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matem=C3=A1tica en la educaci=C3=B3n general b=C3=A1sica en Ecu= ador = Technology in active learning of mathematics in basic general edu= cation in Ecuador <table style=3D"width:396.3pt; margin-bottom:= 0pt; padding:0pt; border-collapse:collapse"><tr><td style=3D"width:3.25pt; = border:0.75pt solid #000000; padding:0pt 5.03pt; vertical-align:top">1</td><td styl= e=3D"width:171.95pt; border:0.75pt solid #000000; padding:0pt 5.03pt; verti= cal-align:top">Enrique Marcelo Bustamante Salda=C3=B1a<= /span></td><td style=3D"width:10.5pt; border:0.75pt solid #000000; padd= ing:0pt 5.03pt; vertical-align:top"><img src=3D"data= :image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAYAAACNiR0NAAAABHNCSVQIC= AgIfAhkiAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAA2pJREFUOI2tlEtoXVUUhr+197n3nNzbJN6o= mdTWRmwbikVq4iMxk0ZU2oGgA1FnQcQiUhUnFqo4cGIRQUGd+KDY+Jp25ouiGCOxElqjhba0URP= zsPQmuY9zzj1nLwcnuU1qQif+mzXZe69/rX/tny2sgy9+7mknn99qrL1TVHcnqu3GyoKxTEhDxp= 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27/A/4F4WeWL1XZmjwAAAAASUVORK5CYII=3D" width=3D"20" height=3D"20" alt=3D"" = style=3D"margin-top:0.45pt; margin-left:-0.3pt; position:absolute" /></span= > </td><td st= yle=3D"width:166.35pt; border:0.75pt solid #000000; padding:0pt 5.03pt; ver= tical-align:top"><a href= =3D"https://orcid.org/0009-0009-7275-4825" style=3D"text-decoration:none"><= span class=3D"Hyperlink" style=3D"line-height:115%; font-family:'Times New = Roman'; font-size:10pt">https://orcid.org/0009-0009-7275-4825</a></p= ></td><td style=3D"border-bottom:0.75pt solid #000000; padding:0pt; vertica= l-align:top"></td></tr><tr><td style=3D"width:3.25pt; border:0.75pt solid #= 000000; padding:0pt 5.03pt; vertical-align:top"> </td><td colspan=3D"4" style= =3D"width:370.7pt; border:0.75pt solid #000000; padding:0pt 5.03pt; vertica= l-align:top">Univer= sidad de Ciencias Pedag=C3=B3gicas Enrique Jos=C3=A9 Varona (UCPEJV), La Ha= bana, Cuba, Maestr=C3=ADa en docencia Matem=C3=A1tica<a href=3D"mailto:rectoria@ucpejv.edu.cu" style=3D"te= xt-decoration:none">rectoria@ucpejv.edu.cu= </a><a href=3D"mailto:marcelo.bustaman= tes@docentes.educacion.edu.ec" style=3D"text-decoration:none">marcelo.bustamantes@docentes.educacion.edu.ec</a>= <a href=3D"mailto:kike018bs@gmail.com" sty= le=3D"text-decoration:none">kike018bs@gmail.com</= span></a></td></tr><tr><td style=3D"width:3.25pt; border:0.75pt solid #= 000000; padding:0pt 5.03pt; vertical-align:top"> </td><td style=3D"width:171.95= pt; border:0.75pt solid #000000; padding:0pt 5.03pt; vertical-align:top"><p= style=3D"margin-left:7.1pt; margin-bottom:0pt; text-indent:-7.1pt; text-al= ign:justify; line-height:115%; font-size:10pt"> </td><td style=3D"width:10.5pt; border:0= .75pt solid #000000; padding:0pt 5.03pt; vertical-align:top"><span= style=3D"font-family:'Times New Roman'"> </td><td style=3D= "width:166.35pt; border:0.75pt solid #000000; padding:0pt 5.03pt; vertical-= align:top"> </td><td st= yle=3D"border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000;= padding:0pt; vertical-align:top"></td></tr><tr><td style=3D"width:3.25pt; = border:0.75pt solid #000000; padding:0pt 5.03pt; vertical-align:top"> </td><td = colspan=3D"4" style=3D"width:370.7pt; border:0.75pt solid #000000; padding:= 0pt 5.03pt; vertical-align:top"> </td><= /tr><tr><td style=3D"width:3.25pt; border:0.75pt solid #000000; padding:0pt= 5.03pt; vertical-align:top"> </td><td style=3D"width:171.95pt; border:0.75pt s= olid #000000; padding:0pt 5.03pt; vertical-align:top">&= #xa0;</td><td style=3D"width:10.5pt; border:0.75pt solid #000000= ; padding:0pt 5.03pt; vertical-align:top"> </td><td style=3D"width:166.35pt; bo= rder:0.75pt solid #000000; padding:0pt 5.03pt; vertical-align:top"> </td><td style=3D"border-top:0= .75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt; verti= cal-align:top"></td></tr><tr><td style=3D"width:3.25pt; border:0.75pt solid= #000000; padding:0pt 5.03pt; vertical-align:top"> </td><td colspan=3D"4" style= =3D"width:370.7pt; border:0.75pt solid #000000; padding:0pt 5.03pt; vertica= l-align:top"> </td></tr><tr><td style= =3D"width:3.25pt; border:0.75pt solid #000000; padding:0pt 5.03pt; vertical= -align:top"> </= span></td><td style=3D"width:171.95pt; border:0.75pt solid #000000; pad= ding:0pt 5.03pt; vertical-align:top"> <= /td><td style=3D"width:10.5pt; border:0.75pt solid #000000; padding:0pt 5.0= 3pt; vertical-align:top"> </td><td style=3D"width:166.35pt; border:0.75pt solid= #000000; padding:0pt 5.03pt; vertical-align:top"> </td><td style=3D"border-top:0.75pt solid #0000= 00; border-bottom:0.75pt solid #000000; padding:0pt; vertical-align:top"></= td></tr><tr><td style=3D"width:3.25pt; border:0.75pt solid #000000; padding= :0pt 5.03pt; vertical-align:top"> </td><td colspan=3D"4" style=3D"width:370.7pt= ; border:0.75pt solid #000000; padding:0pt 5.03pt; vertical-align:top"> </td></tr><tr style=3D"height:0pt"><td sty= le=3D"width:14.05pt"></td><td style=3D"width:182.75pt"></td><td style=3D"wi= dth:21.3pt"></td><td style=3D"width:177.15pt"></td><td style=3D"width:0.3pt= "></td></tr></table> <table style=3D"width:436.35pt; margin-left:0.25pt;= margin-bottom:0pt; padding:0pt; border-collapse:collapse"><tr><td colspan= =3D"3" style=3D"width:156.4pt; padding:0pt 5.4pt; vertical-align:top"><a id=3D"_Hlk92186133"> </a>= </td= ><td colspan=3D"2" style=3D"width:258.35pt; border-top:0.75pt solid #000000= ; padding:0pt 5.4pt; vertical-align:top">Art=C3=ADculo de Investigaci=C3=B3n C= ient=C3=ADfica y Tecnol=C3=B3gicaEnviado: Revisado: Aceptado: Publicado:DOI:= </td></tr><tr style=3D"height:6.55pt"><td col= span=3D"3" style=3D"width:156.4pt; padding:0pt 5.4pt; vertical-align:top"><= p style=3D"margin-bottom:0pt; text-align:right; line-height:115%; font-size= :6pt"> </td><td colspan=3D"2" style=3D"width:258.35pt;= border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"= >&#x= a0;</td></tr><tr><td style=3D"width:37.8pt; padding:0pt 5.4pt; v= ertical-align:top"> 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style=3D"width:324.9pt; border-bottom:0.75pt solid #000000; padding:0pt= 5.4pt; vertical-align:top">Resumen: Introducci=C3=B3n<span= style=3D"font-family:'Times New Roman'">. La ense=C3=B1anza de matem=C3=A1= ticas en la educaci=C3=B3n general b=C3=A1sica en el Ecuador enfrenta difer= entes dificultades ligadas a la comprensi=C3=B3n de s=C3=ADmbolos, a los co= nceptos no concretos, la baja motivaci=C3=B3n estudiantil y el predominio d= e metodolog=C3=ADas centradas en la memorizaci=C3=B3n. Las herramientas dig= itales, como Polypad (desarrollada originalmente en Mathigon y actualmente = siendo parte de Amplify), han ido emergiendo como herramientas para incenti= var y promover en la observaci=C3=B3n, exploraci=C3=B3n y aprendizaje activ= o. O= bjetivo. E= valuar el impacto did=C3=A1ctico del uso de Polypad en el aprendizaje de op= eraciones matem=C3=A1ticas con expresiones algebraicas en los estudiantes d= e octavo a=C3=B1o de una unidad educativa de Cuenca, Ecuador. Metodolog=C3=ADa<= /span>. Se aplic=C3=B3 un dis= e=C3=B1o cuasi-experimental con un enfoque mixto (pre-test/intervenci=C3=B3= n/pos-test), que a su vez fue complementado con el desarrollo de una encues= ta, observaci=C3=B3n estructurada y entrevistas a los docentes. En el proce= dimiento participaron 68 estudiantes de dos paralelos (Paralelo A =3D 35 es= tudiantes; Paralelo B =3D 33 estudiantes). La intervenci=C3=B3n consisti=C3= =B3 en el desarrollo de cinco sesiones con actividades de herramientas digi= tales (Uso de Polypad para la ense=C3=B1anza de expresiones algebraicas). <= /span>Resul= tados. Las mejoras en = el rendimiento fueron significativamente positivas, un ejemplo de esto se l= o da en el paralelo A, que pas=C3=B3 de tener un promedio de 5.83/10 a 8.45= /10, que representa un aumento de 2.62 puntos, mientras que el paralelo B p= as=C3=B3 de tener un promedio de 5.10/10 a 6.24/10, demostrando un aumento = de 1.14 puntos. Para ambos paralelos se observaron incrementos en la compre= nsi=C3=B3n de los ejercicios con expresiones algebraicas. Adem=C3=A1s, los = estudiantes expresaron una alta motivaci=C3=B3n y preferencia por estas act= ividades colaborativas con tecnolog=C3=ADa, tambi=C3=A9n los docentes se=C3= =B1alaron ventajas en la utilizaci=C3=B3n de estas herramientas digitales. = Conc= lusi=C3=B3n. El uso de= Polypad favoreci=C3=B3 el aprendizaje activo, mejora el rendimiento y fort= alece la comprensi=C3=B3n en el estudiante. Pero su integraci=C3=B3n requie= re capacitaci=C3=B3n docente, infraestructura adecuada y pol=C3=ADticas edu= cativas que faciliten su accesibilidad. =C3=81rea de estudio general: Educa= ci=C3=B3n. =C3=81rea de estudio espec=C3=ADfica: Did=C3=A1ctica de la Matem=C3=A1tica. Tipo de estudio: Art=C3=ADculos originales.</p= > <= /td></tr><tr><td style=3D"width:74.75pt; border-top:0.75pt solid #000000; b= order-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"><= p class=3D"Title" style=3D"margin-top:6pt; text-align:justify; line-height:= 115%; font-size:12pt">Keywords: <= /span>Active learning, Digital tools, Polypad, Educational technology.</p= > </td><td style=3D"width:4.3pt; border-top:0.7= 5pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; v= ertical-align:top"> </td><td style=3D"width:324= .9pt; border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; = padding:0pt 5.4pt; vertical-align:top">Abstract: Introduction.</sp= an> Mathematics teaching in b= asic general education in Ecuador faces various challenges related to under= standing symbols, abstract concepts, low student motivation, and the predom= inance of memorization-based methodologies. Digital tools, such as Polypad = (originally developed by Mathigon and currently part of Amplify), have emer= ged as tools to encourage and promote observation, exploration, and active = learning. Objective. To ev= aluate the educational impact of using Polypad in learning mathematical ope= rations with algebraic expressions in eighth-grade students at a school in = Cuenca, Ecuador. Methodology. A quasi-experimental design with a mixed approach (pre-test/interventio= n/post-test) was applied, which was complemented by a survey, structured ob= servation, and interviews with teachers. Sixty-eight students from two para= llel classes participated in the procedure (Parallel A =3D 35 students; Par= allel B =3D 33 students). The intervention consisted of five sessions with digital to= ol activities (use of Polypad for teaching algebraic expressions). <= span style=3D"font-family:'Times New Roman'; font-weight:bold">Results.</sp= an> The improvements in perfo= rmance were significantly positive. An example of this is given in parallel= A, which went from an average of 5.83/10 to 8.45/10, representing an incre= ase of 2.62 points, while parallel B went from an average of 5.10/10 to 6.2= 4/10, demonstrating an increase of 1.14 points. For both parallels, increas= es in the understanding of exercises with algebraic expressions were observ= ed. In addition, students expressed high motivation and preference for thes= e collaborative activities with technology, and teachers also pointed out a= dvantages in the use of these digital tools. Conclusion. The use of Polypad promoted active learning,= improved performance, and strengthened student comprehension. However, its= integration requires teacher training, adequate infrastructure, and educat= ional policies that facilitate its accessibility. General area of study:= Education. Specific area of stud= y: Mathematics teachin= g. T= ype of study: Original= articles. </td></tr></table> <div style=3D"clear:both"><img src=3D"da= ta:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAuQAAAABCAYAAACWsrt9AAAABHNCSVQ= ICAgIfAhkiAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABxJREFUSIntwTEBAAAIwKDZP7TG8AGm2g= AAgA9zmTsBAl+AgmQAAAAASUVORK5CYII=3D" width=3D"740" height=3D"1" alt=3D"" s= tyle=3D"margin-top:-37.82pt; margin-left:-63.3pt; position:absolute" /></sp= an> = 0; = Nombre<span= style=3D"width:141.26pt; letter-spacing:3pt; display:inline-block"> <= /span> 1 </div></div> <div class=3D"Section_2">1. <span= style=3D"font-family:'Times New Roman'; font-weight:bold">Introducci=C3=B3= n</div> = <div class=3D"Section_3"><div style=3D"clear:both"><img src=3D"data:image/jpeg;base= 64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAUDBAQEAwUEBAQFBQUGBwwIBwcHBw8LCwkMEQ8S= EhEPERETFhwXExQaFRERGCEYGh0dHx8fExciJCIeJBweHx7/2wBDAQUFBQcGBw4ICA4eFBEUHh4= eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh7/wAARCARfAz= 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lKW6F9dp4f9V3eFcQPKQqP21WhubV6aBkbM/zWiUFGme5GmwxP7V1fSoeywGaIk0GLOhRkrOPsx= LtpdHn99I6nuLzkGexooxxgwJ1kgxZiAWxt6C0CX9dgC+bI0UY8wWhy6LY6yRYowxxhhjjDHGGG= OMMcYYY4wxxhhjjDHGGGOMMcYYY4wxxhhjjDHGGGOMMcYYY4wxxhhjtlj+Bzko+j36iSy0AAAAA= ElFTkSuQmCC" width=3D"322" height=3D"79" alt=3D"" style=3D"margin-top:-17.4= 5pt; margin-left:239.7pt; position:absolute" /> </div><= p style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-si= ze:12pt">La ense=C3=B1anza de= las matem=C3=A1ticas en la Educaci=C3=B3n General B=C3=A1sica (EGB</s= pan>) enfrenta retos constant= es, los cuales est=C3=A1n asociados con la comprensi=C3=B3n de s=C3=ADmbolo= s y conceptos no concretos, la comprensi=C3=B3n insuficiente de conceptos a= lgebraicos y el predominio en las metodolog=C3=ADas tradicionales centradas= en la repetici=C3=B3n de procedimientos o de memorizaci=C3=B3n ( (=C3=81lv= arez, M., Almeida, B., & Villegas, E., 2014) =C3=81lvarez et al., 2014;= Rodr=C3=ADguez & Reye, 2022). Lo que se=C3=B1ala recientemente que los= estudiantes de EGB presentan dificultades para conectar las representacion= es visuales, concretas y simb=C3=B3licas, causando una repercusi=C3=B3n en = aprendizajes fragmentados y en errores sistem=C3=A1ticos al realizar operac= iones con expresiones algebraicas (Candela-Mu=C3=B1oz & Rodr=C3=ADguez-= G=C3=A1mez, 2023). En Ecuador, el sistema educativo presenta varios desaf=C3=ADos, = que est=C3=A1n vinculados con la brecha digital, la disponibilidad limitada= de recursos tecnol=C3=B3gicos y la insuficiente formaci=C3=B3n docente en = tecnolog=C3=ADa educativa (Albuja et al., 2023; Ministerio de Educaci=C3=B3= n del Ecuador, 2021). Este panorama requiere de un dise=C3=B1o e implementa= ci=C3=B3n de estrategias pedag=C3=B3gicas que integren recursos digitales a= ccesibles, pertinentes y que sean capaces de transformar el proceso de ense= =C3=B1anza-aprendizaje de las matem=C3=A1ticas (Basdogan & Bonk, 2023).