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Unidad Didáctica basada en la resolución de problemas para el abordaje de las habilidades de ecuaciones de primer grado con una incógnit= a.

 

 

Marielos Yuliana Madrigal Araya1, Islande De= lgado Monge2, Katalina Oviedo Rodríguez3 & Johan Espin= oza González 4

 

 

<= span lang=3DES style=3D'mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-= latin; color:black;mso-themecolor:text1;mso-ansi-language:ES;text-decoration:none; text-underline:none'>1.      Estudiante, Universidad Estatal a Distancia, Cartago, Costa Rica. marielos.madrigal@uned.cr<= /a>  

<= span lang=3DES style=3D'mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-= latin; color:black;mso-themecolor:text1;mso-ansi-language:ES;text-decoration:none; text-underline:none'>2.      Académica, Universidad Estatal a Distancia, Sabanilla, Costa Rica. idelgado@uned.ac.cr  

<= span lang=3DES style=3D'mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-= latin; color:black;mso-themecolor:text1;mso-ansi-language:ES;text-decoration:none; text-underline:none'>3.      Académica, Universidad Nacional de Costa Rica, Heredia, Costa Rica. Katalina.oviedo.rodríguez@una.cr=  

<= span style=3D'mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin; color:windowtext;text-decoration:none;text-underline:none'>4.&= nbsp;     Académico, Universidad Nacional de Costa Rica, Heredia, Costa Rica. johan.espinoza.gonzalez@una.cr

 

ABSTRACT: This article presents a teaching un= it to develop the topic of first-degree equations with an unknown, with a gro= up of eighth-year students from Saint Gregory School. In the mediation, diffe= rent activities were used, applying technology and manipulative materials so th= at the students internalized the contents, and not only improved their academ= ic performance in Mathematics, but also managed to apply the process in the different contents in which they must be solved. first degree equations wi= th one unknown. The design of the teaching unit was carried out considering t= he characteristics of the population with whom we worked, their prior knowled= ge, the dynamics of the group and creating activities that were attractive and allowed the proposed objectives to be achieved.

 

Key words: pedagogical mediation, didactic unit, first degree equations with = an unknown, manipulative material. <= /w:sdtPr>

 

RESUMEN: En este artículo se presenta una unidad didáctica para desarrollar el tema de ecuaciones de pr= imer grado con una incógnita, con un grupo de estudiantes de octavo año del col= egio Saint Gregory School. En la mediación se utili= zaron diferentes actividades aplicando tecnología y materiales manipulativos con= el fin de que los estudiantes interiorizaran los contenidos, y no solamente mejoraran su rendimiento académico en Matemática, sino que también lograran aplicar el proceso en los diferentes contenidos en los que se debe resolver ecuaciones de primer grado con una incógnita. El diseño de la unidad didác= tica se llevó a cabo considerando las características propias de la población c= on la que se trabajó, sus conocimientos previos, la dinámica del grupo y crea= ndo actividades que fueran llamativas y permitieran alcanzar los objetivos propuestos.<= /span>

 

: mediación pedagógica, unidad didáctica, ecuaciones de primer grado con una incógnita, material manipulativo.=

 

 

 

 

 

 

introducci= ón

 

El álgebra presenta grandes retos de pensamiento y estructuras lógicas para l= os estudiantes, ya que implica un cambio significativo en su forma de pensar = y en la manera en que han utilizado las letras comúnmente. En este sentido, Martínez y Romero (2019) afirman que: “en el proceso de transición de la aritmética al álgebra no todos los estudiantes distinguen las letras de la misma manera, pues hasta el momento las han utilizado para cuestiones relacionadas con lenguaje en un sentido sintáctico que obtienen una validez según las situaciones.”

El hecho de que un estudiante presente dificultades al resolver una ecuación = de primer grado con una incógnita influye posteriormente en el proceso de resolución de problemas. Al respecto Mateo (2018), afirma que los estudian= tes presentan dificultades al codificar la información del lenguaje natural al matemático, así como identificar el tipo de ecuación que resuelve el probl= ema.

