mención que “hacer  matemática=   implica  razonar,  imaginar,  descubrir,  intuir,  probar,  generalizar,  utilizar técnicas,  aplicar<= span style=3D'mso-spacerun:yes'>  destrezas,  estimar  y  comprobar  resultados,  es  realmente  necesario  que  la enseñanza  de  las  matemáticas  sean  significativas” (p. 23= ).

Por lo antecedido la presente investigación tiene por objetivo fortalecer el razonamiento lógico matemático en los estudiantes de quinto a= ño de básica del CECIB “Daniel Clavijo Iglesias” en la resolución de problemas, mediante el uso de la Taptana kañari, para de esta manera mejorar el nivel = de razonamiento matemático. Para lo cual se plantea la siguiente pregunta de i= nvestigación ¿De qué manera la Taptana kañari fomenta la motivación y la creatividad, pa= ra el desarrollo del pensamiento lógico matemático en los estudiantes de quinto año de básica? 

Históricament= e el proceso de la enseñanza aprendizaje ha sido centrada en la memoria del estudiante, a base de la memorización de diversos conocimientos que transmi= te el docente en su hora clase, por lo expuesto Pulloquinga (2020) manifiesta q= ue el proceso de interaprendizaje de las matemáticas debe estar centrado al desarrollo de la creatividad y habilidades para la resolución de problemas cotidianos, de esa manera lograr un conocimiento significativo en la vida de los alumnos; así también es importante mencionar que la memorización de diversos conocimientos no es nada malo, pero debe ser en momentos oportunos cuando sea necesario para que el estudiante reproduzca su nuevo conocimient= o. 

Desarrollar un pensamiento lógico matemático en los estudiantes constituye una habilidad m= uy importante en cada uno de ellos ya que serán capaces de resolver diversas situaciones cotidianas, como menciona Luna (2016) al fomentar un pensamiento lógico en los estudiantes permitimos resolver situaciones y ejercicios de diversos temas, además hace mención que los docentes no evidenciamos los conocimientos previos de cada = uno de ellos en la hora clase de matemática, solamente limitamos a seguir en lo= s textos que facilita el ministerio. Por lo cual, los estudiantes tienen muchas dificultades en el aprendizaje de las matemáticas, como menciona Medina (20= 18) los estudiantes aprenden los conocimientos de matemáticas por obligación no= por responsabilidad e interés o algo que motive al aprendizaje de su nuevo conocimiento.  

Por lo expues= to, es primordial que los docentes apropiemos las diversas estrategias metodológic= as que permitirán mejorar el proceso de interaprendizaje de las matemáticas, de esa manera formar estudiantes con muchas aptitudes, capacidades y destrezas, como hace énfasis Bustamante el al. (2014) que para desarrollar un razonamiento lógico en los estudiantes es importante que los docentes utilicemos diversas estrategias metodológicas de acuerdo a= los diversos temas y así lograr obtener resultados esperados en la vida de los estudiantes.  

Además, Jaime= (2021) menciona que la utilización de diversas estrategias de aprendizaje del docente trae consigo diversas oportunidades al estudiante ya que permitimos relacionar su conocimiento previo al nuevo conocimiento adaptando a su realidad contextua= l, así también con las diversas estrategias metodológicas brindamos libertad al estudiante para que construya su propio conocimiento y de esa manera su con= ocimiento sea significativo. 

Las diversas estrategias metodológicas que hoy en día existe permiten al docente crear un ambiente dinamizador, creativo y activo en las clases de matemáticas, como = hace menciona (Borbor, 2020) las estrateg= ias que los docentes utilicemos en la hora clase constituyen un camino hacia el desarrollo de un pensamiento lógico matemático en cada uno de los estudiant= es, ya que las matemáticas desde lo antes es considerado complicado de entender para los alumnos como también requiere un alto nivel de entendimiento por la complejidad de sus ejercicios, por lo cual, es primordial que los docentes utilicen estrategias apropiadas según el tema para crear un ambiente dinamizador en la hora clase. 