= Bajo este sentido, las herramientas digitales se han convertido en un sopo= rte did=C3=A1ctico muy importante para incentivar experiencias din=C3=A1mic= as que fomenten el aprendizaje activo (Gusho et al., 2023; Jimpikit et al.,= 2024).B= ajo este contexto, se utilizar=C3=A1 el programa de Polypad, que es una pla= taforma creada originalmente en Mathigon y que actualmente est=C3=A1 dispon= ible en Amplify, la cual ofrece un entorno digital que incluye bloques alge= braicos, balanzas virtuales, rect=C3=A1ngulos geom=C3=A9tricos, l=C3=ADneas= num=C3=A9ricas y m=C3=BAltiples herramientas interactivas para representar= conceptos matem=C3=A1ticos de forma visual y manipulable (Imron et al., 20= 25). Su dise=C3=B1o permite que los estudiantes interact=C3=BAen entre lo c= oncreto y lo abstracto, el cual es un aspecto fundamental para el desarroll= o y dominio de los temas (Delport, 2021).En los =C3=BAltimos a=C3=B1os, la eviden= cia cient=C3=ADfica reciente reporta que las herramientas digitales increme= ntan la motivaci=C3=B3n estudiantil, mejoran la visualizaci=C3=B3n de estru= cturas matem=C3=A1ticas, fortalecen el razonamiento y permiten la construcc= i=C3=B3n colaborativa del conocimiento. Estudios como los de (Escueta et al= . 2017; S=C3=A1nchez & Rodr=C3=ADguez 2022; Gusho et al. 2023) muestran= mejoras significativas en el rendimiento cuando estas herramientas se inte= gran dentro de una secuencia did=C3=A1ctica estructurada y con un rol docen= te centrado en la mediaci=C3=B3n cognitiva (Enr=C3=ADquez Chasin, 2021).</s= pan>Pero para e= l sistema educativo ecuatoriano, las limitaciones en infraestructura y cone= ctividad requieren estrategias adaptativas que favorezcan el acceso equitat= ivo a la tecnolog=C3=ADa, especialmente en instituciones rurales (Albuja et= al., 2023; Anderson & Rivera, 2020). Con la siguiente investigaci=C3= =B3n, que est=C3=A1 fundamentada con datos provenientes del estudio aplicad= o en un aula de una escuela rural, se propone evaluar el impacto del uso de= Polypad en el aprendizaje de matem=C3=A1ticas en estudiantes de octavo a= =C3=B1o, analizando tanto los resultados cuantitativos, cualitativos, as=C3= =AD como las percepciones de estudiantes y docentes.<s= pan style=3D"font-family:'Times New Roman'">Adem=C3=A1s de los desaf=C3=ADo= s estructurales asociados a la ense=C3=B1anza de matem=C3=A1ticas, existen = factores psicol=C3=B3gicos que afectan el desempe=C3=B1o estudiantil. Estud= ios recientes identifican que m=C3=A1s del 60 % de estudiantes de EGB exper= imentan ansiedad matem=C3=A1tica, fen=C3=B3meno que reduce la participaci= =C3=B3n oral, deteriora la memoria de trabajo y dificulta la resoluci=C3=B3= n de problemas (Naranjo Sag=C3=B1ay et al., 2024). Las herramientas digital= es, al ofrecer entornos exploratorios donde el error no es penalizado, dism= inuyen este estr=C3=A9s y favorecen una actitud emocional m=C3=A1s positiva= hacia la asignatura (Delport, 2021). Asimismo, el curr=C3=ADculo ecuatoria= no de matem=C3=A1ticas establece que los estudiantes deben desarrollar habi= lidades de razonamiento, representaci=C3=B3n y modelizaci=C3=B3n; bajo esta= modalidad, plataformas como Polypad facilitan actividades de descubrimient= o y experimentaci=C3=B3n, integrando im=C3=A1genes visuales con s=C3=ADmbol= os matem=C3=A1ticos y fomentando el pensamiento algebraico (Guaypat=C3=ADn = et al., 2024).En este estudio se analiza c=C3=B3mo la intervenci=C3=B3n con Polypad= impacta en el aprendizaje activo de las operaciones algebraicas b=C3=A1sic= as, tomando consideraci=C3=B3n tanto del desempe=C3=B1o acad=C3=A9mico como= las percepciones estudiantiles y docentes. Este acercamiento permite valor= ar no solo los resultados inmediatos, sino tambi=C3=A9n los procesos cognit= ivos y emocionales que emergen durante la interacci=C3=B3n con las herramie= ntas digitales (Wijnia et al., 2024).En este sentido, comprender el impacto de una = herramienta digital como Polypad dentro del proceso de ense=C3=B1anza-apren= dizaje de las matem=C3=A1ticas requiere analizar los fundamentos pedag=C3= =B3gicos y tecnol=C3=B3gicos que sustentan su aplicaci=C3=B3n. La integraci= =C3=B3n de recursos digitales no depende =C3=BAnicamente de la disponibilid= ad de dispositivos o plataformas educativas, sino de la manera en que estos= son incorporados dentro de estrategias did=C3=A1cticas orientadas al desar= rollo del pensamiento matem=C3=A1tico, la participaci=C3=B3n activa y la co= nstrucci=C3=B3n significativa del conocimiento. Por ello, resulta necesario= abordar los principios relacionados con las herramientas digitales educati= vas, las metodolog=C3=ADas activas, las representaciones m=C3=BAltiples y l= os procesos de transici=C3=B3n entre los conceptos concretos, visuales y si= mb=C3=B3licos, elementos que permiten comprender c=C3=B3mo estas tecnolog= =C3=ADas pueden contribuir al aprendizaje del =C3=A1lgebra en estudiantes d= e Educaci=C3=B3n General B=C3=A1sica.1.1. Fundamentos de las herramientas digitales= Las herramienta= s digitales son representaciones virtuales e interactivas de objetos matem= =C3=A1ticos cl=C3=A1sicos como bloques algebraicos, regletas, balanzas, fic= has geom=C3=A9tricas y l=C3=ADneas num=C3=A9ricas (Delport, 2021). En estos= entornos digitales, los objetos se manipulan mediante gestos o controles e= n pantalla, lo que permite visualizar transformaciones de manera din=C3=A1m= ica, recibir una retroalimentaci=C3=B3n inmediata, descubrir diferentes for= mas de resolver un ejercicio en un tiempo m=C3=A1s corto, adem=C3=A1s de in= tegrar audio, color y movimiento para reforzar sus significados (Garc=C3=AD= a et al., 2023). Se destaca que este tipo de herramientas generan represent= aciones simult=C3=A1neas, las cuales facilitan la conexi=C3=B3n entre lo gr= =C3=A1fico, lo num=C3=A9rico y lo simb=C3=B3lico, aspecto esencial para el = desarrollo del pensamiento matem=C3=A1tico profundo (Bozkurt, 2020).= La efectividad = de las herramientas digitales est=C3=A1 ligada a tres componentes: la inter= actividad significativa, la cual se=C3=B1ala que no basta con mover element= os, sino que las acciones deben tener sentido pedag=C3=B3gico; la gu=C3=ADa= docente estrat=C3=A9gica, relacionada con la orientaci=C3=B3n pedag=C3=B3g= ica durante el uso de las herramientas; y las tareas bien dise=C3=B1adas, q= ue promueven el razonamiento, la argumentaci=C3=B3n y las conexiones entre = representaciones (L=C3=B3pez et al., 2022; Mumtaz, 2000).1.2. Comparaci=C3=B3n entre herra= mientas digitales y convencionalesLos estudios recientes han investigado las difere= ncias entre herramientas convencionales y digitales en el aprendizaje de la= s matem=C3=A1ticas, concluyendo que ambos tipos favorecen el rendimiento y = la comprensi=C3=B3n conceptual; sin embargo, las herramientas digitales pre= sentan ventajas log=C3=ADsticas como la accesibilidad y la posibilidad de t= rabajo remoto, mientras que las convencionales resultan =C3=BAtiles en etap= as iniciales donde se requiere manipulaci=C3=B3n f=C3=ADsica directa (Pinto= & Laite, 2020; Oliver & An, 2020). Asimismo, existen combinaciones= h=C3=ADbridas (digital + convencional) que generan efectos superiores a su= uso aislado (Wijnia et al., 2024).Se=C3=B1al=C3=B3 Delport (2021) en un estudio so= bre fracciones que las herramientas digitales favorecen especialmente la vi= sualizaci=C3=B3n de proporciones, la comparaci=C3=B3n de =C3=A1reas y la de= scomposici=C3=B3n de figuras, gracias a los movimientos din=C3=A1micos y la= manipulaci=C3=B3n r=C3=A1pida de elementos. En matem=C3=A1ticas, las inves= tigaciones publicadas han encontrado que las herramientas digitales aportan= ventajas como la comprensi=C3=B3n de la propiedad distributiva, la identif= icaci=C3=B3n de t=C3=A9rminos semejantes, la resoluci=C3=B3n de ecuaciones = mediante balanza algebraica y el descubrimiento de patrones en productos no= tables (Stein et al., 1996; Candela-Mu=C3=B1oz & Rodr=C3=ADguez-G=C3=A1= mez, 2023).= 1.3.= Polypad: plataforma y estudios recientesPolypad, perteneciente a Mathigon y desd= e 2022 integrada en Amplify, se ha convertido en una de las herramientas di= gitales m=C3=A1s utilizadas para la ense=C3=B1anza de matem=C3=A1ticas esco= lares (Imron et al., 2025). Sus principales recursos incluyen bloques algeb= raicos de color, rect=C3=A1ngulos din=C3=A1micos para visualizar multiplica= ciones y productos notables, balanza virtual para ecuaciones, l=C3=ADneas n= um=C3=A9ricas interactivas, mosaicos y herramientas de geometr=C3=ADa.</spa= n>Estudios reci= entes destacan su potencial pedag=C3=B3gico, as=C3=AD como lo menciona Delp= ort (2021) quien evidenci=C3=B3 mejoras en el razonamiento y habilidades ma= tem=C3=A1ticas mediante m=C3=B3dulos basados en Polypad. Por otro lado, Gus= ho et al. (2023) utilizaron Polypad junto con plataformas digitales colabor= ativas, evidenciando beneficios en comprensi=C3=B3n, motivaci=C3=B3n y part= icipaci=C3=B3n. Investigaciones desarrolladas en Europa documentan avances = en habilidades espaciales, razonamiento proporcional y uso de representacio= nes m=C3=BAltiples, demostrando que Polypad facilita el desarrollo del pens= amiento estructural, elemento clave para la comprensi=C3=B3n de expresiones= algebraicas, ecuaciones y factorizaci=C3=B3n (Casi & Sabena, 2024).</s= pan>1.4.= <sp= an style=3D"font-family:'Times New Roman'; font-style:italic">Evidencia del= uso de herramientas digitales en los pa=C3=ADses latinoamericanos</= p>La experiencia en= Ecuador sobre herramientas digitales todav=C3=ADa es incipiente; sin embar= go, trabajos recientes en Am=C3=A9rica Latina y regiones con brechas digita= les similares se=C3=B1alan un incremento en la motivaci=C3=B3n hacia las ma= tem=C3=A1ticas, reducci=C3=B3n de la ansiedad matem=C3=A1tica, mejoras sign= ificativas en estudiantes con bajo rendimiento inicial y mayor participaci= =C3=B3n colaborativa (Guaypat=C3=ADn et al., 2024; Naranjo Sag=C3=B1ay et a= l., 2024).El uso de tecnolog=C3=ADa educativa se muestra especialmente valioso en z= onas rurales donde los recursos f=C3=ADsicos son limitados. La disponibilid= ad de recursos virtuales abre las puertas al acceso de herramientas pedag= =C3=B3gicas avanzadas que tradicionalmente solo estaban disponibles en inst= ituciones con mayor infraestructura (Anderson & Rivera, 2020).</= p>1.5. Pensamiento matem= =C3=A1tico tempranoEntre 2020 y 2025, investigaciones destacan que el pensamiento m= atem=C3=A1tico debe iniciarse desde grados anteriores para evitar la transi= ci=C3=B3n abrupta entre la aritm=C3=A9tica y el =C3=A1lgebra (Candela-Mu=C3= =B1oz & Rodr=C3=ADguez-G=C3=A1mez, 2023; Jimpikit et al., 2024). La com= prensi=C3=B3n profunda del =C3=A1lgebra depende de la coordinaci=C3=B3n de = formas concretas, visuales y simb=C3=B3licas.Polypad permite el tr=C3=A1nsito fluid= o entre estas formas, fortaleciendo la comprensi=C3=B3n de estructuras alge= braicas como la propiedad distributiva, la combinaci=C3=B3n de t=C3=A9rmino= s semejantes, los productos notables y la relaci=C3=B3n entre =C3=A1rea y m= ultiplicaci=C3=B3n (Delport, 2021).1.6. Importancia de los productos notables en el aprend= izaje del =C3=A1lgebraLos productos notables representan una de las estructuras fun= damentales para el desarrollo matem=C3=A1tico avanzado (Stein et al., 1996)= . 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descompone en subregion= es; las =C3=A1reas representan los t=C3=A9rminos algebraicos y los rect=C3= =A1ngulos muestran la duplicidad del t=C3=A9rmino 2ab. Esta visualizaci=C3= =B3n favorece el razonamiento estructural y reduce errores comunes en el us= o de f=C3=B3rmulas (Casi & Sabena, 2024).1.7. Brecha digital y equidad educativa en Ec= uadorLa = brecha digital se manifiesta en dos niveles: la brecha de acceso, relaciona= da con la disponibilidad de dispositivos y conectividad, y la brecha de uso= , relacionada con la competencia digital docente y estudiantil (Albuja et a= l., 2023).Datos recientes muestran que, aunque el acceso a dispositivos m=C3=B3vile= s es relativamente alto, su uso pedag=C3=B3gico sigue siendo limitado. La f= alta de formaci=C3=B3n docente contin=C3=BAa siendo uno de los mayores obst= =C3=A1culos para la integraci=C3=B3n tecnol=C3=B3gica significativa (Cantos= et al., 2025). En este contexto, Polypad presenta ventajas por su accesibi= lidad, su interfaz intuitiva y su capacidad para funcionar incluso con cone= ctividad limitada, siempre que las actividades sean planificadas pedag=C3= =B3gicamente (Anderson & Rivera, 2020).1.8. Fundamentos del aprendizaje activo<= /p>La presente inve= stigaci=C3=B3n se fundamenta en los aportes del socio-constructivismo, las = teor=C3=ADas del aprendizaje activo, el enfoque de representaciones m=C3=BA= ltiples en matem=C3=A1ticas y el pensamiento matem=C3=A1tico temprano (Enr= =C3=ADquez Chasin, 2021).1.8.1. &#= xa0; Socio-constructivismo y mediaci=C3=B3n tecnol=C3=B3gicaDe acuerdo con Vygotsky, e= l aprendizaje ocurre en interacci=C3=B3n con herramientas culturales y con = la mediaci=C3=B3n del docente. Las tecnolog=C3=ADas digitales, dentro de es= te enfoque, act=C3=BAan como herramientas culturales modernas que potencian= la construcci=C3=B3n del conocimiento mediante la interacci=C3=B3n din=C3= =A1mica, las representaciones visuales accesibles y la retroalimentaci=C3= =B3n inmediata (Roschelle et al., 2001).Las herramientas digitales como Polypad per= miten que el estudiante manipule objetos matem=C3=A1ticos en entornos explo= ratorios donde el error es parte natural del aprendizaje, favoreciendo la Z= ona de Desarrollo Pr=C3=B3ximo mediante la combinaci=C3=B3n de gu=C3=ADa do= cente y autonom=C3=ADa estudiantil (Gusho et al., 2023).1.8.2.</= span> Aprendizaje activo<s= pan style=3D"font-family:'Times New Roman'">El aprendizaje activo se caract= eriza por la participaci=C3=B3n cognitiva, social y motora del estudiante d= urante la construcci=C3=B3n del conocimiento. En matem=C3=A1ticas, implica = la argumentaci=C3=B3n, representaci=C3=B3n, manipulaci=C3=B3n y comparaci= =C3=B3n de procedimientos (Jimpikit et al., 2024). Polypad facilita estas p= r=C3=A1cticas al permitir la interacci=C3=B3n directa con representaciones = visuales de expresiones algebraicas, balanzas y mosaicos geom=C3=A9tricos, = convirti=C3=A9ndose en un entorno donde el estudiante experimenta, formula = hip=C3=B3tesis y valida resultados (Delport, 2021).1.8.3.