El interés por realizar esta investigación surgió por las dificultades que presentaban los estudiantes de octavo año del colegio Saint Gregory School y que se evidenciaba en el rendimiento en Matemática. De hecho, se observó que los estudiantes mostraban confusión al llevar a cabo el proceso de despeje de las variables en las ecuaciones, principalmente aquellos que tenían adecuación curricular, éstos cometían errores al balancear ambos lados de la igualdad y al realizar los cambios = de signo a los términos, o bien al resolver operaciones aritméticas básicas; = así lo indica Morales, profesora de matemática de la institución, al expresar = que “una de las mayores dificultades presentadas por los estudiantes de octavo= año al despejar una ecuación, corresponde a interiorizar el proceso de despeje= de variables, junto con el cambio de signos que se lleva a cabo al equilibrar= la ecuación.” (Morales, 2022)

Con este proyecto se buscó aportar un material mediado pedagógicamente para el abordaje de las ecuaciones de primer grado con una incógnita que facilitar= a a los estudiantes de octavo año identificar el proceso para resolver una ecuación de primer grado con una incógnita correctamente, y utilizarlo tan= to en el área de la matemática como en la de física al despejar fórmulas.

Esto ayudaría a que los estudiantes del colegio Saint Gregory School, tuvieran un mejor dominio del contenido como un conocimiento previo y, por ende, que su aplicación en los niveles posteriores sea más favorable. Adem= ás, podría evitar que su rendimiento académico se vea afectado por un mal mane= jo de estos temas, beneficiando tanto a los estudiantes con los que se aplica= rá el proyecto, como a los de generaciones siguientes con las que se podría retomar esta unidad didáctica.

Algunos estudios han diseñado e implementado propuestas didácticas para el abordaje de las ecuaciones de primer grado. Por ejemplo, Pérez (2020), diseñó e implementó una estrategia dirigida a secundaria para favorecer la transición del lenguaje aritmético= al algebraico mediante la resolución de problemas que implicaban el planteami= ento de ecuaciones de primer grado con una incógnita, haciendo uso de vocablos equivalentes a las operaciones básicas aritméticas.

Esta propuesta surge al observar que = los estudiantes lograban resolver correctamente ecuaciones, sin embargo, se les dificultaba traducir una situación a lenguaje algebraico debido a la falta= de manejo del vocabulario que se debía emplear, un aspecto que se ve comúnmen= te en nuestras aulas y que podía visualizarse en la población en estudio.

Agudo (2018), desarrolló una propuest= a de introducción a las ecuaciones de primer grado para un aula inclusiva de 1°= de la E.S.O. (Educación de Enseñanza Obligatoria), la cual tenía como objetivo principal que los alumnos aprendan de manera comprensiva y no de manera mecánica, fomentando la motivación y aumentando la autoestima de las perso= nas con necesidades educativas especiales. Como objetivo específico se buscaba= que el álgebra fuera entendida y no vista como un conjunto de letras y números= sin sentido, esto a partir de la resolución de problemas relacionados con camp= os que el alumno conozca. Se emplearon cuatro técnicas en su desarrollo: tra= ducción al lenguaje algebraico, agrupación de términos semejantes, resolución de ecuaciones y resolución de problemas.

Lo anterior permite reflexionar acerca de la importancia que tiene planear las clases con diferentes enfoques, atreviéndose a construir actividades innovadoras con las que no solamente se aprenda un contenido, sino que, además, desarrolle otro tipo de habilidades en los estudiantes.

Luego, Méndez (2022) diseñó una unidad interactiva basada en un paisaje de aprendizaje, que involucraba actividad= es de invención de problemas matemáticos para el abordaje de la habilidad de resolución de problemas con ecuaciones de primer grado, en estudiantes de octavo año de la Educación General Básica de tres colegios de la Dirección Regional de Educación de Coto.