Como se hizo = mención en los párrafos anteriores para desarrollar un pensamiento lógico matemático depende de las estrategias metodológicas que utilice el docente para así lo= grar un aprendizaje significativo, por lo cual,  Pulloquinga (2020) plantea el aprendizaje cooperativo como u= na estrategia que permite al estudiante trabajar de manera grupal compartiendo= sus experiencias en la solución de problemas, además, con esta metodología los estudiantes que conforman el grupo trabajaran hasta que todos comprendan el nuevo conocimiento. 

Así también es importante mencionar otra estrategia metodológica “Aprendizaje Basado en Problemas” como menciona Tapia et al. (2020) es una metodología de vital importancia en el aprendizaje de las matemática= s, ya que crea la capacidad de razonamiento en los alumnos para solucionar problemas matemáticos y así desarrollar un pensamiento creativo, lógico, reflexivo y analítico que conlleva a una mejor comprensión de las situacion= es planteadas.  

En la Constit= ución del Ecuador (2008)&nb= sp; Art. 2= 7 menciona que la educación se centrará en el ser humano y garantizará su desarrollo holístico, en el marco del respeto a los derechos humanos, al medio ambiente sustentable y a la democracia; será participativa, obligatoria, intercultur= al, democrática, incluyente y diversa, de calidad y calidez; impulsará la equid= ad de género, la justicia, la solidaridad y la paz; estimulará el sentido crít= ico, el arte y la cultura física, la iniciativa individual y comunitaria, y el desarrollo de competencias y capacidades para crear y trabajar (p. 17). 

Tambié= n es importante hacer mención al Art. 42 de LOEI (2017) donde manifiesta que:

la edu= cación general básica desarrolla las capacidades, habilidades, destrezas y competencias de las niñas, niños y adolescentes desde los cinco años de eda= d en adelante, para participar en forma crítica, responsable, solidaria en la vi= da ciudadana y continuar los estudios de bachillerato. La educación general bá= sica está compuesta por diez años de atención obligatoria en los que se refuerza= n, amplían y profundizan las capacidades y competencias adquiridas en la etapa anterio= r, y se introducen las disciplinas básicas garantizando su diversidad cultural y lingüística (P. 32). 

El apr= endizaje de las matemáticas siempre debe estar centrada en la realidad y necesidad de los estudiantes, por lo cual, con el uso de la Taptana permitimos el desarr= ollo del razonamiento lógico matemático en los estudiantes, por lo expuesto se ha analizado el Currículo EIB (= 2017) en la que hace mención que las matemáticas son una ciencia que, debido a los erróneos procedimientos de enseñanza, ha perdido los referentes sociales, en este programa se pretende partir de las necesidades personales y sociales de uso y aplicación del número, pasar al aprendizaje de los conceptos lógico-m= atemáticos y, luego, a su aplicación para solucionar los problemas con los que se enfr= enta la población en la vida cotidiana (p. 37).  

Según = Montaluisa (2018) la Taptana es = un recurso didáctico que surgió en la época de los Incas, las mismas fueron elaboradas en piedras y maderas, hoy en día en las instituciones interculturales bilingües se ha convertido en un recurso innovador ya que permite al estudiante representar diferentes operaciones matemáticas, este recurso innovador (Taptana) está compuesta de filas y columnas, en cada col= umna existe tantos hoyos según la base que se va a utilizar en la representación= de las cantidades, en la parte superior existe un hoyo más grande que es utili= zada para colocar granos o semillas que se utiliza en la simbolización o la fase abstracta de las cantidades. 

Así ta= mbién Montaluisa (2018) hace énfasis que = la enseñanza de las matemáticas debe partir de una representación concreta, po= r lo antecedido manifiesta que:

Es necesario aplicar los conceptos de la semiótica para que las niñas y los niños vayan construyendo y/o descubriend= o el proceso de simbolización a usarse en la comprensión de las ciencias. Desde = el inicio los alumnos deben manejar el proceso de construir representaciones. = Esto hay que comenzar con signos elaborados con materiales concretos. Entre estos materiales están los palillos, las piedras, los atados; las taptanas en pie= dra, madera o en otro material (p.20).