<= span style=3D"width:9pt; font:7pt 'Times New Roman'; display:inline-block">= Representaciones m=C3=BAltiples en matem=C3=A1t= icasLas = representaciones m=C3=BAltiples son fundamentales para la comprensi=C3=B3n = matem=C3=A1tica; el dominio conceptual se fortalece cuando los estudiantes = coordinan representaciones concretas, visuales y simb=C3=B3licas (Stein et = al., 1996). Polypad permite transitar entre estas representaciones de forma= fluida; por ejemplo, una expresi=C3=B3n como <img src=3D"data:image= /png;base64,iVBORw0KGgoAAAANSUhEUgAAADoAAAAVCAYAAAAXQf3LAAAABHNCSVQICAgIfAh= kiAAAAAlwSFlzAAAOxAAADsQBlSsOGwAABe5JREFUWIXdVl9IU20Y/539cXOzWpmJrVT6Y42wKG= hXlaOom2ASFgVdBV7URZjRBEvvgggiq5uwLFCSpLK0CCKiAhtGUQj9MRWXMpWtzbGd49k529l5n= ++iPN8352e78KuPflcb7/O85/d7n9/zvg9HRIQ/HBzHcbrfTeJXwfC7CcwnGGNQVRVEBIPBAJ3u= 7zr+MULj8Th6e3vR19cHANi3bx+Ki4thMHyXmGZdIoIkSeB5Hqqq/hbCqqpClmWIoghZlsEY09Y= SiQQEQUAymcTMq6WzsxMvX75EZWUl7HY7KisrEYlEtHWtoowxhEIhdHd3Y2RkBA0NDbBYLL9KHx= hj4Hkenz59wuvXrzE8PIyysjK43W7Y7Xbk5OTgy5cvuH79Og4cOIAtW7YgLy8PHMcBAKqqqqDT6= WAymbQDSjsQIiLGGAUCATpy5AjdvXuXkskkzQcSiQQNDQ2RJEk/jY3H41RbW0tVVVX0+fNn+vr1= K9XW1lJ5eTkNDAwQY4wYYxQKhejUqVPU2tpKsVgsYx9RFMnj8VBjYyOJokjaq0JEJEkSnT17lur= q6khRlAyysVhMI6uqKgmCQIIgkKqqc5IPh8PkcrnI5/MRY2zOWEmS6MqVK+T1ejVRHz58oLVr19= KTJ0/S8v1+P7ndburp6UkrSjwep0uXLpHH46HJyUktR7NuMBjEvXv3cOfOHa15AUCSJLx79w5tb= W1wOp04fPgwotEoWltbIcsy6uvrYTKZ5sW6ZrMZx48f1/4nEgkMDw8jPz8fpaWlabFFRUVwOp3o= 7u6Gw+FAfn4+FEVBZ2cngsEg6urqoNPpIMsycnNzAQA6IsLbt2+hKApWrlypbUZEEEURr169gtP= pxM2bN+Hz+dDV1YVNmzahoqIi7fqeD0x/s7+/Hw8ePEBXVxfOnz+PkpISrRcBQK/XY8eOHfB6vQ= iHwyAivH//Hk1NTSguLsbz589x8uRJhEIhrUcNRIQ3b95gw4YNGdVZtGgRampqMDo6iubmZnR0d= GDnzp3Ytm0bjEZjBlFRFBGJRKAoCgAgFothamoKfr8fjDGNbGFhIaxW66xix8fH0dbWhv7+fixZ= sgRElHbzTmP58uWQZRnhcBirV6/GyMgI3G43AoEAgsEgSkpK0i5TAxFhcHAQpaWlaafGcRyMRiO= MRiNsNhvKysoQiUTgdDpnFQkA3759g8fjgSiKwI+3bWxsDGfOnIHVatX2v3jxIhwOR0Y+x3FYtW= oVTp8+DZ7n0d7ejhMnTqClpQWbN29Oc5DVatUcQEQ4ePDgrJw0odMfmO3U8OPal2UZgiDAZrOl9= fBMFBYW4vLly0ilUsCPilZXV+PcuXNYsWKFJrSgoODfCRkMWLBgAfLy8nDo0CF0dHTA6/WivLwc= OTk5WhwRZbylcwrlOA4OhwMfP34EEaVVlYjA8zyePXsGl8uFp0+fIhaLYeHChdDr9RmVtVgsaXa= ZnJyE1WqF3W7P6LOZkCQJN27cwO7du7Fu3TpwHAeO42AwGGCz2TJyBUEAx3FpTpkLOo7jsHXrVg= wNDSEej2sL0WgUjY2NePToEYqKilBRUYFAIICHDx+iubkZkiRlfZrZQFEU9PT0oKmpCT6fD2NjY= 7h//z7MZjO2b9+e4SS/3w+TyYSCggLo9frshZrNZoyOjgI/KplKpTA+Po7Fixdj165dWLNmDWpq= ajAwMIC9e/fO+9RksVjQ0NCA9evX4+rVq7h27RqWLVuGW7dupdkeAFKpFF68eAGXy4WlS5dmVVE= QEcmyTBcuXKCjR49qA4OiKDQ1NaU9yIwxkiSJRFGkVCr1kznnO5LJJE1MTFAikcgqXlVVkiSJeJ= 4nnudJluVZBw2fz0d79uyh3t7erKY4Tej0aFVdXU0tLS3zNgLONxhjNDExQceOHaPbt2+TIAhZ5= QEAN/2DMYZoNIrHjx9jcHAQ9fX1v3So/xmICH19fWhvb8f+/fuxceNG5ObmZmVbjuM4TSj+0Zuq= qsJkMmXn/V+IaW56vX7OZ24muP+bkP8SfwHjkGMFRQLXdQAAAABJRU5ErkJggg=3D=3D" width= =3D"58" height=3D"21" alt=3D"" style=3D"vertical-align:middle" /> puede visualizarse simult=C3=A1neament= e como =C3=A1rea, descomposici=C3=B3n rectangular, suma algebraica y patr= =C3=B3n repetitivo, fortaleciendo el razonamiento matem=C3=A1tico estructur= al.= 1.8.4. Pensamiento algebrai= co tempranoEl pensamiento algebraico debe iniciarse desde los primeros niveles de l= a Educaci=C3=B3n General B=C3=A1sica para evitar un aprendizaje fragmentado= en etapas posteriores. Las herramientas digitales permiten comenzar desde = asociaciones visuales simples, como la relaci=C3=B3n entre =C3=A1reas y mul= tiplicaci=C3=B3n, la identificaci=C3=B3n de patrones y la comprensi=C3=B3n = de t=C3=A9rminos semejantes, facilitando una transici=C3=B3n gradual hacia = el lenguaje algebraico formal (Candela-Mu=C3=B1oz & Rodr=C3=ADguez-G=C3= =A1mez, 2023; Delport, 2021).2. Metodolog=C3=ADa</sp= an>La ense=C3= =B1anza de =C3=A1lgebra en Educaci=C3=B3n General B=C3=A1sica (EGB</sp= an>) constituye uno de los ma= yores desaf=C3=ADos pedag=C3=B3gicos en matem=C3=A1ticas. En Ecuador, diver= sos estudios evidenciaron dificultades recurrentes relacionadas con la comp= rensi=C3=B3n superficial de los conceptos abstractos, memorizaci=C3=B3n mec= =C3=A1nica de procedimientos y escaso uso de recursos visuales interactivos= . Estas limitaciones impactan en el rendimiento acad=C3=A9mico y la motivac= i=C3=B3n hacia la asignatura, por parte del estudiante.En los =C3=BAltimos a=C3=B1= os, la incorporaci=C3=B3n de herramientas tecnol=C3=B3gicas demostr=C3=B3 u= n gran potencial para transformar la educaci=C3=B3n, especialmente mediante= las herramientas digitales, que permiten representar conceptos matem=C3=A1= ticos de forma visual, manipulable e interactiva. As=C3=AD, con Polypad se = puede incorporar bloques algebraicos, rect=C3=A1ngulos geom=C3=A9tricos, l= =C3=ADneas num=C3=A9ricas y m=C3=BAltiples componentes que facilitan el tr= =C3=A1nsito entre lo convencional y lo abstracto, elemento clave para el ap= rendizaje del =C3=A1lgebra. Adem=C3=A1s, que su uso, cuando se lo utiliza c= on una gu=C3=ADa docente estructurada, se incrementa la comprensi=C3=B3n co= nceptual, promoviendo as=C3=AD el razonamiento algebraico, lo que potencia = la participaci=C3=B3n activa en el aula.En Ecuador, las brechas de infraestructura,= conectividad y formaci=C3=B3n docente presentan desaf=C3=ADos significativ= os para la integraci=C3=B3n tecnol=C3=B3gica. Pero, a=C3=BAn en institucion= es con el equipamiento limitado, se demuestra efectos positivos, esto graci= as a una mediaci=C3=B3n pedag=C3=B3gica adecuada.<span= style=3D"font-family:'Times New Roman'">En esta investigaci=C3=B3n se va a= evaluar la eficacia de Polypad en una intervenci=C3=B3n real desarrollada = en una instituci=C3=B3n rural de Cuenca, aportando datos cuantitativos y cu= alitativos para comprender sus beneficios y desaf=C3=ADos para la educaci= =C3=B3n matem=C3=A1tica ecuatoriana.2.1. Dise=C3=B1o de la investigaci=C3=B3n<p= style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-siz= e:12pt">A este estudio se emp= le=C3=B3 un dise=C3=B1o cuasi-experimental, el cual tendr=C3=A1 un enfoque = mixto (cuantitativo + cualitativo), en donde se aplic=C3=B3 la siguiente se= cuencia:= Pre-test =E2=86=92 Intervenci=C3=B3n did=C3=A1ctica con Polypad =E2=86=92 P= os-testY= ser=C3=A1 complementada con la realizaci=C3=B3n de encuestas de percepci= =C3=B3n estudiantil, una observaci=C3=B3n/an=C3=A1lisis hacia los participa= ntes, y con entrevistas semiestructuradas hacia los docentes.Esta estructura permit= e comprender el impacto no solo en t=C3=A9rminos de rendimiento acad=C3=A9m= ico de los participantes, sino tambi=C3=A9n en t=C3=A9rminos motivacionales= , cognitivos y pedag=C3=B3gicos. Con este dise=C3=B1o mixto existir=C3=A1 l= a posibilidad de una triangulaci=C3=B3n metodol=C3=B3gica, validaci=C3=B3n = cruzada de hallazgos y de una interpretaci=C3=B3n contextualizada de los re= sultados.Los participantes en esta investigaci=C3=B3n ser=C3=A1 una poblaci=C3=B3n = total de estudiantes de octavo a=C3=B1o de la Unidad Educativa Guillermo Me= nsi, ubicada en El Valle, Cuenca, Azuay (zona rural). La cual estar=C3=A1 c= lasificada en dos grupos, los estudiantes del paralelo A con un total de 35= estudiantes, y los estudiantes del paralelo B con un total de 33 estudiant= es, juntando ambos paralelos de obtiene la poblaci=C3=B3n total de la inves= tigaci=C3=B3n que ser=C3=A1 de 68 participantes.Adem=C3=A1s, participaron todos los= docentes de matem=C3=A1ticas de la instituci=C3=B3n mediante entrevistas s= emiestructuradas orientadas a captar percepciones, barreras y sugerencias s= obre la integraci=C3=B3n de Polypad.Por lo que, se cumple varios escenarios que son= muy importantes para poder determinar los resultados de esta investigaci= =C3=B3n, los cuales son una escuela rural con acceso limitado a infraestruc= tura tecnol=C3=B3gica, laboratorio de inform=C3=A1tica con conectividad med= ia, estudiantes con experiencia m=C3=ADnima en manipulativos virtuales y do= centes con formaci=C3=B3n parcial en tecnolog=C3=ADas educativas.</p= >2.2. Instrumentos y m= ateriales Para la reco= lecci=C3=B3n de informaci=C3=B3n y evaluaci=C3=B3n del impacto de la interv= enci=C3=B3n con Polypad se utilizaron diferentes instrumentos de medici=C3= =B3n y recursos did=C3=A1cticos, dise=C3=B1ados de acuerdo con los objetivo= s planteados en la investigaci=C3=B3n. Estos permitieron analizar los cambi= os en el desempe=C3=B1o acad=C3=A9mico de los estudiantes, as=C3=AD como su= s experiencias durante el proceso de aprendizaje activo de las expresiones = algebraicas. Los instrumentos aplicados estuvieron orientados a obtener inf= ormaci=C3=B3n cuantitativa y cualitativa antes, durante y despu=C3=A9s de l= a implementaci=C3=B3n de la estrategia did=C3=A1ctica.2.2.1.</= span> Pre-test y Post-test<= span style=3D"font-family:'Times New Roman'">Para poder identificar como er= a el conocimiento de matem=C3=A1ticas, de los estudiantes antes y despu=C3= =A9s del uso de Polypad se realizaron pruebas estructuradas con 5 preguntas= de opci=C3=B3n m=C3=BAltiple, evaluando la identificaci=C3=B3n de t=C3=A9r= minos semejantes, suma y resta de expresiones, multiplicaci=C3=B3n algebrai= ca mediante la propiedad distributiva, y divisi=C3=B3n algebraica b=C3=A1si= ca.La es= cala de calificaci=C3=B3n fue de 0 a 10 puntos, se us=C3=B3 el mismo format= o en pre-test y post-test para garantizar comparabilidad.2.2.2.<= /span> Actividades con PolypadEl dise=C3=B1o did=C3=A1ct= ico desarrollado con Polypad se estructur=C3=B3 en una secuencia de cinco s= esiones de 45 minutos durante toda una semana de clases, las sesiones fuero= n orientadas para favorecer la transici=C3=B3n desde la manipulaci=C3=B3n c= oncreta hacia la comprensi=C3=B3n simb=C3=B3lica en el =C3=A1lgebra inicial= . Cada sesi=C3=B3n se fundament=C3=B3 en principios del aprendizaje activo,= el constructivismo y el uso de representaciones m=C3=BAltiples, aprovechan= do las caracter=C3=ADsticas interactivas del entorno digital.La sesi=C3=B3n 1 fue = =E2=80=9CIntroducci=C3=B3n al entorno Polypad=E2=80=9D, la cual estuvo neta= mente dedicada al reconocimiento de la interfaz de Polypad, en donde se pue= do explorar las principales categor=C3=ADas como bloques manipulativos, rec= t=C3=A1ngulos algebraicos, l=C3=ADneas num=C3=A9ricas y controles de edici= =C3=B3n. Se comenz=C3=B3 con una fase inicial de exploraci=C3=B3n libre, se= guida de una exploraci=C3=B3n guiada para identificar funciones clave como = arrastrar, soltar piezas, duplicar y eliminar elementos. Esta sesi=C3=B3n f= ue primordial para disminuir la ansiedad tecnol=C3=B3gica, desarrollar auto= nom=C3=ADa en el estudiante y fomentar la disposici=C3=B3n para las siguien= tes sesiones.<img src=3D"data:image/png;= base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAiCAYAAAApkEs2AAAABHNCSVQICAgIfAhkiAAA= AAlwSFlzAAAOxAAADsQBlSsOGwAAAl9JREFUWIXtlz9r6lAYxp9cuogOXYqDDv0ASgmCgyAoKPg= BXPwWDgUHO4jgVK2lXSy46OAkOOqqqO1SQWkpFJFKaVWoIKJtISXPnSoEpTfmht4/5AdZ3vc55M= fLOYdEIEn85QiCIPz40xJqMUT1xhDVG0NUb/5v0efnZ8RiMUwmE7y+viKTycDtdiMYDKJSqaxyq= VQKrVZLH1Nuyd3dHUVRZLlcpizLjMfjBKB46vU6SbLf79Pv97NUKm37GgVbi85mM3q9Xp6enpIk= Hx4eWCqV+Pb2xpubGzqdTgLg0dHRak2n0yEAXl1dfZ/o+fk5AfDx8ZEkuVgsFP2zszMCYDqdVtT= D4TBDoRA/Pj40i6reo5IkIZfL4eDgADabDQBgNpsVGVmWAQA+n09R93g8qNVq6HQ6mreoatHBYI= Db21s4HA4IgrAx0263EY1G4XK5FHW73Q4A6Ha7mkV31Aan0ykAwGKxbOxfX19jOp3i4uJirWcym= QAAo9FIs6jqiX5OcdM0F4sFjo+Pkc/nsbu7u9b/3BK/8+mrWnRvbw8AsFwuFXWSyGazSCQS2N/f= hyzLqFareHl5WWXe398BAFarVbOo6lMvSRJFUaQoiop6oVBYu0c9Ho8ic3JyQgC8vLzUfOq3up5= 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Los estudiantes visualizaron c=C3=B3mo la multiplic= aci=C3=B3n se descompone en partes, cada parte corresponde a un t=C3=A9rmin= o del desarrollo algebraico, la propiedad distributiva emerge naturalmente = del modelo. Con estas actividades se reforzaron la relaci=C3=B3n entre =C3= =A1rea y producto algebraico.<img src=3D= "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAiCAYAAAApkEs2AAAABHNC= SVQICAgIfAhkiAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAjVJREFUWIXtlz1rIlEUht+72ARsQwr= NLzAQLqYKCAqSKqnG1jrML5g2CGIjks7YKmgTSCuJkBATDAhKhCiEYCH4MYUQAhJBxneL3ZUd3A= RndmQ/mKc89xzuc89lzmUESeIvRwghvvxpiVVxRZ3GFXUaV9Rp/m/RwWAATdOg67op/v7+jqOjI= 1xdXQEAkskk7u/vnTGlRTqdDqWUPD8/53w+N62lUikC4OXlJUny5eWFkUiExWLR6jYmLIu+vr4y= FArx9PR0ae36+prb29smUZJsNBoEwIeHh98StXT1hUIB1WoViqKY4rquo16v4/DwcKlGSolYLIa= TkxMYhmH75lcWnc1mODs7w+7uLnw+3yJuGAZyuRxUVf2wdn9/H+VyGY1GY/2i3W4XT09P2NnZgR= BiES+VSlAUBV6v98Nav98PAHh8fFy/6Hg8BgCTULvdBgAEAoFPazc2NgAAw+HQrufqoj+6+HM3K= 5UK4vE4hBAQQiCbzQIADg4OcHNzs8ibz+fAtw93/aKbm5sAgMlkYnmT6XQKANja2rJcu2DVETGb= zSilpJTywxxVVZfGE0lmMhkCYK1WW/948ng8OD4+RrPZRK/Xs9SMer2OaDSKvb09G638jpWTvb2= 9MRwOM51Or1zTarUIgHd3d3aaSdp5mUjy+fmZwWCQFxcXS0/or3IjkQjz+bxtSdoVJcl+v09N0z= gajT7NSyQSvL29teu3AAAE3d9lZ3FFncYVdRpX1Gn+GVEXp/kKUjsC77UubnQAAAAASUVORK5CY= II=3D" width=3D"42" height=3D"34" alt=3D"" style=3D"margin-top:61.7pt; marg= in-left:300pt; position:absolute" />La sesi=C3=B3n 4 fue =E2=80=9CDivisi=C3=B3n algebraica median= te agrupaciones y particiones visuales=E2=80=9D, en donde los estudiantes t= rabajaron problemas de partici=C3=B3n, utilizando rect=C3=A1ngulos y bloque= s para representar divisiones como los que se observan en la Ecuaci=C3=B3n 4</s= pan>: <im= g src=3D"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAmCAYAAADJJcvs= AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAA+VJREFUSIndlrtLK1sUxr8= 94xwmxkcwmBBsJGihhaiJiGKjYGFlIWIjWClY2gSttLTwAYIIPkDs4h8QEFSiCAoSUVAbMURNIG= ggJpkwmee6hSTn3pPxXu/1VuerhrXht/f61t5rDSMiwjfFGGPcdyFFVfwaICIYhvGxWFG2/M8gI= kKhUEA6ncbFxQUURcHo6OiXYVwRkslksL29jZGRETw8PMDr9eJf2UdEJEkSLSwsUFdXFyUSCbKS= qqokSRIpikJERIZhUD6fJ1mWP3YzTZNOT0/J6/VSNBq1hOTzeTo4OKDJyUm6urqiQqFAsViMAoE= AHR4eEgBwqqpibW0NbW1tMAwDkUgE5+fneHp6gq7rICIkEgm8vr4CABYXF/H4+IhgMIiWlhbU19= cDAFgqlaK+vj709vbC7XbD7Xbj8vISyWQSS0tLaGtrg6ZpMAwDV1dXmJ2dRX9/P8bHx+H1eiEIA= hhjDPF4nBoaGmh1dZVkWSbTNOnl5YUGBgZoenq65AkRUTQaJb/fT1tbWyRJUikOABzHceB5Hs3N= zRBFEYwx1NbWwu/3I5lMQtf1opdQFAWMMYiiCEEQ/lp+u90Oj8eDWCxWCpqmCUmSUFdXB57nQUR= Ip9PY399HV1cXbm5uIEkSFEUpbVRht9sxNTWFnZ0dDA4OwuFw4P7+Hre3t5ifn0c2m8XR0RGen5= 8xPDyMh4cHbGxsIBwOAwCGhoY+zCYiymQyOD4+xt3dHTRNg8PhQHd3Nzo6OvD8/IylpSVMTEzA5= /Ph/f0dy8vLcDgcmJiYgMfjgSAIjBXN0jQN+XwehmFAFEXYbDZwHAdFUVAoFGCz2fDjxw+YpglZ= lkFEsNls4HkejLGfoO/of20jvzGoYmVl5VsAu93+Acpms98CFdvyb1x+yxGh6zpkWS51SCKCKIq= orKwEY+xrIF3XcX19jcXFRTQ2NqK6uhrhcBg+nw9zc3NwOp3WR/q10cuyTGtrazQzM0OyLJOmaX= RyckJNTU10dHREpmmWDQfLEwmCgLGxMXAcB1EUQURwOp2lbyKyTK8MxPM8XC4XiAiqqiKdTiMUC= qGzsxOtra3gOOv6WJpdbK2hUAiHh4eoqalBIBCAy+Wy9ufvyl9MqaenB4lEApubm0gmk5+PccvR= +idpmkaRSITa29tpb2+PVFW1NLvsRIZhIJVKIZfLfeReUQGPxwOn04l4PA7TNL+WmqIoWF9fRzA= YhK7rME0TmUwGsizD7/d/+ptTFuU4DjabDbu7u0in03A6nTg7O8Po6Ch8Ph94nrcElb1+0zSRy+= Xw9vYGTdNK96murg5VVVWWd4h99m7+i/4AGxehDnRcBXEAAAAASUVORK5CYII=3D" width=3D"= 18" height=3D"38" alt=3D"" style=3D"vertical-align:middle" /><img src=3D"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADYAAAAnCAYAAAB= Ez7vjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAOxAAADsQBlSsOGwAABg9JREFUaIHtmF9IVN= sXxz/nzDiHGWcMlEnE0kBImswkpSnQIMuCIAvMl4QIaiDrrUnQssgeAsOnHgqzCImeeigwKhA1x= KxByV7EqMhJscmmEZ3ROR7Ov9/DzeEnv9+9ze02dYs+j4e1917fvfdaZ68lmKZp8oshCIIg/mgn= UoU1GSPDMFBVFU3TME0TURSRJAmLxZJ6D7+SpITNz8/T3t7OyMgIq1ev5vXr1zQ3N1NSUoIo/js= PPSmvFEVhcXGR1tZWGhsbyc/P58qVKyiK8s0d0nWdWCxGOBxmenqaUCjEzMwMqqr+rXmSOjG328= 