<= span style=3D'mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>Es importante mencionar que la Unidad Didáctica permite planificar las leccio= nes de forma integral tomando en cuenta todos los elementos implicados en el proceso educativo, adaptándolo al entorno, al contexto de los estudiantes,= a los recursos con los que cuentan y a las características propias de la población con la que se está trabajando.

<= span style=3D'mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>Lo anterior es importante porque todas las comunidades educativas son diferen= tes en cuanto a sus características, recursos, facilidades y limitaciones. Por tanto, no siempre resulta factible basarse en un libro de texto para impar= tir las lecciones, sino que es necesario construir las herramientas que permit= an desarrollar una habilidad en los estudiantes y buscar que estos la interioricen de manera efectiva.

La elaboración de una Unidad Didáctica implica tomar en cuenta los tres nivel= es del diseño curricular macro, meso y micro, y con ellos, los lineamientos teóricos, los cuales van a depender de la estructura que tengan los Progra= mas de Estudio de cada país o región, sus contenidos y estrategias de mediación propuestas.

En Costa Rica, a nivel de secundaria, actualmente se utilizan los Programas de Estudio de Matemática que se aprobaron en el año 2012, en los cuales se implementa la resolución de problemas y la contextualización activa como e= jes principales para el desarrollo de las habilidades propuestas, y es el Ministerio de Educación Pública la institución que define los lineamientos= a seguir en la elaboración de una Unidad Didáctica a partir de los ejes disciplinares, las áreas matemáticas, los procesos matemáticos, la evaluac= ión, los conocimientos y habilidades específicas que se desean alcanzar. 

<= span style=3D'mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin; color:black;mso-color-alt:windowtext;background:white'>Otro elemento por considerar en la mediación pedagógica es el tomar en cuenta el uso de diferentes estrategias y herramientas desde su contexto, puesto que en la ense= ñanza de las matemáticas ayuda a que el proceso de aprendizaje por parte de los estudiantes se vuelva más llamativo para ellos y además que no sea rutinar= io.

               De= ntro de estas herramientas se encuentra el material manipulativo, el cual se de= fine según Extremiana (2019) de la siguiente manera= :

<= span style=3D'mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>Aqu= el elemento empleado por los docentes como recurso para el aprendizaje basado= en la obtención de conocimiento a través de la interacción con él. Así pues, están orientados a un fin y, en función de éste, han de cumplir una serie = de criterios y características. (p.23)

<= span style=3D'mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>Est= e tipo de objetos pueden ser construidos por el docente con diferentes tipos de materiales y acorde a lo que desee trabajar con sus estudiantes, inclusive puede involucrarlos a ellos en el proceso de construcción, esto hará aún m= ás significativo el proceso de aprendizaje que se esté desarrollando.

 =

estrategia metodológica<= /p>

 

Los participantes del proyecto fueron 13 estudiant= es de octavo año, de los cuales dos tienen adecuación curricular relacionada con dislexia y disgrafía, tres estudiantes tenían adecuación no significativa p= or problemas de atención y concentración que afectan el proceso de aprendizaje= , y déficit atencional. Además, se encuentra un alumno con una alta capacidad de aprendizaje y finalmente un alumno diagnosticado con Trastorno del Espectro Autista nivel 1 y Trastorno de Déficit Atencional de tipo combinado, al cua= l se le debe adecuar el material con un número de letra mayor al de sus compañer= os, brindarle más tiempo para terminar los trabajos y las pruebas, y de ser posible, presentarle la materia en pequeños tractos con el fin de que logre= una mayor comprensión de la misma y mantener un acompañamiento constante durante las lecciones. La población estudian= til del Saint Gregory posee un estatus económico de clase media alta, ya que, e= n la mayoría de los casos, ambos padres de familia trabajan fuera de casa en diferentes ámbitos como salud, educación, derecho o bien se dedican a negoc= ios propios como supermercados y restaurantes. Además, se trabaja con alumnos de diferentes nacionalidades, que ya tienen mucho tiempo de vivir en el país p= or lo tanto dominan bien el idioma español, lo cual facilita el proceso educat= ivo, sin embargo, la mayoría son estudiantes costarricenses.