Además= , Montaluisa (2018) menciona que la funcionalidad de la Taptana es enseñar las matemáticas en un Espacio Matemá= tico de Representación de la realidad, así también recomienda que la pedagogía d= e la matemática siga practicando la construcción de diversos conocimientos que surgieron en las diversas culturas del mundo. Además, menciona que la cienc= ia surge de la observación, estudio e interpretación de los elementos y fenóme= nos del Cosmos, para lo cual, los seres humanos utilizamos los sentidos, las emociones y sentimientos. 

La Tap= tana hoy en día se ha convertido en un recurso dinamizador del proceso del interaprendizaje Alquinga (2= 019) menciona que la Taptana aporta muchísimo a la comprensión lógica del sistema decimal y en la resolución de diferentes operaciones matemáticas como: suma, resta, multiplicación y división, su metodología permite al docente trabajar según el interaprendizaje matemático de lo concreto a lo abstracto. Por lo cual, es importante difundir en las instituciones educativas el uso de este recurso educativo la Taptana. 

En la = actualidad existen diversos recursos, estrategias que permite que el aprendizaje de las matemáticas sea crítica, analítica y reflexiva, como menciona Campos (2021) que el aprendizaje d= e las matemáticas hoy en día brinda diversas posibilidades que conlleva al desarr= ollo de la personalidad del estudiante, así también permite el perfeccionamiento= de distintas habilidades intelectuales como: la creatividad, la memoria, el razonamiento, la comprensión verbal, etc. 

Por último, es importan= te hacer mención del conectivismo en la educación del siglo XXI, la tecnología brinda diversas oportunidades a la sociedad actual en diversos campos como: educat= ivo, social, cultural…por lo cual es fundamental que los docentes y demás actores que formamos parte del campo educativo innovemos nuestros conocimientos en = el uso de las diferentes plataformas digitales que permitan lograr una educaci= ón híbrida y significativa en los educandos, también al trabajar con los aplicativos digitales mejoramos nuestra comunicación con los educandos.

La transición de un enf= oque tradicional a lo conectivismo permite al estudiante aprender mediante juegos creados por los docentes en las diferentes plataformas digitales y de esa manera el docente brinda oportunidades a los estudiantes desarrollar sus habilidades, competencias, capacidades, actitudes hacia la construcción de = su propio conocimiento adaptadas a su realidad educativo, social, cultural.

Metodologia.

La presente investigación es cuasi experimental, con un enfoque epistemológico mixto, de muestreo aleatorio estratificado y de cohorte longitudinal que se realizó en sus dos momentos: Pretest y post-test. Para la aplicación de la ficha pretest se utilizó la T= aptana kañari sin una explicación minuciosa del uso del material, mientras para la aplicación de la ficha post-test primeramente se realizó una explicación minuciosa de las partes de la Taptana kañari, codificación de las semillas = y el proceso para la resolución de ejercicios que permita fortalecer el razonami= ento lógico matemático en los estudiantes de quinto año de básica.

Como población de estudi= o en la presente investigación tuvo una participación directa y voluntaria de 12 estudiantes de quinto de básica del CECIB “Daniel Clavijo Iglesias” que está ubicada a 3200 m.s.n.m. en la jurisdicción de la comunid= ad de Cebadas, parroquia Ingapirca, cantón y provincia Cañar. Ade= más, por ser una investigación con los estudiantes se ha basado en diferentes pr= incipios éticos como: respeto, justicia, responsabilidad, honestidad y libertad.

La ficha de observación fue aplicada por el docente el aula con el acompañamiento de un docente de la institución de ma= nera presencial a 4 niños y 8 niñas, para conocer la fiabilidad del instrumento = se procedió con la prueba Alfa de Cronbach en SPSS resultando un 0,956 de coeficiente de las 24 fichas de observación.