3Zs2cBmJ6eRlEUSktLk76K8/PzWCwW7Hb7X9qZpkkwGOT8+fOsWLECj8dDX18fsizT2tpKYWEhV= mtSLid3YkvEYjGePHnC4uIiNTU12Gy2pMZdv36dhw8fftHOMAzGx8fRdZ0zZ85QX19PW1sbU1NT= dHR0EI/Hk/bVCjA7O8vIyAh2u52ysjIMwyAYDDI5OUl5eTmSJBGLxejp6aG7u5uWlhbcbnfSi4R= CIRwOxxftRFHE6/WyceNGMjMzEQQBSZJwOp04HA4EQUhswOTkJKOjoxQXF5OTk4OqqgQCAZxO5x= /CVFWlq6uLQCDA4OAg9+7dQ9M02tvbkWUZr9eLaZoMDQ1x9+5d/H4/hmHQ09NDRUUFkiQlLfBLC= IKAy+XC5XKhaRozMzP09fWRl5dHXV1dYnMikQi3bt1iYGCAgoICLly4QHd3N4FAgJKSkj+EARQV= FVFVVcXevXvp7e0lGAzi9/txuVzY7XZmZ2fp7Oxkbm6Oa9euEY1GycrKYuvWrd9U2BKyLHP79m2= ePn1KLBbj+PHj5OfnJ2Ja0zR8Ph+bN2/G7/fT29uLxWLh3LlzWK1WDh8+jLD08pBlmVOnTjE2Ns= bVq1dZu3Zt4ujj8Tjj4+OJLCgIAllZWeTm5v5PAlEUhRs3bjA6OophGAA8e/aMjIwMPB4PfL5y6= 9ato76+/v8mIEVRePXqFaFQiL6+Pl68eEFjYyNbtmxZtpHhcJjt27dTVVVFc3Nz4voKgiAkUowg= CBQWFtLf309eXl5CFIDD4WD9+vVJ7bYoihQXF7Ny5UqWXmvv378nJyeHysrKxFrZ2dnL1vhvJEl= iw4YNFBUVUVJSwrFjx7h58yYej2dZbKelpWGaJmVlZaSnpy+bz8rnYAyFQgSDQURRRJblL6bmPy= MtLY3y8vJl34aHhykoKKC2tvYvxxqGQTQaRVEU3G43oiiSkZFBQUEBExMTaJqWsNU0jfv377Np0= yZGRkbYt2/fsrnEqakpQqEQly9f5siRIwAMDQ0xPj7Omzdvvkrc16LrOl1dXbS0tBCJRACIRqO8= fPmSoqIinE4ni4uLRCIRBgYGcLlcVFdX09PTQyQS4c6dO4lwEU+fPo3P5+PEiROsWbOGPXv24Pf= 7aWtrY9WqVd9VmCiKuN1uxsbGaGho4NKlS5w8eZLS0lJ8Ph/p6elMTExQU1PD48ePqaiooLKyEp= vNRm1tLdnZ2YmYFT59+mRarVYyMjLgc6KQZRmHw4Hdbv/TOPg7dHZ2kpOTw65du75oq6oqsiyj6= /pSIsBmsyFJEqIooqoq8/Pz2Gy2RLjEYjE0TcPpdCJJEoIgCML3qMdUVUUQhKSfQ/+U7ybse/NL= F5q/hf1sWBcWFn60DynBeujQoR/tQ0oQAoHAL5cVvV7v73T/0/Fb2M/Gb2Ffg67rfPjwgY8fPya= q6Xg8zrt371LSbF2GmSJ0XTf7+/vNAwcOmNu2bTPD4bAZjUbNhoYGc//+/ebs7GyqljZJthP8NR= iGwdzcHBcvXqS6uprnz58zNjbGwYMHE33CVJKy/5hpmmiahiiK1NXVoaoqPp+PnTt3prwuS+l/T= BAE0tLSsFgs7N69m+HhYcrLy79bsZnyrBiPxxkcHMQwjGVdplSTUmGaptHR0cHRo0exWCy8ffuW= hYWFRAcqlaQkxnRdp6mpiVgslmidV1dXoygKHo+HpqYmcnNzv/WyCVLW89A0jUePHpGZmYnX68V= isRAOh3nw4AE7duxIeVvvl27m/AdkWEi9TRsBdwAAAABJRU5ErkJggg=3D=3D" width=3D"54"= height=3D"39" alt=3D"" style=3D"vertical-align:middle" /><sp= an style=3D"font-family:'Times New Roman'">Con esta manipulaci=C3=B3n digit= al se favoreci=C3=B3 la comprensi=C3=B3n intuitiva de la divisi=C3=B3n como= distribuci=C3=B3n equitativa, c=C3=A1lculo de cu=C3=A1ntas veces cabe un b= loque dentro de otro, e identificaci=C3=B3n de factores ocultos. </p= >La sesi=C3=B3n 5 f= ue =E2=80=9CSesi=C3=B3n integradora=E2=80=9D, en esta =C3=BAltima sesi=C3= =B3n se desarrollaron actividades que exig=C3=ADan mezclar operaciones. Los= estudiantes deb=C3=ADan reforzar sus estrategias, explicar los pasos reali= zados y contrastar sus modelos con los de sus compa=C3=B1eros. Esta fase co= nsolid=C3=B3 la autonom=C3=ADa en la resoluci=C3=B3n de problemas, el pensa= miento cr=C3=ADtico y la capacidad de relacionar lo concreto, lo representa= tivo y lo simb=C3=B3lico.3. Resultados<= p style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-si= ze:12pt"> <spa= n style=3D"font-family:'Times New Roman'">Los resultados obtenidos durante = la investigaci=C3=B3n permiten analizar los efectos de la implementaci=C3= =B3n de Polypad como estrategia did=C3=A1ctica para fortalecer el aprendiza= je activo de las operaciones algebraicas en estudiantes de octavo a=C3=B1o = de educaci=C3=B3n general b=C3=A1sica. La informaci=C3=B3n recopilada media= nte los instrumentos aplicados fue organizada considerando los componentes = cuantitativos y cualitativos del estudio, permitiendo establecer una compar= aci=C3=B3n entre el desempe=C3=B1o acad=C3=A9mico antes y despu=C3=A9s de l= a intervenci=C3=B3n, as=C3=AD como conocer las percepciones de los estudian= tes respecto al uso de herramientas digitales en el proceso de aprendizaje.= De esta manera, los resultados presentados permiten valorar tanto la incid= encia de la estrategia tecnol=C3=B3gica en la comprensi=C3=B3n de contenido= s matem=C3=A1ticos como los aspectos motivacionales y pedag=C3=B3gicos asoc= iados a su aplicaci=C3=B3n en el aula.3.1. Resultados del pre-test y post-test<= p style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-si= ze:12pt">El an=C3=A1lisis com= parativo entre los resultados del pre-test y post-test permiti=C3=B3 corrob= orar el impacto significativo que tuvo el uso de la herramienta digital Pol= ypad en el aprendizaje de las operaciones algebraicas en estudiantes de oct= avo a=C3=B1o de Educaci=C3=B3n General B=C3=A1sica. <s= pan style=3D"font-family:'Times New Roman'">Antes de la intervenci=C3=B3n, = los estudiantes presentaban dificultades notorias en la identificaci=C3=B3n= de t=C3=A9rminos semejantes, la aplicaci=C3=B3n de la propiedad distributi= va y la resoluci=C3=B3n de expresiones algebraicas simples, lo que coincid= =C3=ADa con las observaciones previas realizadas durante las clases tradici= onales.E= n el paralelo A, el promedio inicial fue de 5,83/10, mientras que tras la i= ntervenci=C3=B3n se alcanz=C3=B3 un promedio de 8,45/10, lo que representa = un incremento de 2,62 puntos. Este crecimiento evidencia una mejora sustanc= ial no solo en los resultados cuantitativos, sino tambi=C3=A9n en la compre= nsi=C3=B3n conceptual, ya que los estudiantes demostraron mayor seguridad a= l explicar procedimientos, justificar resultados y representar gr=C3=A1fica= mente las operaciones.Por su parte, el paralelo B mostr=C3=B3 un aumento de 1,14 pu= ntos, pasando de 5,10/10 a 6,24/10. Aunque el incremento fue menor en compa= raci=C3=B3n con el paralelo A, los datos indican una mejora positiva en la = comprensi=C3=B3n de conceptos algebraicos, especialmente en estudiantes que= al inicio presentaban mayores dificultades. Esta diferencia entre grupos puede atr= ibuirse a diferentes factores como el nivel de participaci=C3=B3n, la famil= iaridad previa con herramientas digitales y el ritmo de trabajo grupal.</sp= an>Por lo que, = los resultados evidencian que el uso sistem=C3=A1tico de Polypad favorece l= a consolidaci=C3=B3n del aprendizaje significativo, permitiendo que los est= udiantes transiten progresivamente desde representaciones concretas hacia n= iveles m=C3=A1s abstractos del pensamiento matem=C3=A1tico.3.2. Resultados de la encuest= a sobre aprendizaje activoEl an=C3=A1lisis de los resultados obtenidos a partir de = la encuesta aplicada a los estudiantes permite comprender de manera m=C3=A1= s profunda el impacto del uso de herramientas digitales (espec=C3=ADficamen= te Polypad) en el aprendizaje activo de las matem=C3=A1ticas. Esta informac= i=C3=B3n cualitativa complementa los datos cuantitativos del pretest y post= est, permitiendo una visi=C3=B3n m=C3=A1s integra del proceso educativo des= arrollado durante la intervenci=C3=B3n.Tabla 1Inter=C3= =A9s en aprender matem=C3=A1ticas mediante herramientas tecnol=C3=B3gicas</= span><table style=3D"width:100%; margin-right:auto; margin-left:auto; m= argin-bottom:0pt; padding:0pt; border-collapse:collapse"><tr><td style=3D"w= idth:41.6%; border-top:0.75pt solid #000000; border-bottom:0.75pt solid #00= 0000; padding:0pt 5.4pt; vertical-align:top">Nivel de acuerdo</td><td style=3D"width:25.52%; border-top= :0.75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4p= t; vertical-align:top">Frecuencia</td><td style=3D"width:32.9%; border-top:0.75pt s= olid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertic= al-align:top">Porce= ntaje (%)</td></tr><tr><td style=3D"width:41.6%; border-top:0.75= pt solid #000000; padding:0pt 5.4pt; vertical-align:top">Muy de acuerdo</td><td sty= le=3D"width:25.52%; border-top:0.75pt solid #000000; padding:0pt 5.4pt; ver= tical-align:top">39= </td><td style=3D"width:32.9%; border-top:0.75pt solid #000000; = padding:0pt 5.4pt; vertical-align:top">58 %</td></tr><tr><td style=3D"width:41.6%; = padding:0pt 5.4pt; vertical-align:top">De acuerdo</td><td style=3D"width:25.52%; pa= dding:0pt 5.4pt; vertical-align:top">22</td><td style=3D"width:32.9%; padding:0pt 5= .4pt; vertical-align:top">33 %</td></tr><tr><td style=3D"width:41.6%; padding:0pt 5= .4pt; vertical-align:top">En desacuerdo</td><td style=3D"width:25.52%; padding:0pt = 5.4pt; vertical-align:top">4</td><td style=3D"width:32.9%; padding:0pt 5.4pt; verti= cal-align:top">6 %<= /span></td></tr><tr><td style=3D"width:41.6%; padding:0pt 5.4pt; vertic= al-align:top">Muy en desacuerdo<= /p></td><td style=3D"width:25.52%; padding:0pt 5.4pt; vertical-align:top"><= p style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-si= ze:10pt">3</td><td= style=3D"width:32.9%; padding:0pt 5.4pt; vertical-align:top"><sp= an style=3D"font-family:'Times New Roman'">3 %</td></tr><tr><td = style=3D"width:41.6%; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt= ; vertical-align:top">Total</td><td style=3D"width:25.52%; border-bottom:0.75pt sol= id #000000; padding:0pt 5.4pt; vertical-align:top">68</td><td style=3D"width:32.9%;= border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"= >100 %</= td></tr></table>Nota= : pregunta sobre el inter=C3=A9s y mot= ivaci=C3=B3n hacia el aprendizaje matem=C3=A1tico<span= style=3D"font-family:'Times New Roman'">Los resultados evidencian que el 9= 1% de los estudiantes manifest=C3=B3 estar muy de acuerdo o de acuerdo con = sentirse m=C3=A1s motivado al aprender matem=C3=A1ticas mediante herramient= as tecnol=C3=B3gicas. Este hallazgo confirma que la incorporaci=C3=B3n de r= ecursos digitales incrementa el inter=C3=A9s y la disposici=C3=B3n hacia el= aprendizaje, especialmente en contenidos que tradicionalmente generan rech= azo o ansiedad, como el =C3=A1lgebra.Este aumento en la motivaci=C3=B3n puede expli= carse por el car=C3=A1cter interactivo, visual y din=C3=A1mico de Polypad, = el cual transforma el aprendizaje en una experiencia activa y participativa= . Al permitir que los estudiantes manipulen objetos, observen cambios en ti= empo real y experimenten sin temor al error, generando un entorno que favor= ece la curiosidad y el compromiso cognitivo. Este resultado coincide con es= tudios previos que sostienen que las tecnolog=C3=ADas educativas bien integ= radas promueven mayor involucramiento emocional y cognitivo.Tabla 2Comprensi=C3=B3n de los contenidos mediante act= ividades interactivas<table style=3D"margin-right:auto; margin-l= eft:auto; margin-bottom:0pt; padding:0pt; border-collapse:collapse"><tr><td= style=3D"width:78.35pt; border-top:0.75pt solid #000000; border-bottom:0.7= 5pt solid #000000; padding:0pt 5.4pt; vertical-align:top">Nivel de acuerdo</td><td style=3D"width:1pt; = border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; paddin= g:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75= pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; ve= rtical-align:top">&= #xa0;</td><td style=3D"width:1pt; border-top:0.75pt solid #00000= 0; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:to= p"> </p= ></td><td style=3D"width:1pt; border-top:0.75pt solid #000000; border-botto= m:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"><s= pan style=3D"font-family:'Times New Roman'"> </td><td style= =3D"width:1pt; border-top:0.75pt solid #000000; border-bottom:0.75pt solid = #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; = border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; paddin= g:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75= pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; ve= rtical-align:top">&= #xa0;</td><td style=3D"width:1pt; border-top:0.75pt solid #00000= 0; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:to= p"> </p= ></td><td style=3D"width:47.25pt; border-top:0.75pt solid #000000; border-b= ottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top">Frecuencia</td><= td style=3D"width:1pt; border-top:0.75pt solid #000000; border-bottom:0.75p= t solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"wid= th:1pt; border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000= ; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-= top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5= .4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75pt soli= d #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-= align:top"> </= span></td><td style=3D"width:1pt; border-top:0.75pt solid #000000; bord= er-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><= td style=3D"width:1pt; border-top:0.75pt solid #000000; border-bottom:0.75p= t solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"wid= th:1pt; border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000= ; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:65.25pt; bor= der-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0= pt 5.4pt; vertical-align:top">Porcentaje (%)</td></tr><tr><td style=3D"width:78.35p= t; border-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top">= Muy de acuerdo</spa= n></td><td style=3D"width:1pt; border-top:0.75pt solid #000000; padding= :0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75p= t solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"wid= th:1pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:= top"> <= /p></td><td style=3D"width:1pt; border-top:0.75pt solid #000000; padding:0p= t 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75pt s= olid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width= :1pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:to= p"> </p= ></td><td style=3D"width:1pt; border-top:0.75pt solid #000000; padding:0pt = 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75pt sol= id #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:47= .25pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:t= op">42</= td><td style=3D"width:1pt; border-top:0.75pt solid #000000; padding:0pt 5.4= pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75pt solid = #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; = border-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td>= <td style=3D"width:1pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt;= vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75pt solid #00= 0000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; bor= der-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td= style=3D"width:1pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt; ve= rtical-align:top">&= #xa0;</td><td style=3D"width:65.25pt; border-top:0.75pt solid #0= 00000; padding:0pt 5.4pt; vertical-align:top">61 %</td></tr><tr><td style=3D"width:= 78.35pt; padding:0pt 5.4pt; vertical-align:top">De acuerdo</td><td style=3D"width:1= pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; paddi= ng:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.