El colegio brinda el recurso de intern= et a docentes y los estudiantes mediante red wifi, también cuenta con dispositiv= os electrónicos como tabletas las cuales están a disposición de los estudiantes durante las lecciones o fuera de ellas, con el fin de realizar trabajos, sin embargo, la mayoría de los estudiantes tienen su propio dispositivo electrónico, ya sea celular, tableta o computadora.

Para la elaboración de la Unidad Didác= tica primero se llevó a cabo el diagnóstico, para el cuál se aplicaron entrevis= tas a diferentes personas del colegio entre ellas una profesora de matemática y= un profesor de ciencias, los cuales respondieron el mismo cuestionario, luego = la psicopedagoga del colegio para quien el cuestionario fue diferente acorde a= su área de trabajo y finalmente dos estudiantes para quienes la entrevista fue= la misma y contemplaba diferentes tipos de preguntas, además, a estos últimos = se les aplicó una prueba corta con ejercicios sencillos considerados conocimie= ntos previos.

Para recolectar los datos se grabaron = las entrevistas que se realizaron a los docentes y psicopedagoga de la instituc= ión, además, las entrevistas de los estudiantes se llevaron a cabo de forma escr= ita, anónima y de manera individual con cada uno. En cuanto a la prueba corta, s= e le brindó un material con ejercicios considerados como conocimientos previos a cada uno de los estudiantes para que la realizaran y posteriormente se extr= ajo la información necesaria, relacionada con la cantidad de resultados correct= os, el proceso llevado a cabo para obtener el resultado y la descripción que realizaron los estudiantes del procedimiento que realizaron.

Una vez aplicadas las entrevistas y pr= ueba corta, se organizaron los datos los cuales se utilizaron para la planificac= ión de la aplicación de la unidad didáctica con el grupo, así como para determi= nar el grado de dificultad de los ejercicios que se desarrollaron. <= /span>

               Finalmente, aplicado el recurso didáctico y los datos emanados de las entrevistas a docentes y los estudiantes, se construyeron categorías para organizar los d= atos y posteriormente analizarlos.

Diseño e implementación de la Unidad Didáctica

La unidad didáctica se desarrolló en tres momentos. En el primero de ellos se llevó a cabo un repaso de conocimientos previos mediante una actividad en <= span class=3DSpellE>Kahoot que incluyó definiciones, operaciones básicas y despejes sencillos. Este recurso fue elaborado por la docente investigadora para garantizar que fuese accesible para los estudiantes, por ende, se les facilitó el enlace y código de ingreso para que pudieran responder las preguntas y al finalizar observar los resultados (Ver figura 1).=

Figura 1

Actividad: “Kahoot

En el segundo momento se llevó a cabo el desarrollo de las habilidades. Para introducir el tema, se colocó una balanza para que los estudiantes equilibr= aran cada lado (Ver figura 2). Luego se formalizaron los conceptos con una clase magistral, y para el método formal para poder resolver ecuaciones se trabajó mediante una actividad con material concreto, con el fin de que pudieran visualizar de una forma más clara el proceso de balancear la ecuación. Finalmente, los estudiantes realizaron los ejercicios propuestos en la unid= ad didáctica para verificar que hubiese quedado claro el contenido.