Resultados.= =

Se realizó una prueba de normalidad a través de la prueba Shapiro Wilk en la q= ue se nota que las 12 variables son paramétricas con una significación menor a 0,05, además el intervalo de confianza para la media es 95%.

Los resultados fueron obtenidos mediante la aplicación de ficha de observación, evidentemente las interrogantes planteadas se encaminaban a lograr el objet= ivo general, reflejando los siguientes datos:

Tabla 1.

Est= adístico del grupo participó activamente en el uso de la Taptana

 

Test

N

Media

Desviación típ.

Error típ. de la media

Participó activamente en el uso de la Taptana

Pretest

24

3,33<= /p>

,761<= /p>

,155<= /p>

= Postest

24

4,13

,537

,110

Prueba de muestras independientes

 

Varianzas iguales<= /o:p>

No varianzas iguales

Prueba de Levene para la igualdad de varianzas

F

4,298=

 

Sig.

,044<= /p>

 

Prueba T para la igualdad de medias

t

-4,163

-4,163

gl

46

41,331

Sig. (bilateral)

,000<= /p>

,000<= /p>

Diferencia de medias

-,792=

-,792=

Error típ. de la diferencia

,190<= /p>

,190<= /p>

95% Intervalo de confianza para la diferencia

Inferior

-1,174

-1,176

= Superior

-,409<= /p>

-,408<= /p>

Fuente: Elaboración propia.

En = la tabla 2 se puede evidenciar un cambio significativo entre pretest y pos-tes= t, ya que la significación bilateral es menor a 0,05 que está enfocado dentro = de la teoría asociados con un 95 % de intervalo de confianza.

 

Tabla 2.

Estadísticos de grupo variables de análisis

 

Test

N

Media

Desviación típ.

Error típ. de la media

Re= suelvo el problema planteado

Pretest

24

3,08

,776

,158

Postest

24

3,88

,537

,110

Observo un trabajo cooperativo

Pretest

24

3,25

,737

,150

Postest

24

4,79

,415

,085

Aplico la Taptana<= /o:p>

Pretest

24

2,83

,816

,167

Postest

24

4,04

,550

,112

Codificó correctamente = las semillas

Pretest

24

3,50

,780

,159

Postest

24

4,75

,442

,090

Resuelvo correctamente = el problema con Taptana

Pretest

24

2,92

,776

,158

Postest

24

3,88

,537

,110

Conozco el proceso para= la solución de problemas

Pretest

24

2,83

,917

,187

Postest

24

3,88

,612

,125

Reconozco las partes de= una Taptana

Pretest

24

3,25

,608

,124

Postest

24

4,83

,381

,078

Muestra interés por el = tema

Pretest

24

3,25

,737

,150

Postest

24

4,79

,415

,085

Demuestro motivación en= la clase

Pretest

24

3,67

,761

,155

Postest

24

4,79

,415

,085

Material es pertinente<= o:p>

Pretest

24

3,83

,381

,078

Postest

24

4,79

,415

,085

Qué tiempo utilizo en resolver ejercicios

Pretest

24

1,17

,565

,115

Postest

24

3,08

,282

,058

Participó activamente e= n el uso de la Taptana

Pretest

24

3,33

,761

,155

Postest

24

4,13

,537

,110

Prueba de muestras independientes

 

Prueba de Levene para la igualdad de varianzas

Prueba T para la igualdad de medias

F

Sig.<= /p>

t

gl

Sig. (bilateral)

Diferencia de medias

Error típ. de la difere= ncia

95% Intervalo de confia= nza para la diferencia

Inferior

Superior

Re= suelvo el problema planteado

Se han asumido varianzas iguales

4,039=

,050<= /p>

-4,112

46

,000<= /p>

-,792=

,193<= /p>

-1,179

-,404=

No se han asumido varia= nzas iguales

 

 

-4,112

40,920

,000<= /p>

-,792=

,193<= /p>

-1,180

-,403=

 

 

Tabla 2.