= 4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; vert= ical-align:top">&#x= a0;</td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-alig= n:top"> </span= ></td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"><p= style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-siz= e:10pt"> </td= ><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"><= span style=3D"font-family:'Times New Roman'"> </td><td styl= e=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"widt= h:47.25pt; padding:0pt 5.4pt; vertical-align:top">22</td><td style=3D"width:1pt; pa= dding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt= 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; v= ertical-align:top">= </td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-a= lign:top"> </s= pan></td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"= > <= /td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td s= tyle=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"w= idth:65.25pt; padding:0pt 5.4pt; vertical-align:top">32 %</td></tr><tr><td style= =3D"width:78.35pt; padding:0pt 5.4pt; vertical-align:top">En desacuerdo</td><td sty= le=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"wid= th:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; p= adding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0p= t 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; = vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-= align:top"> </= span></td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top= "> = </td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td = style=3D"width:47.25pt; padding:0pt 5.4pt; vertical-align:top"><s= pan style=3D"font-family:'Times New Roman'">3</td><td style=3D"w= idth:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt;= padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:= 0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt= ; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; vertica= l-align:top"> = </td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:t= op"> </= p></td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><t= d style=3D"width:65.25pt; padding:0pt 5.4pt; vertical-align:top">5 %</td></tr><tr= ><td style=3D"width:78.35pt; padding:0pt 5.4pt; vertical-align:top">Muy en desacuerdo</td><td style=3D"= width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt= ; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding= :0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4p= t; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; vertic= al-align:top"> = ;</td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:= top"> <= /p></td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><= td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"><sp= an style=3D"font-family:'Times New Roman'"> </td><td style= =3D"width:47.25pt; padding:0pt 5.4pt; vertical-align:top">1</td><td style=3D"width:= 1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padd= ing:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5= .4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; ver= tical-align:top">&#= xa0;</td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-ali= gn:top"> </spa= n></td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"><= p style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-si= ze:10pt"> </t= d><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td s= tyle=3D"width:65.25pt; padding:0pt 5.4pt; vertical-align:top"><sp= an style=3D"font-family:'Times New Roman'">2 %</td></tr><tr><td = style=3D"width:78.35pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4= pt; vertical-align:top">Total</td><td style=3D"width:1pt; border-bottom:0.75pt soli= d #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt= ; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top= "> = </td><td style=3D"width:1pt; border-bottom:0.75pt solid #000000; padding:0p= t 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-bottom:0.75p= t solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"wid= th:1pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-ali= gn:top"> </spa= n></td><td style=3D"width:1pt; border-bottom:0.75pt solid #000000; padd= ing:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-bottom= :0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"><sp= an style=3D"font-family:'Times New Roman'"> </td><td style= =3D"width:1pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; verti= cal-align:top"> = 0;</td><td style=3D"width:47.25pt; border-bottom:0.75pt solid #0= 00000; padding:0pt 5.4pt; vertical-align:top">68</td><td style=3D"width:1pt; border= -bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td= style=3D"width:1pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt;= vertical-align:top"> </td><td style=3D"width:1pt; border-bottom:0.75pt solid = #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; = border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top">= </= td><td style=3D"width:1pt; border-bottom:0.75pt solid #000000; padding:0pt = 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-bottom:0.75pt = solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width= :1pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align= :top"> = </td><td style=3D"width:65.25pt; border-bottom:0.75pt solid #000000; pa= dding:0pt 5.4pt; vertical-align:top">100 %</td></tr></table> En relaci=C3=B3n con la comprensi=C3=B3n= de los contenidos matem=C3=A1ticos, el 93% de los estudiantes indic=C3=B3 = que las actividades interactivas facilitaron la comprensi=C3=B3n de los con= ceptos abordados. Este dato evidencia que el uso de representaciones visual= es y manipulativas permiti=C3=B3 superar barreras asociadas al aprendizaje = abstracto, especialmente en temas como la suma y resta de expresiones algeb= raicas, productos notables y factorizaci=C3=B3n.El uso de Polypad permiti=C3=B3 a l= os estudiantes observar relaciones matem=C3=A1ticas de manera simult=C3=A1n= ea desde diferentes perspectivas: simb=C3=B3lica, gr=C3=A1fica y espacial. = Este enfoque favorece a la construcci=C3=B3n de significados y fortalece la= comprensi=C3=B3n profunda, afirmando que el aprendizaje matem=C3=A1tico se= consolida cuando los estudiantes pueden transitar entre diferentes formas = de representaci=C3=B3n.Adem=C3=A1s, los estudiantes demostraron mayor capacidad par= a explicar sus procedimientos, justificar resultados y corregir errores de = forma aut=C3=B3noma, lo que evidencia un avance hacia niveles superiores de= pensamiento matem=C3=A1tico.Tabla 3<p= style=3D"margin-bottom:0pt; text-align:center; line-height:115%; font-size= :12pt">Uso= frecuente de tecnolog=C3=ADa en las clases de matem=C3=A1ticas<= table style=3D"margin-right:auto; margin-left:auto; margin-bottom:0pt; padd= ing:0pt; border-collapse:collapse"><tr><td style=3D"width:142.65pt; border-= top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5= .4pt; vertical-align:top">Nivel de acuerdo</td><td style=3D"width:147.6pt; border-top= :0.75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4p= t; vertical-align:top">Frecuencia</td><td style=3D"width:88.45pt;= border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; paddi= ng:0pt 5.4pt; vertical-align:top">Porcentaje (%)</td></tr><tr><td= style=3D"width:142.65pt; border-top:0.75pt solid #000000; padding:0pt 5.4p= t; vertical-align:top">Muy de acuerdo</td><td style=3D"width:147.6pt; border-top:0.= 75pt solid #000000; padding:0pt 5.4pt; vertical-align:top">37</td><td style=3D"widt= h:88.45pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-ali= gn:top">55 %= </td></tr><tr><td style=3D"width:142.65pt; padding:0pt 5.4pt; vertical-= align:top">De acuer= do</td><td style=3D"width:147.6pt; padding:0pt 5.4pt; vertical-a= lign:top">25= </td><td style=3D"width:88.45pt; padding:0pt 5.4pt; vertical-align:top"= >37 %</t= d></tr><tr><td style=3D"width:142.65pt; padding:0pt 5.4pt; vertical-align:t= op">En desacuerdo</= span></td><td style=3D"width:147.6pt; padding:0pt 5.4pt; vertical-align= :top">4<= /td><td style=3D"width:88.45pt; padding:0pt 5.4pt; vertical-align:top">6 %</td></tr= ><tr><td style=3D"width:142.65pt; padding:0pt 5.4pt; vertical-align:top"><p= style=3D"margin-bottom:0pt; line-height:115%; font-size:10pt">Muy en desacuerdo</td><td sty= le=3D"width:147.6pt; padding:0pt 5.4pt; vertical-align:top"><span= style=3D"font-family:'Times New Roman'">2</td><td style=3D"widt= h:88.45pt; padding:0pt 5.4pt; vertical-align:top">2 %</td></tr><tr><td style=3D"wid= th:142.65pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertica= l-align:top">Total</td><td style=3D"width:147.6pt; border-bottom:= 0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"><spa= n style=3D"font-family:'Times New Roman'; font-weight:bold">68</= td><td style=3D"width:88.45pt; border-bottom:0.75pt solid #000000; padding:= 0pt 5.4pt; vertical-align:top">100 %</td></tr></table><= span style=3D"font-family:'Times New Roman'"> <sp= an style=3D"font-family:'Times New Roman'">El 92% de los estudiantes manife= st=C3=B3 a favor con que la tecnolog=C3=ADa deber=C3=ADa emplearse con mayo= r frecuencia en las clases de matem=C3=A1ticas. Este resultado refleja una = aceptaci=C3=B3n generalizada de los entornos digitales como aliados del apr= endizaje, y sugiere que los estudiantes perciben estas herramientas como re= cursos leg=C3=ADtimos y efectivos para comprender contenidos complejos.</sp= an>La aceptaci= =C3=B3n positiva de la tecnolog=C3=ADa se asocia con la posibilidad de apre= nder a un ritmo propio, recibir retroalimentaci=C3=B3n inmediata y experime= ntar diferentes formas de resoluci=C3=B3n sin la presi=C3=B3n del error. Es= tas caracter=C3=ADsticas fortalecen la autonom=C3=ADa del estudiante y favo= recen la autorregulaci=C3=B3n del aprendizaje.Tab= la 4Trabajo colaborativo mediante herramientas tecnol=C3=B3gicas<= /span><table style=3D"margin-right:auto; margin-left:auto; margin-botto= m:0pt; padding:0pt; border-collapse:collapse"><tr><td style=3D"width:167.8p= t; border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; pad= ding:0pt 5.4pt; vertical-align:top">Niv= el de acuerdo</td><td style=3D"width:113.9pt; border-top:0.75pt = solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; verti= cal-align:top">Frec= uencia</td><td style=3D"width:74.25pt; border-top:0.75pt solid #= 000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-ali= gn:top">Porcentaje = (%)</td></tr><tr><td style=3D"width:167.8pt; border-top:0.75pt s= olid #000000; padding:0pt 5.4pt; vertical-align:top">Muy de acuerdo</td><td style= =3D"width:113.9pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt; vert= ical-align:top">39<= /span></td><td style=3D"width:74.25pt; border-top:0.75pt solid #000000;= padding:0pt 5.4pt; vertical-align:top">57 %</td></tr><tr><td style=3D"width:167.8p= t; padding:0pt 5.4pt; vertical-align:top">De acuerdo</td><td style=3D"width:113.9pt= ; padding:0pt 5.4pt; vertical-align:top">23</td><td style=3D"width:74.25pt; padding= :0pt 5.4pt; vertical-align:top">34 %</td></tr><tr><td style=3D"width:167.8pt; paddi= ng:0pt 5.4pt; vertical-align:top">En desacuerdo</td><td style=3D"width:113.9pt; pad= ding:0pt 5.4pt; vertical-align:top">5</td><td style=3D"width:74.25pt; padding:0pt 5= .4pt; vertical-align:top">7 %</td></tr><tr><td style=3D"width:167.8pt; padding:0pt = 5.4pt; vertical-align:top">Muy en desac= uerdo</td><td style=3D"width:113.9pt; padding:0pt 5.4pt; vertica= l-align:top">1</spa= n></td><td style=3D"width:74.25pt; padding:0pt 5.4pt; vertical-align:to= p">2 %</= td></tr><tr><td style=3D"width:167.8pt; border-bottom:0.75pt solid #000000;= padding:0pt 5.4pt; vertical-align:top">Total</td><td style=3D"width:113.9pt; borde= r-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top">68</td><td st= yle=3D"width:74.25pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt= ; vertical-align:top">100 %</td></tr></table> En cuanto al trabajo colaborativo, el 91% de los estudiante= s afirm=C3=B3 que el uso de herramientas digitales favorece el trabajo en e= quipo y el intercambio de ideas. Durante las sesiones, se observ=C3=B3 que = los estudiantes discut=C3=ADan estrategias, comparaban resultados y justifi= caban procedimientos, lo que promovi=C3=B3 un aprendizaje socialmente const= ruido.El= entorno digital facilit=C3=B3 la comunicaci=C3=B3n entre pares y permiti= =C3=B3 que los estudiantes aprendieran unos de otros, fortaleciendo habilid= ades sociales, argumentativas y comunicativas. Este resultado se alinea con= los principios del aprendizaje socio-constructivista, donde el conocimient= o se construye mediante la interacci=C3=B3n y el di=C3=A1logo guiado.</span= >Tabla 5Acceso a dispositivos tecnol=C3=B3gico= s en el hogar<table style=3D"margin-right:auto; margin-left:auto= ; margin-bottom:0pt; padding:0pt; border-collapse:collapse"><tr><td style= =3D"width:116.75pt; border-top:0.75pt solid #000000; border-bottom:0.75pt s= olid #000000; padding:0pt 5.4pt; vertical-align:top">Respuesta</td><td style=3D"width:116.75pt; border-= top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5= .4pt; vertical-align:top">Frecuencia</td><td style=3D"width:116.75pt; border-top:0.= 75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; = vertical-align:top">Porcentaje (%)</td></tr><tr><td style=3D"width:116.75pt; border= -top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top">S=C3=AD</td><td = style=3D"width:116.75pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt= ; vertical-align:top">47</td><td style=3D"width:116.75pt; border-top:0.75pt solid #= 000000; padding:0pt 5.4pt; vertical-align:top">69 %</td></tr><tr><td style=3D"width= :116.75pt; padding:0pt 5.4pt; vertical-align:top">No</td><td style=3D"width:116.75p= t; padding:0pt 5.4pt; vertical-align:top">21</td><td style=3D"width:116.75pt; paddi= ng:0pt 5.4pt; vertical-align:top">31 %</td></tr><tr><td style=3D"width:116.75pt; bo= rder-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"><p= style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-siz= e:10pt">Total</td>= <td style=3D"width:116.75pt; border-bottom:0.75pt solid #000000; padding:0p= t 5.4pt; vertical-align:top">68</td><td style=3D"width:116.75pt; border-bottom:0.75= pt solid #000000; padding:0pt 5.4pt; vertical-align:top">100 %</td></tr></table> Finalmente, el 69% de lo= s estudiantes report=C3=B3 contar con acceso a dispositivos tecnol=C3=B3gic= os en el hogar, mientras que el 31% indic=C3=B3 no disponer de ellos. Este = resultado evidencia que, aunque el acceso ha mejorado, a=C3=BAn persisten b= rechas digitales que influyen en las oportunidades de aprendizaje.</= p>No obstante, la i= mplementaci=C3=B3n de Polypad demostr=C3=B3 que, incluso en situaciones con= limitaciones tecnol=C3=B3gicas, es posible generar experiencias educativas= significativas si se cuenta con planificaci=C3=B3n pedag=C3=B3gica adecuad= a y uso estrat=C3=A9gico del tiempo y los recursos disponibles. Esto refuer= za la necesidad de pol=C3=ADticas educativas orientadas a garantizar condic= iones de equidad tecnol=C3=B3gica, especialmente en espacios rurales.</span= >3.3.