 

 

 

 

 

 

Figura 2

Actividad: “Balanza”

3D"Imagen

En cuanto a la habilidad de problemas de aplicación, se introdujo el tema con situaciones que propiciaran el análisis por parte de los estudiantes y que, además, se empleara el enfoque de resolución de problemas que propone el programa de estudios del MEP. El trabajo se realizó en grupos de máximo tres personas y una vez que cada grupo planteó su estrategia de solución (Ver Fi= gura 3) se expuso a los compañeros con el fin de socializar el proceso de anális= is de los alumnos, y luego formalizar el procedimiento para resolver este tipo= de problemas.

Figura 3

Actividad: “Resolución de problemas”

3D"Imagen

En el tercer momento se llevó a cabo la evaluación de los aprendizajes mediante u= na evaluación formativa, debido a que solo se deseaba obtener información sobr= e el proceso de aprendizaje que se desarrolló y posteriormente realizar la respectiva retroalimentación con los estudiantes. Esta evaluación se realizó mediante la actividad que se observa en la Figura 4 la cual se le facilitó a cada uno de los estudiantes, un juego de dominó de ecuaciones, y por último, cuatro problemas de aplicación para que = los resolvieran empleando una ecuación de primer grado con una incógnita.<= /o:p>

Figura 4

Actividad: “Laberinto de ecuacione= s”

 =

Discusión y valoración de los resultados 

La valoración de la mediación pedagógica de la Unidad Didáctica se realizó a partir de las siguientes cin= co categorías de análisis: lineamientos de la unidad didáctica, utilización de= la tecnología en la clase de matemática, utilización de material manipulativo = en la clase de matemática, motivación en la clase de matemática y optimización del proceso de instrucción matemática= . A continuación, se presentan los resultados obtenidos según cada categoría. 

Lineamientos de la Unidad Didáctica

Las actividades de mediación propuesta= s en la Unidad Didáctica se desarrollaron tanto con tecnología como con material concreto. Para el primer momento de diagnóstico se llevó a cabo una partida= de Kahoot, con la cual se lograron identificar las forta= lezas y debilidades de los estudiantes en conocimientos previos como conceptos relacionados con expresiones algebraicas, operaciones básicas y despejes sencillos relacionados con ecuaciones. Al respecto, se pudo observar que los estudiantes sabían identificar una ecuación como una igualdad, sin embargo,= al despejar la variable cometían errores al aplicar la operación inversa.=

Posteriormente, se llevaron a cabo dos actividades de mediación en las que se utilizó material concreto, que permitieron la interacción de la profesora y los estudiantes en diferentes momentos, además la participación del grupo de estudiantes.

Utilización de la tecnología en la clase de matemá= tica

El acceso a aplicaciones de uso libre = como lo es Kahoot llama mucho la atención de los estudiantes por ser una competencia entre ellos, les gusta ir ascendiendo e= n el ranking que se va visualizando conforme van respondiendo las preguntas. Al tener tantas opciones para construir las preguntas es una herramienta que se puede utilizar para diferentes temas y contenidos, incluso no necesariamente académicos; sino de algún tema que sea de interés para los adolescentes y sacarlos de la rutina.

Uso de material manipulativo en la clase de matemá= tica

Se llevaron a cabo dos actividades de mediación en las que se utilizó material concreto. En la primera actividad (figura 5) se buscaba que los estudiantes comprendieran el concepto de igualdad, seguidamente se construyó una balanza con diferentes materiales y= se rellenaron globos de diferentes colores con harina, de manera que tuvieran pesos distintos para alcanzar el objetivo de la actividad de “La Balanza” e= n la que se iban a utilizar. Para la segunda actividad (figura 6) se tenían paqu= etes con una situación problema y sus respectivas indicaciones, cartulina y marcadores para facilitarlo a los grupos de trabajo en la actividad de resolución de problemas.

Figura 5

Actividad “La balanza”

 <= /span>

Figura 6

Representación de = la balanza

3D"Texto,

 

En la actividad de resolución de problemas, desarrollada en grupos de trabajo, fue interesante cómo de manera colaborat= iva el grupo de estudiantes interpretó la situación que se le propuso y logró resolverla llegando a la respuesta correcta.