Estadísticos de grupo variables de análisis (c= ontinuación)

 

 

Prueba de Levene para la igualdad de varianzas

Prueba T para la igualdad de medias

 

 

F

Sig.<= /p>

t

gl

Sig. (bilateral)

Diferencia de medias

Error típ. de la difere= ncia

95% Intervalo de confia= nza para la diferencia

 

 

 

 

 

 

 

 

 

Inferior

Superior

Observo un trabajo cooperativo

Se han asumido varianzas iguales

10,752

,002<= /p>

-8,928

46

,000<= /p>

-1,542

,173<= /p>

-1,889

-1,194

No se han asumido varia= nzas iguales

 

 

-8,928

36,239

,000<= /p>

-1,542

,173<= /p>

-1,892

-1,192

Aplicó la Taptana<= /o:p>

Se han asumido varianzas iguales

9,388=

,004<= /p>

-6,013

46

,000<= /p>

-1,208

,201<= /p>

-1,613

-,804=

No se han asumido varia= nzas iguales

 

 

-6,013

40,310

,000<= /p>

-1,208

,201<= /p>

-1,614

-,802=

Codificó correctamente = las semillas

Se han asumido varianzas iguales

10,533

,002<= /p>

-6,828

46

,000<= /p>

-1,250

,183<= /p>

-1,619

-,881=

No se han asumido varia= nzas iguales

 

 

-6,828

36,401

,000<= /p>

-1,250

,183<= /p>

-1,621

-,879=

Resuelvo correctamente = el problema con Taptana

Se han asumido varianzas iguales

4,039=

,050<= /p>

-4,978

46

,000<= /p>

-,958=

,193<= /p>

-1,346

-,571=

No se han asumido varia= nzas iguales

 

 

-4,978

40,920

,000<= /p>

-,958=

,193<= /p>

-1,347

-,570=

Conozco el proceso para= la solución de problemas

Se han asumido varianzas iguales

12,913

,001<= /p>

-4,629

46

,000<= /p>

-1,042

,225<= /p>

-1,495

-,589=

No se han asumido varia= nzas iguales

 

 

-4,629

40,115

,000<= /p>

-1,042

,225<= /p>

-1,496

-,587=

 

Tabla 2.

Estadísticos de grupo variables de análisis (c= ontinuación)

 

 

Prueba de Levene para la igualdad de varianzas

Prueba T para la igualdad de medias

 

 

F

Sig.<= /p>

t

gl

Sig. (bilateral)

Diferencia de medias

Error típ. de la difere= ncia

95% Intervalo de confia= nza para la diferencia

 

 

 

 

 

 

 

 

 

Inferior

Superior

Reconozco las partes de= una Taptana

Se han asumido varianzas iguales

6,847=

,012<= /p>

-10,814

46

,000<= /p>

-1,583

,146<= /p>

-1,878

-1,289

No se han asumido varia= nzas iguales

 

 

-10,814

38,635

,000<= /p>

-1,583

,146<= /p>

-1,880

-1,287

Muestra interés por el = tema

Se han asumido varianzas iguales

10,752

,002<= /p>

-8,928

46

,000<= /p>

-1,542

,173<= /p>

-1,889

-1,194

No se han asumido varia= nzas iguales

 

 

-8,928

36,239

,000<= /p>

-1,542

,173<= /p>

-1,892

-1,192

Demuestro motivación en= la clase

Se han asumido varianzas iguales

3,866=

,055<= /p>

-6,356

46

,000<= /p>

-1,125

,177<= /p>

-1,481

-,769=

No se han asumido varia= nzas iguales

 

 

-6,356

35,550

,000<= /p>

-1,125

,177<= /p>

-1,484

-,766=

Material es pertinente<= o:p>

Se han asumido varianzas iguales

,529<= /p>

,471<= /p>

-8,338

46

,000<= /p>

-,958=

,115<= /p>

-1,190

-,727=

No se han asumido varia= nzas iguales

 