<sp= an style=3D"font-family:'Times New Roman'; font-weight:bold"> An=C3=A1lisis in= tegral de los resultadosLos resultados obtenidos confirman que la implementaci=C3= =B3n de Polypad favorece significativamente el aprendizaje activo, la compr= ensi=C3=B3n conceptual y la motivaci=C3=B3n estudiantil. La mejora en el re= ndimiento acad=C3=A9mico no se limita a la memorizaci=C3=B3n de procedimien= tos, sino que se refleja en la capacidad de los estudiantes para razonar, e= xplicar y transferir conocimientos a nuevas situaciones.El uso de representaciones = visuales permiti=C3=B3 que los estudiantes comprendieran relaciones algebra= icas complejas mediante procesos intuitivos, reduciendo la ansiedad matem= =C3=A1tica y fortaleciendo la autoconfianza. Asimismo, la interacci=C3=B3n = constante con los recursos digitales promovi=C3=B3 un ambiente de aprendiza= je colaborativo, donde el error fue asumido como parte del proceso formativ= o.Estos = resultados confirman que la tecnolog=C3=ADa, cuando es utilizada de manera = planificada y con intencionalidad pedag=C3=B3gica, se convierte en un recur= so poderoso para mejorar la calidad educativa, especialmente en situaciones= donde se cuente con limitaciones estructurales.4. = 0; D= iscusi=C3=B3nLos resultados obtenidos en esta investigaci=C3=B3n confirman que la i= ntegraci=C3=B3n de herramientas digitales, espec=C3=ADficamente Polypad, co= nstituye una estrategia pedag=C3=B3gica efectiva para fortalecer el aprendi= zaje activo en matem=C3=A1ticas dentro de la Educaci=C3=B3n General B=C3=A1= sica. La mejora observada en el rendimiento acad=C3=A9mico, la motivaci=C3= =B3n estudiantil y la comprensi=C3=B3n conceptual coincide con los hallazgo= s reportados por diversas investigaciones recientes.<s= pan style=3D"font-family:'Times New Roman'">Uno de los principales aportes = de este estudio radica en evidenciar c=C3=B3mo el uso de representaciones v= isuales y manipulativas facilita la transici=C3=B3n desde un pensamiento ar= itm=C3=A9tico hacia un pensamiento algebraico m=C3=A1s estructurado. A dife= rencia de los enfoques tradicionales, que se centran en la memorizaci=C3=B3= n de procedimientos, la intervenci=C3=B3n realizada permiti=C3=B3 que los e= studiantes comprendieran el significado subyacente de las operaciones algeb= raicas, favoreciendo la construcci=C3=B3n de aprendizajes duraderos.= Asimismo, los r= esultados confirman que el aprendizaje activo no solo mejora el desempe=C3= =B1o acad=C3=A9mico, sino que tambi=C3=A9n impacta positivamente en factore= s emocionales como la motivaci=C3=B3n, la confianza y la reducci=C3=B3n de = la ansiedad matem=C3=A1tica. Los entornos digitales interactivos reducen el= miedo al error y promueven una actitud positiva hacia el aprendizaje, lo c= ual se evidenci=C3=B3 claramente durante las sesiones desarrolladas.= Otro aspecto re= levante es el papel del docente como mediador del aprendizaje. Los resultad= os indican que la tecnolog=C3=ADa no reemplaza la labor pedag=C3=B3gica, si= no que la potencia cuando se utiliza con intencionalidad did=C3=A1ctica. La= planificaci=C3=B3n de actividades, la formulaci=C3=B3n de preguntas orient= adoras y la retroalimentaci=C3=B3n constante fueron factores clave para que= los estudiantes aprovecharan al m=C3=A1ximo el entorno digital.= Esta investigaci=C3= =B3n aporta evidencia relevante para el sistema educativo ecuatoriano, espe= cialmente en zonas rurales donde existen limitaciones de infraestructura. L= os resultados demuestran que, aun en escenarios con recursos limitados, es = posible generar experiencias de aprendizaje significativas mediante el uso = estrat=C3=A9gico de herramientas digitales accesibles, como Polypad. Esto c= oincide con lo planteado por (Albuja et al. 2023) respecto a la necesidad d= e reducir las brechas educativas mediante propuestas pedag=C3=B3gicas innov= adoras.A= simismo, los hallazgos refuerzan la importancia de promover el pensamiento = matem=C3=A1tico temprano, tal como lo plantean Candela-Mu=C3=B1oz & Rod= r=C3=ADguez-G=C3=A1mez (2023) y Jimpikit et al. (2024) quienes destacan que= el desarrollo temprano de habilidades algebraicas facilita la transici=C3= =B3n hacia contenidos m=C3=A1s complejos en niveles superiores.<= p style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-si= ze:12pt">Finalmente, los resu= ltados de esta investigaci=C3=B3n confirman que la integraci=C3=B3n de tecn= olog=C3=ADas educativas no debe entenderse como una moda pedag=C3=B3gica, s= ino como una estrategia fundamentada en evidencia cient=C3=ADfica que contr= ibuye al fortalecimiento de competencias matem=C3=A1ticas, cognitivas y soc= ioemocionales. La implementaci=C3=B3n de Polypad no solo mejora el rendimie= nto acad=C3=A9mico, sino que transforma la experiencia de aprendizaje, haci= =C3=A9ndola m=C3=A1s significativa, inclusiva y sostenible en el tiempo.</s= pan>5.<span= style=3D"width:9pt; font:7pt 'Times New Roman'; display:inline-block"> = 0; ConclusionesEl uso de Polypad como herramienta did=C3=A1ctic= a contribuye de manera significativa al fortalecimiento del aprendizaje act= ivo en matem=C3=A1ticas, especialmente en la comprensi=C3=B3n de operacione= s algebraicas.La implementaci=C3=B3n de estrategias basadas en herramientas digital= es permiti=C3=B3 mejorar el rendimiento acad=C3=A9mico, la motivaci=C3=B3n = y la participaci=C3=B3n estudiantil, evidenciando un impacto positivo tanto= cognitivo como emocional.El uso de representaciones visuales favoreci=C3=B3 la com= prensi=C3=B3n de conceptos abstractos como productos notables, t=C3=A9rmino= s semejantes y propiedades algebraicas, reduciendo errores frecuentes y for= taleciendo el razonamiento matem=C3=A1tico.La mediaci=C3=B3n docente desempe=C3=B1= =C3=B3 un rol fundamental en el =C3=A9xito de la intervenci=C3=B3n, confirm= ando que la tecnolog=C3=ADa debe ser utilizada como un medio pedag=C3=B3gic= o y no como un fin en s=C3=AD mismo.A pesar de las limitaciones de infraestructura,= el uso estrat=C3=A9gico de herramientas digitales demostr=C3=B3 ser viable= y eficaz en zonas educativas rurales.&= #xa0;6.</= span> Conflicto de InteresesLos autores declaran que no= existe conflicto de intereses en relaci=C3=B3n con el art=C3=ADculo presen= tado.= 7. Derechos de autor (copyri= gth) Los autores son los titulares de los derechos = de autor (patrimoniales y/= o de explotaci=C3=B3n) de los contenidos de la revista (copyright<span= style=3D"font-family:'Times New Roman'">).8. &#= xa0; Declaraci=C3=B3n de contribuci=C3=B3n de los autores</p= >Los autores declar= an haber participado de manera equitativa y sustancial en la realizaci=C3= =B3n de esta investigaci=C3=B3n, bajo las responsabilidades seg=C3=BAn la <= /span><a href=3D"https://credit.niso.org/" style=3D"text-decoration:none"><= span class=3D"Hyperlink" style=3D"font-family:'Times New Roman'">Taxonom=C3= =ADa CRediT</a> para d= escribir las contribuciones individuales de cada autor al trabajo. <= /p>Enrique Marcelo = Bustamante Salda=C3=B1a realiz=C3=B3 la conceptualizaci=C3=B3n de la invest= igaci=C3=B3n, organizaci=C3=B3n y ejecuci=C3=B3n del ensayo, recopilaci=C3= =B3n y curaci=C3=B3n de los datos, revisi=C3=B3n del an=C3=A1lisis estad=C3= =ADstico, interpretaci=C3=B3n de los resultados, elaboraci=C3=B3n del borra= dor original, preparaci=C3=B3n de tablas y figuras, revisi=C3=B3n cr=C3=ADt= ica del contenido y aprobaci=C3=B3n de la versi=C3=B3n final del manuscrito= .Divulgaci=C3=B3n de la delegaci=C3=B3n a la IA generativa</span= >Los autores de= claran que no se emplearon herramientas de apoyo para la elaboraci=C3=B3n d= e la presente investigaci=C3=B3n.Declaraci=C3=B3n presentada por: Enrique Marcelo Bustamante Salda=C3= =B1a. 9. 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ht=3D"79" alt=3D"" style=3D"margin-top:-17.45pt; margin-left:239.7pt; posit= ion:absolute" /> </div> La tecnolog=C3=ADa en el aprendizaje a= ctivo de la matem=C3=A1tica en la educaci=C3=B3n general b=C3=A1sica en Ecu= ador = Technology in active learning of mathematics in basic general edu= cation in Ecuador <table style=3D"width:396.3pt; margin-bottom:= 0pt; padding:0pt; border-collapse:collapse"><tr><td style=3D"width:3.25pt; = border:0.75pt solid #000000; padding:0pt 5.03pt; vertical-align:top">1</td><td styl= e=3D"width:171.95pt; border:0.75pt solid #000000; padding:0pt 5.03pt; verti= cal-align:top">Enrique Marcelo Bustamante Salda=C3=B1a<= /span></td><td style=3D"width:10.5pt; border:0.75pt solid #000000; padd= ing:0pt 5.03pt; vertical-align:top"><img src=3D"data= :image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAYAAACNiR0NAAAABHNCSVQIC= AgIfAhkiAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAA2pJREFUOI2tlEtoXVUUhr+197n3nNzbJN6o= 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Pedag=C3=B3gicas Enrique Jos=C3=A9 Varona (UCPEJV), La Ha= bana, Cuba, Maestr=C3=ADa en docencia Matem=C3=A1tica<a href=3D"mailto:rectoria@ucpejv.edu.cu" style=3D"te= xt-decoration:none">rectoria@ucpejv.edu.cu= </a><a href=3D"mailto:marcelo.bustaman= tes@docentes.educacion.edu.ec" style=3D"text-decoration:none">marcelo.bustamantes@docentes.educacion.edu.ec</a>= <a href=3D"mailto:kike018bs@gmail.com" sty= le=3D"text-decoration:none">kike018bs@gmail.com</= span></a></td></tr><tr><td style=3D"width:3.25pt; border:0.75pt solid #= 000000; padding:0pt 5.03pt; vertical-align:top"> </td><td style=3D"width:171.95= pt; border:0.75pt solid #000000; padding:0pt 5.03pt; vertical-align:top"><p= style=3D"margin-left:7.1pt; margin-bottom:0pt; text-indent:-7.1pt; text-al= ign:justify; line-height:115%; font-size:10pt"> </td><td style=3D"width:10.5pt; border:0= .75pt solid #000000; padding:0pt 5.03pt; vertical-align:top"><span= style=3D"font-family:'Times New Roman'"> </td><td style=3D= "width:166.35pt; 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#000000; padding:0pt 5.03pt; vertical-align:top"> </td></tr><tr style=3D"height:0pt"><td sty= le=3D"width:14.05pt"></td><td style=3D"width:182.75pt"></td><td style=3D"wi= dth:21.3pt"></td><td style=3D"width:177.15pt"></td><td style=3D"width:0.3pt= "></td></tr></table> <table style=3D"width:436.35pt; margin-left:0.25pt;= margin-bottom:0pt; padding:0pt; border-collapse:collapse"><tr><td colspan= =3D"3" style=3D"width:156.4pt; padding:0pt 5.4pt; vertical-align:top"><a id=3D"_Hlk92186133"> </a>= </td= ><td colspan=3D"2" style=3D"width:258.35pt; border-top:0.75pt solid #000000= ; padding:0pt 5.4pt; vertical-align:top">Art=C3=ADculo de Investigaci=C3=B3n C= ient=C3=ADfica y Tecnol=C3=B3gicaEnviado: Revisado: Aceptado: Publicado:DOI:= </td></tr><tr style=3D"height:6.55pt"><td col= span=3D"3" style=3D"width:156.4pt; padding:0pt 5.4pt; vertical-align:top"><= p style=3D"margin-bottom:0pt; text-align:right; line-height:115%; font-size= :6pt"> </td><td colspan=3D"2" style=3D"width:258.35pt;= 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TybjbC0ph8u4v1sIveN/X4fJg4d/hVuWuRkzZgybN2/+zUZbtVqNwceARqNBpVLhdEpYzGbqTSY= aTKY/1KTr5+fH4MGDMRgM1NbWkpGRgdPppG/fvjdV6G1EqVTStWtXKisr0ev1tGnThrS0NJKSkg= gPD2f//v1kZmbeVNlVq9Vyxx13EBERQUFBAUqlkqKiImpraxkwYAArV668LjCSy+XMmzfvTyvpe= vDgwYMHDx7+NW5JcGM0GnnyySevrpa6yYb+xAqjP0vjvL9eYv7r7f/yf3/98++N5xfHcKPjuNlY= hULBm2++ycSJE3/nKDx48ODBgwcPt4JbEtw4nU7Ky8uxWCw339BfGNzcKv6KfZTJZAQEBKDT6dw= NnB48ePDgwYOHv45bEtx48ODBgwcPHjz8p+BJJXjw4MGDBw8e/qvwBDcePHjw4MGDh/8q/tRS8J= ycHLcLtwcPHjx48ODBw/8LNBoNLVu2vOn7fyq4+e67726owuvBgwcPHjx48PB3ER4ezpQpU276v= qeh2IMHDx48ePDwX4Wn58aDBw8ePHjw8F+FJ7jx4MGDBw8ePPxX4QluPHjw4MGDBw//VfxfkrKy= 3GCTp2MAAAAASUVORK5CYII=3D" width=3D"567" height=3D"140" alt=3D"" /> <table style=3D"width:436.35pt; margin-l= eft:0.25pt; margin-bottom:0pt; padding:0pt; border-collapse:collapse"><tr><= td style=3D"width:74.75pt; border-bottom:0.75pt solid #000000; padding:0pt = 5.4pt; vertical-align:top">Palabras claves: Aprendi= zaje activo, Herramientas digitales, Polypad, Tecnolog=C3=ADa educativa. </= span></td><td style=3D"width:4.3pt; border-bottom:0.75pt solid #000000;= padding:0pt 5.4pt; vertical-align:top"> </td>= <td style=3D"width:324.9pt; border-bottom:0.75pt solid #000000; padding:0pt= 5.4pt; vertical-align:top">Resumen: Introducci=C3=B3n<span= style=3D"font-family:'Times New Roman'">. La ense=C3=B1anza de matem=C3=A1= ticas en la educaci=C3=B3n general b=C3=A1sica en el Ecuador enfrenta difer= entes dificultades ligadas a la comprensi=C3=B3n de s=C3=ADmbolos, a los co= nceptos no concretos, la baja motivaci=C3=B3n estudiantil y el predominio d= e metodolog=C3=ADas centradas en la memorizaci=C3=B3n. Las herramientas dig= itales, como Polypad (desarrollada originalmente en Mathigon y actualmente = siendo parte de Amplify), han ido emergiendo como herramientas para incenti= var y promover en la observaci=C3=B3n, exploraci=C3=B3n y aprendizaje activ= o. O= bjetivo. E= valuar el impacto did=C3=A1ctico del uso de Polypad en el aprendizaje de op= eraciones matem=C3=A1ticas con expresiones algebraicas en los estudiantes d= e octavo a=C3=B1o de una unidad educativa de Cuenca, Ecuador. Metodolog=C3=ADa<= /span>. Se aplic=C3=B3 un dis= e=C3=B1o cuasi-experimental con un enfoque mixto (pre-test/intervenci=C3=B3= n/pos-test), que a su vez fue complementado con el desarrollo de una encues= ta, observaci=C3=B3n estructurada y entrevistas a los docentes. En el proce= dimiento participaron 68 estudiantes de dos paralelos (Paralelo A =3D 35 es= tudiantes; Paralelo B =3D 33 estudiantes). La intervenci=C3=B3n consisti=C3= =B3 en el desarrollo de cinco sesiones con actividades de herramientas digi= tales (Uso de Polypad para la ense=C3=B1anza de expresiones algebraicas). <= /span>Resul= tados. Las mejoras en = el rendimiento fueron significativamente positivas, un ejemplo de esto se l= o da en el paralelo A, que pas=C3=B3 de tener un promedio de 5.83/10 a 8.45= /10, que representa un aumento de 2.62 puntos, mientras que el paralelo B p= as=C3=B3 de tener un promedio de 5.10/10 a 6.24/10, demostrando un aumento = de 1.14 puntos. Para ambos paralelos se observaron incrementos en la compre= nsi=C3=B3n de los ejercicios con expresiones algebraicas. Adem=C3=A1s, los = estudiantes expresaron una alta motivaci=C3=B3n y preferencia por estas act= ividades colaborativas con tecnolog=C3=ADa, tambi=C3=A9n los docentes se=C3= =B1alaron ventajas en la utilizaci=C3=B3n de estas herramientas digitales. = Conc= lusi=C3=B3n. El uso de= Polypad favoreci=C3=B3 el aprendizaje activo, mejora el rendimiento y fort= alece la comprensi=C3=B3n en el estudiante. Pero su integraci=C3=B3n requie= re capacitaci=C3=B3n docente, infraestructura adecuada y pol=C3=ADticas edu= cativas que faciliten su accesibilidad. =C3=81rea de estudio general: Educa= ci=C3=B3n. =C3=81rea de estudio espec=C3=ADfica: Did=C3=A1ctica de la Matem=C3=A1tica. Tipo de estudio: Art=C3=ADculos originales.</p= > <= /td></tr><tr><td style=3D"width:74.75pt; border-top:0.75pt solid #000000; b= order-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"><= p class=3D"Title" style=3D"margin-top:6pt; text-align:justify; line-height:= 115%; font-size:12pt">Keywords: <= /span>Active learning, Digital tools, Polypad, Educational technology.