Utilizar material manipulativo en la c= lase de matemática ayudó a que los estudiantes visualicen de una manera concreta conceptos, definiciones, procedimientos, objetos, etcétera, que, en muchas ocasiones, al trabajarlo solamente de manera escrita se les complica y no logran comprender cómo llevarlo a cabo por sí solos.

Los materiales manipulativos son una estrategia de aprendizaje, y como pueden ser creados por el docente, este puede tomar en cuenta el contexto de la población estudiantil con la que va a trabajar, así como sus características.

Finalmente, en las actividades de evaluación tanto formativas como sumativas, los estudiantes trabajaron de una manera positiva resolviendo cada una de las ecuaciones, así fuera para avanzar, en el caso = del laberinto, o para ganar el juego, en los casos del dominó de ecuaciones y d= e la resolución de problemas, en las cuales la estrategia era importante para ga= nar el turno, obtener resultados correctos y avanzar o ganar puntos.=

Durante el proceso de enseñanza – aprendizaje es importante mezclar diferentes herramientas y estrategias. En esta investigación se utilizó tecnología, material manipulativo en diferent= es actividades y la explicación magistral, en el cual también se utilizó mater= ial concreto. Hacer este tipo de combinaciones ayudó a que lograran pasar de lo concreto a lo abstracto de una manera más sencilla.

Al ser un grupo tan activo, el uso de = la balanza, por ejemplo, les gustó porque podían tocar el material y sentir có= mo los globos variaban de peso, pero no lograban adivinar al tacto cuál era ese peso, solamente al hacer el trabajo de balanceo con la balanza determinaban= la equivalencia.

Posteriormente, explicar con las ficha= s en la pizarra el proceso formal de despeje de ecuaciones y la repetición de ejercicios proporcionó que ellos mismos llegaran a la conclusión de que pod= ían hacer directamente una relación de opuestos aditivos y multiplicativos a ca= da lado de la igualdad y obtener el resultado.

Motivación en la clase de matemática

La matemática suele ser la materia en = la que la mayoría de los estudiantes presentan indisposición, dificultad, apat= ía, etcétera, por lo que fomentar la motivación en la clase de matemática de diferentes formas es importante para que el proceso de enseñanza – aprendiz= aje sea mucho más favorable.

               En el caso del grupo de estudiantes de octavo año con el que se trabajó, inicialmente se mostró ansiedad por el hecho de que se iba a trabajar un te= ma nuevo y en el caso de los estudiantes que no tienen tanta afinidad con la materia, mostraron un poco de resistencia pensando en el nivel de dificultad que iba a tener. Sin embargo, al aplicar la estrategia fue interesante obse= rvar la motivación de los estudiantes cuando vieron la balanza y no sabían para = qué era, porque estaban a la expectativa de qué íbamos a hacer. Esa motivación = se mantuvo durante las diferentes actividades porque estaban viendo un tema nu= evo de una manera diferente y no como se hace tradicionalmente.

Durante la aplicación de la Unidad Didáctica, la docente mostró entusiasmo al plantear la actividad y llevarla= a cabo, esto ayudó a que el grupo de estudiantes participara de forma activa = en todo momento, así mismo, se les motivó con comentarios positivos sobre lo q= ue estaban haciendo, y en caso de que sintieran que no avanzaban o no comprend= ían, se conversó con ellos y se les apoyó para que alcanzaran el objetivo.<= /o:p>

Fomentar la interacción entre el docen= te y los estudiantes durante la aplicación del recurso, favoreció a que estos últimos, al sentirse participes del proceso, alcanzaran un aprendizaje más significativo; de manera que, al completar la Unidad Didáctica, todos los estudiantes lograron resolver correctamente las ecuaciones que se les plantearon y además pudieron resolver bien los problemas planteando adecuadamente la ecuación que les permitiera obtener la solución.