 

-8,338

45,665

,000<= /p>

-,958=

,115<= /p>

-1,190

-,727=

Qué tiempo utilizo en resolver ejercicios

Se han asumido varianzas iguales

2,024=

,162<= /p>

-14,873

46

,000<= /p>

-1,917

,129<= /p>

-2,176

-1,657

No se han asumido varia= nzas iguales

 

 

-14,873

33,824

,000<= /p>

-1,917

,129<= /p>

-2,179

-1,655

 

Tabla 2.

Estadísticos de grupo variables de análisis (c= ontinuación)

 

 

Prueba de Levene para la igualdad de varianzas

Prueba T para la igualdad de medias

 

 

F

Sig.<= /p>

t

gl

Sig. (bilateral)

Diferencia de medias

Error típ. de la difere= ncia

95% Intervalo de confia= nza para la diferencia

 

 

 

 

 

 

 

 

 

Inferior

Superior

Participó activamente e= n el uso de la Taptana

Se han asumido varianzas iguales

4,298=

,044<= /p>

-4,163

46

,000<= /p>

-,792=

,190<= /p>

-1,174

-,409=

No se han asumido varian= zas iguales

 

 

-4,163=

41,331=

,000

-,792<= /p>

,190

-1,176=

-,408<= /p>

Fuente: Elaboración propia.

Seg= ún el análisis de tabla 3 reflejada del T de estudio de las 12 variables observamos un cambio significativo entre pretest y pos-test, ya que la significación bilateral es menor a 0,05 que está enfocado dentro de la teor= ía asociados con un 95 % de intervalo de confianza.

Discusión.<= o:p>

Una vez procedido con el trab= ajo investigativo cuasi experimental se inició la interpretación de los resulta= dos obtenidos en la ficha pretest y pos-test haciendo énfasis en los siguientes apartados: la Taptana kañari y su utilización, estrategias metodológicas y = su influencia, recursos didácticos y su motivación, uso de la TIC (Tecnologías de la Información y las Comunicaciones) en la enseñanza de las matemáticas.

La Tapt= ana kañari y su utilización. Con la aplicación de la ficha pretest y pos test s= e ha evidenciado una considerable desviación típica como se observa en la tabla = 2, la Taptana kañari que es un recurso innovador ha permitido desarrollar habilid= ades, competencias y destrezas en los estudiantes, además mediante la utilización= de este recurso andino los estudiantes interpretan de forma concreta la composición y descomposición de cantidades, así también han fortalecido el razonamiento lógico en la solución de problemas, como hace mención <= span class=3Dnormaltextrun>Alquinga (2019)la Taptana presenta un valiosísimo aporte a la comprensió= n de la lógica implícita en el sistema decimal y en cada una de las operaciones matemáticas, su metodología facilita el tránsito de lo concreto a lo abstra= cto” (p. 127).

Estrate= gias metodológicas y su influencia. Los nuevos modelos pedagógicos de la educaci= ón del siglo XXI se enfocan en mejorar la calidad educativa, para lo cual hoy = en día existen diversas estrategias metodológicas como son: aprendizaje cooperativo, aprendizaje basado en problemas, aprendizaje basado en proyect= os, las mismas que han permitido mejorar el nivel de aprendizaje de los estudia= ntes que tenían dificultades en especial en la solución de problemas, esto se ha= ce posible mediante un trabajo en equipo y contextualizado a la realidad y necesidad de los educandos, como menciona Pulloquinga (2020) “para desarrollar el razonamiento lógico matemático, necesitamos un trabajo donde todos aporten sus experiencias para solucionar un problema, hasta que todos= los estudiantes logren comprender” (p. 16).