</p= > </td><td style=3D"width:4.3pt; border-top:0.7= 5pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; v= ertical-align:top"> </td><td style=3D"width:324= .9pt; border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; = padding:0pt 5.4pt; vertical-align:top">Abstract: Introduction.</sp= an> Mathematics teaching in b= asic general education in Ecuador faces various challenges related to under= standing symbols, abstract concepts, low student motivation, and the predom= inance of memorization-based methodologies. Digital tools, such as Polypad = (originally developed by Mathigon and currently part of Amplify), have emer= ged as tools to encourage and promote observation, exploration, and active = learning. Objective. To ev= aluate the educational impact of using Polypad in learning mathematical ope= rations with algebraic expressions in eighth-grade students at a school in = Cuenca, Ecuador. Methodology. A quasi-experimental design with a mixed approach (pre-test/interventio= n/post-test) was applied, which was complemented by a survey, structured ob= servation, and interviews with teachers. Sixty-eight students from two para= llel classes participated in the procedure (Parallel A =3D 35 students; Par= allel B =3D 33 students). The intervention consisted of five sessions with digital to= ol activities (use of Polypad for teaching algebraic expressions). <= span style=3D"font-family:'Times New Roman'; font-weight:bold">Results.</sp= an> The improvements in perfo= rmance were significantly positive. An example of this is given in parallel= A, which went from an average of 5.83/10 to 8.45/10, representing an incre= ase of 2.62 points, while parallel B went from an average of 5.10/10 to 6.2= 4/10, demonstrating an increase of 1.14 points. For both parallels, increas= es in the understanding of exercises with algebraic expressions were observ= ed. In addition, students expressed high motivation and preference for thes= e collaborative activities with technology, and teachers also pointed out a= dvantages in the use of these digital tools. Conclusion. The use of Polypad promoted active learning,= improved performance, and strengthened student comprehension. However, its= integration requires teacher training, adequate infrastructure, and educat= ional policies that facilitate its accessibility. General area of study:= Education. Specific area of stud= y: Mathematics teachin= g. T= ype of study: Original= articles. </td></tr></table> <div style=3D"clear:both"><img src=3D"da= ta:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAuQAAAABCAYAAACWsrt9AAAABHNCSVQ= ICAgIfAhkiAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABxJREFUSIntwTEBAAAIwKDZP7TG8AGm2g= AAgA9zmTsBAl+AgmQAAAAASUVORK5CYII=3D" width=3D"740" height=3D"1" alt=3D"" s= tyle=3D"margin-top:-37.82pt; margin-left:-63.3pt; position:absolute" /></sp= an> = 0; = Nombre<span= style=3D"width:141.26pt; letter-spacing:3pt; display:inline-block"> <= /span> 1 </div></div> <div class=3D"Section_2">1. <span= style=3D"font-family:'Times New Roman'; font-weight:bold">Introducci=C3=B3= n</div> = <div class=3D"Section_3"><div style=3D"clear:both"><img src=3D"data:image/jpeg;base= 64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAUDBAQEAwUEBAQFBQUGBwwIBwcHBw8LCwkMEQ8S= EhEPERETFhwXExQaFRERGCEYGh0dHx8fExciJCIeJBweHx7/2wBDAQUFBQcGBw4ICA4eFBEUHh4= eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh4eHh7/wAARCARfAz= 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lKW6F9dp4f9V3eFcQPKQqP21WhubV6aBkbM/zWiUFGme5GmwxP7V1fSoeywGaIk0GLOhRkrOPsx= LtpdHn99I6nuLzkGexooxxgwJ1kgxZiAWxt6C0CX9dgC+bI0UY8wWhy6LY6yRYowxxhhjjDHGGG= OMMcYYY4wxxhhjjDHGGGOMMcYYY4wxxhhjjDHGGGOMMcYYY4wxxhhjtlj+Bzko+j36iSy0AAAAA= ElFTkSuQmCC" width=3D"322" height=3D"79" alt=3D"" style=3D"margin-top:-17.4= 5pt; margin-left:239.7pt; position:absolute" /> </div><= p style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-si= ze:12pt">La ense=C3=B1anza de= las matem=C3=A1ticas en la Educaci=C3=B3n General B=C3=A1sica (EGB</s= pan>) enfrenta retos constant= es, los cuales est=C3=A1n asociados con la comprensi=C3=B3n de s=C3=ADmbolo= s y conceptos no concretos, la comprensi=C3=B3n insuficiente de conceptos a= lgebraicos y el predominio en las metodolog=C3=ADas tradicionales centradas= en la repetici=C3=B3n de procedimientos o de memorizaci=C3=B3n ( (=C3=81lv= arez, M., Almeida, B., & Villegas, E., 2014) =C3=81lvarez et al., 2014;= Rodr=C3=ADguez & Reye, 2022). Lo que se=C3=B1ala recientemente que los= estudiantes de EGB presentan dificultades para conectar las representacion= es visuales, concretas y simb=C3=B3licas, causando una repercusi=C3=B3n en = aprendizajes fragmentados y en errores sistem=C3=A1ticos al realizar operac= iones con expresiones algebraicas (Candela-Mu=C3=B1oz & Rodr=C3=ADguez-= G=C3=A1mez, 2023). En Ecuador, el sistema educativo presenta varios desaf=C3=ADos, = que est=C3=A1n vinculados con la brecha digital, la disponibilidad limitada= de recursos tecnol=C3=B3gicos y la insuficiente formaci=C3=B3n docente en = tecnolog=C3=ADa educativa (Albuja et al., 2023; Ministerio de Educaci=C3=B3= n del Ecuador, 2021). Este panorama requiere de un dise=C3=B1o e implementa= ci=C3=B3n de estrategias pedag=C3=B3gicas que integren recursos digitales a= ccesibles, pertinentes y que sean capaces de transformar el proceso de ense= =C3=B1anza-aprendizaje de las matem=C3=A1ticas (Basdogan & Bonk, 2023).= Bajo este sentido, las herramientas digitales se han convertido en un sopo= rte did=C3=A1ctico muy importante para incentivar experiencias din=C3=A1mic= as que fomenten el aprendizaje activo (Gusho et al., 2023; Jimpikit et al.,= 2024).B= ajo este contexto, se utilizar=C3=A1 el programa de Polypad, que es una pla= taforma creada originalmente en Mathigon y que actualmente est=C3=A1 dispon= ible en Amplify, la cual ofrece un entorno digital que incluye bloques alge= braicos, balanzas virtuales, rect=C3=A1ngulos geom=C3=A9tricos, l=C3=ADneas= num=C3=A9ricas y m=C3=BAltiples herramientas interactivas para representar= conceptos matem=C3=A1ticos de forma visual y manipulable (Imron et al., 20= 25). Su dise=C3=B1o permite que los estudiantes interact=C3=BAen entre lo c= oncreto y lo abstracto, el cual es un aspecto fundamental para el desarroll= o y dominio de los temas (Delport, 2021).En los =C3=BAltimos a=C3=B1os, la eviden= cia cient=C3=ADfica reciente reporta que las herramientas digitales increme= ntan la motivaci=C3=B3n estudiantil, mejoran la visualizaci=C3=B3n de estru= cturas matem=C3=A1ticas, fortalecen el razonamiento y permiten la construcc= i=C3=B3n colaborativa del conocimiento. Estudios como los de (Escueta et al= . 2017; S=C3=A1nchez & Rodr=C3=ADguez 2022; Gusho et al. 2023) muestran= mejoras significativas en el rendimiento cuando estas herramientas se inte= gran dentro de una secuencia did=C3=A1ctica estructurada y con un rol docen= te centrado en la mediaci=C3=B3n cognitiva (Enr=C3=ADquez Chasin, 2021).</s= pan>Pero para e= l sistema educativo ecuatoriano, las limitaciones en infraestructura y cone= ctividad requieren estrategias adaptativas que favorezcan el acceso equitat= ivo a la tecnolog=C3=ADa, especialmente en instituciones rurales (Albuja et= al., 2023; Anderson & Rivera, 2020). Con la siguiente investigaci=C3= =B3n, que est=C3=A1 fundamentada con datos provenientes del estudio aplicad= o en un aula de una escuela rural, se propone evaluar el impacto del uso de= Polypad en el aprendizaje de matem=C3=A1ticas en estudiantes de octavo a= =C3=B1o, analizando tanto los resultados cuantitativos, cualitativos, as=C3= =AD como las percepciones de estudiantes y docentes.<s= pan style=3D"font-family:'Times New Roman'">Adem=C3=A1s de los desaf=C3=ADo= s estructurales asociados a la ense=C3=B1anza de matem=C3=A1ticas, existen = factores psicol=C3=B3gicos que afectan el desempe=C3=B1o estudiantil. Estud= ios recientes identifican que m=C3=A1s del 60 % de estudiantes de EGB exper= imentan ansiedad matem=C3=A1tica, fen=C3=B3meno que reduce la participaci= =C3=B3n oral, deteriora la memoria de trabajo y dificulta la resoluci=C3=B3= n de problemas (Naranjo Sag=C3=B1ay et al., 2024). Las herramientas digital= es, al ofrecer entornos exploratorios donde el error no es penalizado, dism= inuyen este estr=C3=A9s y favorecen una actitud emocional m=C3=A1s positiva= hacia la asignatura (Delport, 2021). Asimismo, el curr=C3=ADculo ecuatoria= no de matem=C3=A1ticas establece que los estudiantes deben desarrollar habi= lidades de razonamiento, representaci=C3=B3n y modelizaci=C3=B3n; bajo esta= modalidad, plataformas como Polypad facilitan actividades de descubrimient= o y experimentaci=C3=B3n, integrando im=C3=A1genes visuales con s=C3=ADmbol= os matem=C3=A1ticos y fomentando el pensamiento algebraico (Guaypat=C3=ADn = et al., 2024).En este estudio se analiza c=C3=B3mo la intervenci=C3=B3n con Polypad= impacta en el aprendizaje activo de las operaciones algebraicas b=C3=A1sic= as, tomando consideraci=C3=B3n tanto del desempe=C3=B1o acad=C3=A9mico como= las percepciones estudiantiles y docentes. Este acercamiento permite valor= ar no solo los resultados inmediatos, sino tambi=C3=A9n los procesos cognit= ivos y emocionales que emergen durante la interacci=C3=B3n con las herramie= ntas digitales (Wijnia et al., 2024).En este sentido, comprender el impacto de una = herramienta digital como Polypad dentro del proceso de ense=C3=B1anza-apren= dizaje de las matem=C3=A1ticas requiere analizar los fundamentos pedag=C3= =B3gicos y tecnol=C3=B3gicos que sustentan su aplicaci=C3=B3n. La integraci= =C3=B3n de recursos digitales no depende =C3=BAnicamente de la disponibilid= ad de dispositivos o plataformas educativas, sino de la manera en que estos= son incorporados dentro de estrategias did=C3=A1cticas orientadas al desar= rollo del pensamiento matem=C3=A1tico, la participaci=C3=B3n activa y la co= nstrucci=C3=B3n significativa del conocimiento. Por ello, resulta necesario= abordar los principios relacionados con las herramientas digitales educati= vas, las metodolog=C3=ADas activas, las representaciones m=C3=BAltiples y l= os procesos de transici=C3=B3n entre los conceptos concretos, visuales y si= mb=C3=B3licos, elementos que permiten comprender c=C3=B3mo estas tecnolog= =C3=ADas pueden contribuir al aprendizaje del =C3=A1lgebra en estudiantes d= e Educaci=C3=B3n General B=C3=A1sica.1.1. Fundamentos de las herramientas digitales= Las herramienta= s digitales son representaciones virtuales e interactivas de objetos matem= =C3=A1ticos cl=C3=A1sicos como bloques algebraicos, regletas, balanzas, fic= has geom=C3=A9tricas y l=C3=ADneas num=C3=A9ricas (Delport, 2021). En estos= entornos digitales, los objetos se manipulan mediante gestos o controles e= n pantalla, lo que permite visualizar transformaciones de manera din=C3=A1m= ica, recibir una retroalimentaci=C3=B3n inmediata, descubrir diferentes for= mas de resolver un ejercicio en un tiempo m=C3=A1s corto, adem=C3=A1s de in= tegrar audio, color y movimiento para reforzar sus significados (Garc=C3=AD= a et al., 2023). Se destaca que este tipo de herramientas generan represent= aciones simult=C3=A1neas, las cuales facilitan la conexi=C3=B3n entre lo gr= =C3=A1fico, lo num=C3=A9rico y lo simb=C3=B3lico, aspecto esencial para el = desarrollo del pensamiento matem=C3=A1tico profundo (Bozkurt, 2020).= La efectividad = de las herramientas digitales est=C3=A1 ligada a tres componentes: la inter= actividad significativa, la cual se=C3=B1ala que no basta con mover element= os, sino que las acciones deben tener sentido pedag=C3=B3gico; la gu=C3=ADa= docente estrat=C3=A9gica, relacionada con la orientaci=C3=B3n pedag=C3=B3g= ica durante el uso de las herramientas; y las tareas bien dise=C3=B1adas, q= ue promueven el razonamiento, la argumentaci=C3=B3n y las conexiones entre = representaciones (L=C3=B3pez et al., 2022; Mumtaz, 2000).1.2. Comparaci=C3=B3n entre herra= mientas digitales y convencionalesLos estudios recientes han investigado las difere= ncias entre herramientas convencionales y digitales en el aprendizaje de la= s matem=C3=A1ticas, concluyendo que ambos tipos favorecen el rendimiento y = la comprensi=C3=B3n conceptual; sin embargo, las herramientas digitales pre= sentan ventajas log=C3=ADsticas como la accesibilidad y la posibilidad de t= rabajo remoto, mientras que las convencionales resultan =C3=BAtiles en etap= as iniciales donde se requiere manipulaci=C3=B3n f=C3=ADsica directa (Pinto= & Laite, 2020; Oliver & An, 2020). Asimismo, existen combinaciones= h=C3=ADbridas (digital + convencional) que generan efectos superiores a su= uso aislado (Wijnia et al., 2024).Se=C3=B1al=C3=B3 Delport (2021) en un estudio so= bre fracciones que las herramientas digitales favorecen especialmente la vi= sualizaci=C3=B3n de proporciones, la comparaci=C3=B3n de =C3=A1reas y la de= scomposici=C3=B3n de figuras, gracias a los movimientos din=C3=A1micos y la= manipulaci=C3=B3n r=C3=A1pida de elementos. En matem=C3=A1ticas, las inves= tigaciones publicadas han encontrado que las herramientas digitales aportan= ventajas como la comprensi=C3=B3n de la propiedad distributiva, la identif= icaci=C3=B3n de t=C3=A9rminos semejantes, la resoluci=C3=B3n de ecuaciones = mediante balanza algebraica y el descubrimiento de patrones en productos no= tables (Stein et al., 1996; Candela-Mu=C3=B1oz & Rodr=C3=ADguez-G=C3=A1= mez, 2023).= 1.3.= Polypad: plataforma y estudios recientesPolypad, perteneciente a Mathigon y desd= e 2022 integrada en Amplify, se ha convertido en una de las herramientas di= gitales m=C3=A1s utilizadas para la ense=C3=B1anza de matem=C3=A1ticas esco= lares (Imron et al., 2025). Sus principales recursos incluyen bloques algeb= raicos de color, rect=C3=A1ngulos din=C3=A1micos para visualizar multiplica= ciones y productos notables, balanza virtual para ecuaciones, l=C3=ADneas n= um=C3=A9ricas interactivas, mosaicos y herramientas de geometr=C3=ADa.</spa= n>Estudios reci= entes destacan su potencial pedag=C3=B3gico, as=C3=AD como lo menciona Delp= ort (2021) quien evidenci=C3=B3 mejoras en el razonamiento y habilidades ma= tem=C3=A1ticas mediante m=C3=B3dulos basados en Polypad. Por otro lado, Gus= ho et al. (2023) utilizaron Polypad junto con plataformas digitales colabor= ativas, evidenciando beneficios en comprensi=C3=B3n, motivaci=C3=B3n y part= icipaci=C3=B3n. Investigaciones desarrolladas en Europa documentan avances = en habilidades espaciales, razonamiento proporcional y uso de representacio= nes m=C3=BAltiples, demostrando que Polypad facilita el desarrollo del pens= amiento estructural, elemento clave para la comprensi=C3=B3n de expresiones= algebraicas, ecuaciones y factorizaci=C3=B3n (Casi & Sabena, 2024).