Optimización Del Proceso De Instrucción Matemática=

Finalmente se analizaron las idoneidad= es y los componentes del enfoque ontosemiótico el cu= al es un sistema teórico que trata de integrar diversas aproximaciones y modelos teóricos usados en la educación matemática, se apoya en supuestos antropológicos y semióticos sobre las matemáticas. Las idoneidades didáctic= as se utilizaron para evaluar la Unidad Didáctica como óptima o adecuada para conseguir la adaptación entre los significados personales logrados por los estudiantes y los significados institucionales.

La Unidad Didáctica se construyó toman= do en cuenta las diferencias individuales de los estudiantes pensando en que t= odos tuvieran acceso a las actividades, por ejemplo, en el caso del Kahoot se verificó que el dispositivo con que contaba= cada uno permitía el ingreso al enlace, se incluyeron también actividades de ampliación y refuerzo con el fin de que se lograran los objetivos propuesto= s. Además, en el recurso se procuró que las actividades de evaluación formativ= a y sumativa tuvieran distintos niveles de comprensión y competencia, para este componente se tomó en cuenta lo propuesto por los programas de estudio de matemática del MEP.

En relación con la idoneidad afectiva = se tomaron en cuenta las actitudes promoviendo la participación en las actividades, la perseverancia, la responsabilidad, el trabajo en equipo y el compañerismo. Lo anterior se concluye de la guía de observación aplicada pa= ra evaluar la Unidad Didáctica, en la cual se incluyó este aspecto y los tres expertos que realizaron la evaluación indicaron que en las actividades propuestas se promovían las actitudes que el indicador mencionaba, tanto en= las individuales como en las grupales.

El componente de idoneidad interaccion= al tomó en cuenta la interacción docente – discente, facilitando la inclusión = de los estudiantes en la dinámica de clase en cada una de las actividades que = se desarrollaron, interacción entre los estudiantes favoreciendo el diálogo y = la comunicación entre los estudiantes, por ejemplo, en la actividad de resoluc= ión de problemas debían dar sus puntos de vista y llegar a un consenso para presentarlo al resto del grupo.

 

conclusion= es y recomendaciones

 

Desarrollar un tema mediante una unidad didáctica requiere que se tomen en cuenta una serie de aspectos con el fin de diseña= r un material que se adapte a la población en estudio, en este caso las entrevi= stas realizadas tanto a docentes como estudiantes brindaron la información necesaria que permitió construir una unidad didáctica en la que se tomaron= en cuenta los conocimientos previos de los estudiantes y sus características.=

Al implementar la Unidad Didáctica se consideraron las características del gr= upo, por ejemplo, su participación, interés y colaboración entre los estudiantes con el fin de crear actividades que fueran llamativas para ellos y que cumplieran el objetivo. Esto permitió que, al explicar el proceso formal, = los estudiantes llegaran a conclusiones verdaderas y realizaran de forma más práctica el despeje de variables.

Se pudo observar como la variedad de actividades llamó la atención del grupo de estudiantes, los cuales se mostraron activos, interesados en los temas, obteniendo así que les quedar= an claros los procedimientos y lograran resolver ejercicios por cuenta propia= de forma correcta.

Al mismo tiempo, la evaluación eviden= ció el aprendizaje obtenido por los estudiantes y diferentes aspectos, por ejemplo, al realizar el Kahoot los estudiantes analizaban las preguntas antes de responder utilizando los conocimientos previos que tenían de valor numérico para encontrar el valor de las variab= les. Además, luego de la actividad de la balanza y la explicación formal de des= peje de ecuaciones, su análisis al resolver ejercicios fue más rápido y no necesitaban aplicar todos los pasos para obtener la respuesta correcta.

Por otra parte, trabajar en equipo y resolver los problemas tomando en cuenta las opiniones de todos, les permi= tió darse cuenta de que no existía solamente un camino para resolverlos, sino = que, aunque se interprete de diferentes maneras, sí el proceso es el correcto se obtendrá la solución de forma efectiva.