Recursos didácticos y su motivación. El uso de diversos recursos didácticos en nuest= ras prácticas educativas fomenta la motivación, concentración y lo más importan= te desarrolla la creatividad en los educandos, mediante el uso de la Taptana y diversos recursos concretos como: palillos, semillas y otros hemos logrado desarrollar en los estudiantes un pensamiento lógico en la solución de problemas y formación de cantidades, además es importante recalcar que los estudiantes mantienen motivados durante todo el proceso de la enseñanza, po= r lo cual es importante que los docentes seleccionemos recursos que despierten interés en los estudiantes.

Uso de la TIC (Tecnologías de la Información y las Comunicaciones) en la enseñanza de las matemáticas. Las Tics en la educación del siglo XXI son herramientas primordiales para lograr los objetivos de aprendizajes propuestos ya que con el uso de diversas plataformas digitales= que ofrece la tecnología logramos mejorar la calidad educativa. En la presente investigación además del uso de la Taptana y materiales concretos se trabajó utilizando plataformas digitales como Educaplay, Genially y Canva con actividades gamificadas enfocadas hacia el desarrollo del razonamiento lógi= co matemático en los educandos, asimismo de manera autónoma logran fortalecer = su nuevo conocimiento.

 =

 =

 =

 =

 =

 =

 =

Propuesta.<= o:p>

Figura 1.

Taptana kañari como recurso didáctico, para desarrollar razonamiento ló= gico Matemático

Fuente: Elaboración propia

La presente investigación fue planificada siguiendo la metodología del Sistema= de conocimiento “dominio, aplicación, creación y socialización” con el objetiv= o de fortalecer el razonamiento lógico matemático en los estudiantes de quinto año de básica mediante el uso de la= Taptana, para de esta manera mejorar el nivel de razonamiento matemático. En una pri= mera instancia se elaboró una ficha de observación la misma se aplicó en dos hor= as clases, para el desarrollo de las dos horas clases se planificó según el proceso del sistema de conocimiento. Luego de la primera hora clase se proc= edió con el llenado de la ficha pretest y después de una segunda hora clase se aplicó la ficha post-test; en los dos momentos se hizo énfasis en diversos aspectos como: motivación, uso del material, participación, resolución del problema, aplicación de la Taptana, codificación del material.

Una vez procedido con las dos horas académicas en el proceso del dominio de conocimiento se pudo observar lo siguiente: activación de los sentidos en los alumnos mediante la manipulaci= ón y observación de la Taptana; en la parte de la problematización se evidencia = los conocimientos previos relacionado al uso de la Taptana en la resolución del problema, en el desarrollo del contenido científico en primera instancia se explicó la importancia de la codificación de materiales a utilizar y el uso correcto de la Taptana en la resolución de problema, una vez apropiado el conocimiento del uso de la Taptana en la fase de la verificación se planteó= un problema contextualizado a la realidad de los estudiantes para que mediante= un trabajo colaborativo resuelvan y como conclusión se menciona que utilizando= la Taptana los estudiantes tienen mayor participación en los grupos colaborativos y desarrollan creatividad que permite lograr un conocimiento significativo adaptando a su realidad contextual.

Según el sistema de conocimiento en la fase del dominio las actividades son dirigidas por el docente durante el proceso de una hora clase, mientras en los siguientes procesos que son: aplicación, creación y socialización del conocimiento las actividades son autónomas donde el estudiante pone en práctica lo aprendido. Luego de esta investigación de campo se plantea diversas propuestas que permitirán lograr= un razonamiento lógico matemático en los estudiantes de quinto año de básica: =

·&nb= sp;        Es fundamental que los docentes tengan conocimiento del uso de la Taptana kaña= ri que permitirá desarrollar destrezas, habilidades en los estudiantes y así lograr el razonamiento lógico en la resolución de problemas, por lo cual es primordial organizar una capacitación masiva a los docentes de la utilizaci= ón de la Taptana que a lo futuro se convertirá en un recurso dinámico y motiva= dor en el aula.