               Es importante además conocer el grupo, realizar observaciones previas a la creación del recurso, conocer la dinámica que tienen, sus fortalezas, debilidades, etcétera, ya que esto permite crear actividades que de verdad generen el interés de los estudiantes y que la mediación alcance los objet= ivos planteados inicialmente.

               Por último, es conveniente, en la medida de lo posible, mantener una comunicac= ión constante con el profesor del grupo al que se va a aplicar el recurso, ya = que este tendrá las herramientas para brindar retroalimentación y modificar aspectos importantes antes de ejecutar o poner en práctica el recurso, como por ejemplo, el tiempo en el que se va desarrollar para que las sesiones en que se van a realizar cada una de las actividades sean efectivas y se cump= la el objetivo para el que fueron diseñadas.

               Lo anterior es importante porque en esta investigación fue necesario extender= la cantidad de lecciones para las que estaba diseñada la Unidad Didáctica, po= rque no se contempló el hecho de que después de una actividad que involucrara material concreto o trabajo en grupos es difícil organizar nuevamente a los estudiantes para continuar con la explicación formal debido a lo acelerados que están.

=  

referencia= s

Agudo, A. (2018). = Introducción a las ecuaciones de primer grado, Propuesta para un aula

inclusiva de1º de la E.S.O. [Tes= is para optar por el grado de Máster Universitario

de Profesorado de Educación Secund= aria Obligatoria, Bachillerato, Formación

Profesional y Enseñanzas de los Idiomas, Artísticas y Deportivas. Especialidad

Matemática por la Universidad de Zaragoza] TAZ-= TFM-2018-342.pdf

 

Extremiana, L. (2019). Los materiales didácticos manipulativos en el aprendizaje basado=

en proyectos. [Te= sis para optar por el grado de Educación Infantil por la

Universidad de Valladolid] = http= s://uvadoc.uva.es/bitstream/handle/10324/39139/TFG-G3787.pdf;jsessionid=3DC= 08617BBB4547E9E24FF9CF366C27402?sequence=3D1  

Martínez, M.= y Romero, T. (2019). Transición de la aritmética al álgebra: Un estudio co= n

estudiantes universitarios de Nicaragua. Revista Electrónica de Conocimientos, Saberes y Prácticas. 2(2), 29-39. file:///C:/Users/yulim/Downloads/10607.pdf

Mateo, M. (2018). Dificultades que presentan los estudiantes en la resolución de

problemas de ecuaciones de primer grado con una incógnita en segundo básico.<= /span>

[Tesis de Gr= ado, Universidad Rafael Landívar] http://biblio3.url.edu.gt/publijrcifuente/TES= IS/2018/05/86/Mateo-Marta.pdf

Méndez, A. (2022). Unidad didáctica interactiva, basada en un paisaje de aprendizaje que<= /o:p>

involucra actividades de invención de problemas matemáticos, para el abordaje de

la habilidad de resolución de problemas con ecuaciones de primer gra= do, en

estudiantes de octavo año de la Educación General Básica de tres colegios de la

Dirección Regional de Educación de Coto en el año 2021. [Tesis para optar por el

grado de Licenciatura, Universidad Estatal a Distancia, Costa Rica= ]

file:///C:/Users/yulim/Documents/TFG/NSYXEN3SEE6PF= DP66SVYGE8A7YFC9U.pdf

Morales, A., comunicación personal, setiembre 2022.=

Pérez, M. (2020). La transición del lenguaje aritmético al algebra= ico en secundaria. Una

propuesta didáctica. [Tesis de Maestría, Benemérita Universidad Autónoma de

Puebla] http= s://www.fcfm.buap.mx/posgrados/assets/docs/catalogo-tesis/mem/2020/MonicaPe= rezGarcia.pdf

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