·&nb= sp;        Es importante contar con una galería de arte “taptanas” elaboradas en nuestras= instituciones educativas ya que contamos con diversos materiales que servirán para elabor= ar nuestros propios recursos y así también integraremos a los padres de famili= a de familia en los procesos de la enseñanza aprendizaje.

·&nb= sp;        Nuestras innovaciones educativas en el aula deben ser conocidas por los demás estudiantes y docentes, por tal razón es oportuno organizar una casa abiert= a en nuestras instituciones educativas para que los estudiantes expongan los conocimientos apropiados en el aula con el uso de recursos educativos.=

·&nb= sp;        Hoy en día el enfoque tradicional está quedando en el pasado, con las innovacio= nes de los docentes estamos enfocando en diversas teorías que permite al estudi= ante ser constructor de su propio conocimiento. Por tal motivo, no todos los recursos deben estar organizados en el aula como bibliotecas, debemos fortalecer nuestras bibliotecas vivas y transformar nuestro contexto en un recurso de autoaprendizaje.

·&nb= sp;        Los docentes debemos innovar nuestros conocimientos en la utilización de divers= as plataformas digitales que hoy en día ofrece la tecnología, ya que de esa ma= nera mejoraremos la calidad educativa de la niñez y la sociedad que forman parte= de la comunidad educativa, además con la aplicación de plataformas digitales en nuestras prácticas educativas lograremos una educación híbrida y holística = en nuestros educandos.

·&nb= sp;        Para lograr una excelencia académica primeramente es importante la actitud del docente frente a su labor pedagógica, frente a ello cada docente debe investigar, diferentes estrategias metodológicas que permitan fortalecer el nivel de aprendizaje de los educandos sea de manera individual o grupal. Además, las diversas estrategias metodológicas se pueden apropiar mediante intercambio de experiencias en círculo de estudios, comunidades de aprendiz= ajes.

·      =    Los estudiantes poseen una diversidad de experiencias vividas en su diario vivi= r, por lo cual debemos en primer lugar evidenciar dichos conocimientos para a partir de ello construir su nuevo conocimiento.

Conclusiones.

·&nb= sp;        En esta investigación se fortaleció el razonamiento lógico matemático en los estudiantes de quinto año de básica del CECIB “Daniel Clavijo Iglesias” en = la resolución de problemas, mediante el uso de la Taptana kañari, y así logran= do un aprendizaje crítico, reflexivo, cooperativo y significativo. 

·&nb= sp;        La ficha de observación (pretest) es un instrumento que orientó a evidenciar el nivel de conocimiento del uso de la Taptana en los estudiantes, mientras al aplicar la ficha (post-test) identificamos las destrezas y habilidades desarrolladas en el proceso de la investigación.

·&nb= sp;        La Taptana kañari permitió que el aprendizaje matemático se parta de lo concre= to a lo abstracto, permitiendo al estudiante su desarrollo holístico de las capacidades cognitivas e intelectuales.

·&nb= sp;        El material didáctico utilizado en los niños permitió lograr un cambio significativo, ya que la significación bilateral es menor a 0,05 en todas l= as variables, de esa manera logrando un razonamiento lógico matemático.

·&nb= sp;        La Taptana kañari aportó a la comprensión de la lógica en la resolución de problemas de manera autónoma. Por lo cual, es primordial la utilización de = la Taptana en el proceso de la enseñanza.

·&nb= sp;        Las estrategias metodológicas permitieron motivar el proceso de enseñanza aprendizaje de manera individual y grupal. Además, permitimos al estudiante= ser constructor de su propio conocimiento enfocados en su realidad contextual.<= o:p>

·&nb= sp;        Al evidenciar los conocimientos previos de los estudiantes, permitimos a los educandos fortalecer los conocimientos aprendidos en su contexto familiar o social.

·&nb= sp;        Mediante el uso de las Tics y un trabajo gamificado en diversas plataformas digitale= s se fortaleció el razonamiento lógico matemático en los estudiantes.=

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=

 

 

&nb= sp;

 

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