</s= pan>1.4.= <sp= an style=3D"font-family:'Times New Roman'; font-style:italic">Evidencia del= uso de herramientas digitales en los pa=C3=ADses latinoamericanos</= p>La experiencia en= Ecuador sobre herramientas digitales todav=C3=ADa es incipiente; sin embar= go, trabajos recientes en Am=C3=A9rica Latina y regiones con brechas digita= les similares se=C3=B1alan un incremento en la motivaci=C3=B3n hacia las ma= tem=C3=A1ticas, reducci=C3=B3n de la ansiedad matem=C3=A1tica, mejoras sign= ificativas en estudiantes con bajo rendimiento inicial y mayor participaci= =C3=B3n colaborativa (Guaypat=C3=ADn et al., 2024; Naranjo Sag=C3=B1ay et a= l., 2024).El uso de tecnolog=C3=ADa educativa se muestra especialmente valioso en z= onas rurales donde los recursos f=C3=ADsicos son limitados. La disponibilid= ad de recursos virtuales abre las puertas al acceso de herramientas pedag= =C3=B3gicas avanzadas que tradicionalmente solo estaban disponibles en inst= ituciones con mayor infraestructura (Anderson & Rivera, 2020).</= p>1.5. Pensamiento matem= =C3=A1tico tempranoEntre 2020 y 2025, investigaciones destacan que el pensamiento m= atem=C3=A1tico debe iniciarse desde grados anteriores para evitar la transi= ci=C3=B3n abrupta entre la aritm=C3=A9tica y el =C3=A1lgebra (Candela-Mu=C3= =B1oz & Rodr=C3=ADguez-G=C3=A1mez, 2023; Jimpikit et al., 2024). La com= prensi=C3=B3n profunda del =C3=A1lgebra depende de la coordinaci=C3=B3n de = formas concretas, visuales y simb=C3=B3licas.Polypad permite el tr=C3=A1nsito fluid= o entre estas formas, fortaleciendo la comprensi=C3=B3n de estructuras alge= braicas como la propiedad distributiva, la combinaci=C3=B3n de t=C3=A9rmino= s semejantes, los productos notables y la relaci=C3=B3n entre =C3=A1rea y m= ultiplicaci=C3=B3n (Delport, 2021).1.6. Importancia de los productos notables en el aprend= izaje del =C3=A1lgebraLos productos notables representan una de las estructuras fun= damentales para el desarrollo matem=C3=A1tico avanzado (Stein et al., 1996)= . 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HBwW6ZhYiwe/duzJs3D6tWrfJwulKplK9ukpKS5GytUCgwb948dHZ24ubNm8jMzMTMmTOh1Wrh7= ++P9evXj+gNBcuy0Ol0WLRoEc6fP49r165h9erVWL58uVttiP5S6tNPP0VWVhZmz549YjYMxs/P= DzNnzkRlZSUCAwOxfv16REdH4+rVq3j88cexYMECqNXq+xbEer0earUaGo0GhYWF6OzsxKZNmxA= XF3fHg+3tvPvuu+/KzY7Dhw9TRkaGW2dGkiRyOp1ktVrJ5XKRJEnkcDiIZdkhu2WDsVgs1NPTc1= e5gbkcDgdZrVayWCzynLfT1dVFM2fOpNbW1jvq6+vro82bN1N+fr5bs2OgcTNwuS9JElmt1nvSk= RJFkex2OzmdTjKbzWS1Wr36jeM4OnnyJK1bt05u994rXC6XvF5JkojnebLZbKPS0RQEgex2Ozkc= DjKbzWSz2f52wwkY1Ha22WyUk5NDu3fvHrV3DIaDTqejtLQ0OnPmzJALFkWRGhsbae3atXTx4kW= Prt8/BZfLRVeuXKHU1FRqbW29axd0DHcAgBn4Z+AgV1hYiN9//x07duwYsXp3pLh06RKOHDmCLV= u2yPfWQyGKInQ6Hfbv34/p06ePeLnw3+J0OnH06FG0t7dj69atCA0NHbI8G8MThmEYOYgHEAQBg= iBArVb/4xzK8zwEQYCvr++wX9ImIrkDdj/rveEwYBsRwcfH5x9l2/8KzJjTxvh/4F/fevPGZrM0= 8wAAAABJRU5ErkJggg=3D=3D" width=3D"177" height=3D"21" alt=3D"" style=3D"ver= tical-align:middle" /> Polypad posibilita la visualizaci=C3=B3n de estas identidades mediante= =C3=A1reas compuestas, donde el cuadrado grande se descompone en subregion= es; las =C3=A1reas representan los t=C3=A9rminos algebraicos y los rect=C3= =A1ngulos muestran la duplicidad del t=C3=A9rmino 2ab. Esta visualizaci=C3= =B3n favorece el razonamiento estructural y reduce errores comunes en el us= o de f=C3=B3rmulas (Casi & Sabena, 2024).1.7. Brecha digital y equidad educativa en Ec= uadorLa = brecha digital se manifiesta en dos niveles: la brecha de acceso, relaciona= da con la disponibilidad de dispositivos y conectividad, y la brecha de uso= , relacionada con la competencia digital docente y estudiantil (Albuja et a= l., 2023).Datos recientes muestran que, aunque el acceso a dispositivos m=C3=B3vile= s es relativamente alto, su uso pedag=C3=B3gico sigue siendo limitado. La f= alta de formaci=C3=B3n docente contin=C3=BAa siendo uno de los mayores obst= =C3=A1culos para la integraci=C3=B3n tecnol=C3=B3gica significativa (Cantos= et al., 2025). En este contexto, Polypad presenta ventajas por su accesibi= lidad, su interfaz intuitiva y su capacidad para funcionar incluso con cone= ctividad limitada, siempre que las actividades sean planificadas pedag=C3= =B3gicamente (Anderson & Rivera, 2020).1.8. Fundamentos del aprendizaje activo<= /p>La presente inve= stigaci=C3=B3n se fundamenta en los aportes del socio-constructivismo, las = teor=C3=ADas del aprendizaje activo, el enfoque de representaciones m=C3=BA= ltiples en matem=C3=A1ticas y el pensamiento matem=C3=A1tico temprano (Enr= =C3=ADquez Chasin, 2021).1.8.1. &#= xa0; Socio-constructivismo y mediaci=C3=B3n tecnol=C3=B3gicaDe acuerdo con Vygotsky, e= l aprendizaje ocurre en interacci=C3=B3n con herramientas culturales y con = la mediaci=C3=B3n del docente. Las tecnolog=C3=ADas digitales, dentro de es= te enfoque, act=C3=BAan como herramientas culturales modernas que potencian= la construcci=C3=B3n del conocimiento mediante la interacci=C3=B3n din=C3= =A1mica, las representaciones visuales accesibles y la retroalimentaci=C3= =B3n inmediata (Roschelle et al., 2001).Las herramientas digitales como Polypad per= miten que el estudiante manipule objetos matem=C3=A1ticos en entornos explo= ratorios donde el error es parte natural del aprendizaje, favoreciendo la Z= ona de Desarrollo Pr=C3=B3ximo mediante la combinaci=C3=B3n de gu=C3=ADa do= cente y autonom=C3=ADa estudiantil (Gusho et al., 2023).1.8.2.</= span> Aprendizaje activo<s= pan style=3D"font-family:'Times New Roman'">El aprendizaje activo se caract= eriza por la participaci=C3=B3n cognitiva, social y motora del estudiante d= urante la construcci=C3=B3n del conocimiento. En matem=C3=A1ticas, implica = la argumentaci=C3=B3n, representaci=C3=B3n, manipulaci=C3=B3n y comparaci= =C3=B3n de procedimientos (Jimpikit et al., 2024). Polypad facilita estas p= r=C3=A1cticas al permitir la interacci=C3=B3n directa con representaciones = visuales de expresiones algebraicas, balanzas y mosaicos geom=C3=A9tricos, = convirti=C3=A9ndose en un entorno donde el estudiante experimenta, formula = hip=C3=B3tesis y valida resultados (Delport, 2021).1.8.3.<= span style=3D"width:9pt; font:7pt 'Times New Roman'; display:inline-block">= Representaciones m=C3=BAltiples en matem=C3=A1t= icasLas = representaciones m=C3=BAltiples son fundamentales para la comprensi=C3=B3n = matem=C3=A1tica; el dominio conceptual se fortalece cuando los estudiantes = coordinan representaciones concretas, visuales y simb=C3=B3licas (Stein et = al., 1996). Polypad permite transitar entre estas representaciones de forma= fluida; por ejemplo, una expresi=C3=B3n como <img src=3D"data:image= /png;base64,iVBORw0KGgoAAAANSUhEUgAAADoAAAAVCAYAAAAXQf3LAAAABHNCSVQICAgIfAh= kiAAAAAlwSFlzAAAOxAAADsQBlSsOGwAABe5JREFUWIXdVl9IU20Y/539cXOzWpmJrVT6Y42wKG= hXlaOom2ASFgVdBV7URZjRBEvvgggiq5uwLFCSpLK0CCKiAhtGUQj9MRWXMpWtzbGd49k529l5n= ++iPN8352e78KuPflcb7/O85/d7n9/zvg9HRIQ/HBzHcbrfTeJXwfC7CcwnGGNQVRVEBIPBAJ3u= 7zr+MULj8Th6e3vR19cHANi3bx+Ki4thMHyXmGZdIoIkSeB5Hqqq/hbCqqpClmWIoghZlsEY09Y= SiQQEQUAymcTMq6WzsxMvX75EZWUl7HY7KisrEYlEtHWtoowxhEIhdHd3Y2RkBA0NDbBYLL9KHx= hj4Hkenz59wuvXrzE8PIyysjK43W7Y7Xbk5OTgy5cvuH79Og4cOIAtW7YgLy8PHMcBAKqqqqDT6= WAymbQDSjsQIiLGGAUCATpy5AjdvXuXkskkzQcSiQQNDQ2RJEk/jY3H41RbW0tVVVX0+fNn+vr1= K9XW1lJ5eTkNDAwQY4wYYxQKhejUqVPU2tpKsVgsYx9RFMnj8VBjYyOJokjaq0JEJEkSnT17lur= q6khRlAyysVhMI6uqKgmCQIIgkKqqc5IPh8PkcrnI5/MRY2zOWEmS6MqVK+T1ejVRHz58oLVr19= KTJ0/S8v1+P7ndburp6UkrSjwep0uXLpHH46HJyUktR7NuMBjEvXv3cOfOHa15AUCSJLx79w5tb= W1wOp04fPgwotEoWltbIcsy6uvrYTKZ5sW6ZrMZx48f1/4nEgkMDw8jPz8fpaWlabFFRUVwOp3o= 7u6Gw+FAfn4+FEVBZ2cngsEg6urqoNPpIMsycnNzAQA6IsLbt2+hKApWrlypbUZEEEURr169gtP= pxM2bN+Hz+dDV1YVNmzahoqIi7fqeD0x/s7+/Hw8ePEBXVxfOnz+PkpISrRcBQK/XY8eOHfB6vQ= iHwyAivH//Hk1NTSguLsbz589x8uRJhEIhrUcNRIQ3b95gw4YNGdVZtGgRampqMDo6iubmZnR0d= GDnzp3Ytm0bjEZjBlFRFBGJRKAoCgAgFothamoKfr8fjDGNbGFhIaxW66xix8fH0dbWhv7+fixZ= sgRElHbzTmP58uWQZRnhcBirV6/GyMgI3G43AoEAgsEgSkpK0i5TAxFhcHAQpaWlaafGcRyMRiO= MRiNsNhvKysoQiUTgdDpnFQkA3759g8fjgSiKwI+3bWxsDGfOnIHVatX2v3jxIhwOR0Y+x3FYtW= oVTp8+DZ7n0d7ejhMnTqClpQWbN29Oc5DVatUcQEQ4ePDgrJw0odMfmO3U8OPal2UZgiDAZrOl9= fBMFBYW4vLly0ilUsCPilZXV+PcuXNYsWKFJrSgoODfCRkMWLBgAfLy8nDo0CF0dHTA6/WivLwc= OTk5WhwRZbylcwrlOA4OhwMfP34EEaVVlYjA8zyePXsGl8uFp0+fIhaLYeHChdDr9RmVtVgsaXa= ZnJyE1WqF3W7P6LOZkCQJN27cwO7du7Fu3TpwHAeO42AwGGCz2TJyBUEAx3FpTpkLOo7jsHXrVg= wNDSEej2sL0WgUjY2NePToEYqKilBRUYFAIICHDx+iubkZkiRlfZrZQFEU9PT0oKmpCT6fD2NjY= 7h//z7MZjO2b9+e4SS/3w+TyYSCggLo9frshZrNZoyOjgI/KplKpTA+Po7Fixdj165dWLNmDWpq= ajAwMIC9e/fO+9RksVjQ0NCA9evX4+rVq7h27RqWLVuGW7dupdkeAFKpFF68eAGXy4WlS5dmVVE= QEcmyTBcuXKCjR49qA4OiKDQ1NaU9yIwxkiSJRFGkVCr1kznnO5LJJE1MTFAikcgqXlVVkiSJeJ= 4nnudJluVZBw2fz0d79uyh3t7erKY4Tej0aFVdXU0tLS3zNgLONxhjNDExQceOHaPbt2+TIAhZ5= QEAN/2DMYZoNIrHjx9jcHAQ9fX1v3So/xmICH19fWhvb8f+/fuxceNG5ObmZmVbjuM4TSj+0Zuq= qsJkMmXn/V+IaW56vX7OZ24muP+bkP8SfwHjkGMFRQLXdQAAAABJRU5ErkJggg=3D=3D" width= =3D"58" height=3D"21" alt=3D"" style=3D"vertical-align:middle" /> puede visualizarse simult=C3=A1neament= e como =C3=A1rea, descomposici=C3=B3n rectangular, suma algebraica y patr= =C3=B3n repetitivo, fortaleciendo el razonamiento matem=C3=A1tico estructur= al.= 1.8.4. Pensamiento algebrai= co tempranoEl pensamiento algebraico debe iniciarse desde los primeros niveles de l= a Educaci=C3=B3n General B=C3=A1sica para evitar un aprendizaje fragmentado= en etapas posteriores. Las herramientas digitales permiten comenzar desde = asociaciones visuales simples, como la relaci=C3=B3n entre =C3=A1reas y mul= tiplicaci=C3=B3n, la identificaci=C3=B3n de patrones y la comprensi=C3=B3n = de t=C3=A9rminos semejantes, facilitando una transici=C3=B3n gradual hacia = el lenguaje algebraico formal (Candela-Mu=C3=B1oz & Rodr=C3=ADguez-G=C3= =A1mez, 2023; Delport, 2021).2. Metodolog=C3=ADa</sp= an>La ense=C3= =B1anza de =C3=A1lgebra en Educaci=C3=B3n General B=C3=A1sica (EGB</sp= an>) constituye uno de los ma= yores desaf=C3=ADos pedag=C3=B3gicos en matem=C3=A1ticas. En Ecuador, diver= sos estudios evidenciaron dificultades recurrentes relacionadas con la comp= rensi=C3=B3n superficial de los conceptos abstractos, memorizaci=C3=B3n mec= =C3=A1nica de procedimientos y escaso uso de recursos visuales interactivos= . Estas limitaciones impactan en el rendimiento acad=C3=A9mico y la motivac= i=C3=B3n hacia la asignatura, por parte del estudiante.En los =C3=BAltimos a=C3=B1= os, la incorporaci=C3=B3n de herramientas tecnol=C3=B3gicas demostr=C3=B3 u= n gran potencial para transformar la educaci=C3=B3n, especialmente mediante= las herramientas digitales, que permiten representar conceptos matem=C3=A1= ticos de forma visual, manipulable e interactiva. As=C3=AD, con Polypad se = puede incorporar bloques algebraicos, rect=C3=A1ngulos geom=C3=A9tricos, l= =C3=ADneas num=C3=A9ricas y m=C3=BAltiples componentes que facilitan el tr= =C3=A1nsito entre lo convencional y lo abstracto, elemento clave para el ap= rendizaje del =C3=A1lgebra. Adem=C3=A1s, que su uso, cuando se lo utiliza c= on una gu=C3=ADa docente estructurada, se incrementa la comprensi=C3=B3n co= nceptual, promoviendo as=C3=AD el razonamiento algebraico, lo que potencia = la participaci=C3=B3n activa en el aula.En Ecuador, las brechas de infraestructura,= conectividad y formaci=C3=B3n docente presentan desaf=C3=ADos significativ= os para la integraci=C3=B3n tecnol=C3=B3gica. Pero, a=C3=BAn en institucion= es con el equipamiento limitado, se demuestra efectos positivos, esto graci= as a una mediaci=C3=B3n pedag=C3=B3gica adecuada.<span= style=3D"font-family:'Times New Roman'">En esta investigaci=C3=B3n se va a= evaluar la eficacia de Polypad en una intervenci=C3=B3n real desarrollada = en una instituci=C3=B3n rural de Cuenca, aportando datos cuantitativos y cu= alitativos para comprender sus beneficios y desaf=C3=ADos para la educaci= =C3=B3n matem=C3=A1tica ecuatoriana.2.1. Dise=C3=B1o de la investigaci=C3=B3n<p= style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-siz= e:12pt">A este estudio se emp= le=C3=B3 un dise=C3=B1o cuasi-experimental, el cual tendr=C3=A1 un enfoque = mixto (cuantitativo + cualitativo), en donde se aplic=C3=B3 la siguiente se= cuencia:= Pre-test =E2=86=92 Intervenci=C3=B3n did=C3=A1ctica con Polypad =E2=86=92 P= os-testY= ser=C3=A1 complementada con la realizaci=C3=B3n de encuestas de percepci= =C3=B3n estudiantil, una observaci=C3=B3n/an=C3=A1lisis hacia los participa= ntes, y con entrevistas semiestructuradas hacia los docentes.Esta estructura permit= e comprender el impacto no solo en t=C3=A9rminos de rendimiento acad=C3=A9m= ico de los participantes, sino tambi=C3=A9n en t=C3=A9rminos motivacionales= , cognitivos y pedag=C3=B3gicos. Con este dise=C3=B1o mixto existir=C3=A1 l= a posibilidad de una triangulaci=C3=B3n metodol=C3=B3gica, validaci=C3=B3n = cruzada de hallazgos y de una interpretaci=C3=B3n contextualizada de los re= sultados.Los participantes en esta investigaci=C3=B3n ser=C3=A1 una poblaci=C3=B3n = total de estudiantes de octavo a=C3=B1o de la Unidad Educativa Guillermo Me= nsi, ubicada en El Valle, Cuenca, Azuay (zona rural). La cual estar=C3=A1 c= lasificada en dos grupos, los estudiantes del paralelo A con un total de 35= estudiantes, y los estudiantes del paralelo B con un total de 33 estudiant= es, juntando ambos paralelos de obtiene la poblaci=C3=B3n total de la inves= tigaci=C3=B3n que ser=C3=A1 de 68 participantes.Adem=C3=A1s, participaron todos los= docentes de matem=C3=A1ticas de la instituci=C3=B3n mediante entrevistas s= emiestructuradas orientadas a captar percepciones, barreras y sugerencias s= obre la integraci=C3=B3n de Polypad.Por lo que, se cumple varios escenarios que son= muy importantes para poder determinar los resultados de esta investigaci= =C3=B3n, los cuales son una escuela rural con acceso limitado a infraestruc= tura tecnol=C3=B3gica, laboratorio de inform=C3=A1tica con conectividad med= ia, estudiantes con experiencia m=C3=ADnima en manipulativos virtuales y do= centes con formaci=C3=B3n parcial en tecnolog=C3=ADas educativas.</p= >2.2. Instrumentos y m= ateriales Para la reco= lecci=C3=B3n de informaci=C3=B3n y evaluaci=C3=B3n del impacto de la interv= enci=C3=B3n con Polypad se utilizaron diferentes instrumentos de medici=C3= =B3n y recursos did=C3=A1cticos, dise=C3=B1ados de acuerdo con los objetivo= s planteados en la investigaci=C3=B3n. Estos permitieron analizar los cambi= os en el desempe=C3=B1o acad=C3=A9mico de los estudiantes, as=C3=AD como su= s experiencias durante el proceso de aprendizaje activo de las expresiones = algebraicas. Los instrumentos aplicados estuvieron orientados a obtener inf= ormaci=C3=B3n cuantitativa y cualitativa antes, durante y despu=C3=A9s de l= a implementaci=C3=B3n de la estrategia did=C3=A1ctica.2.2.1.</= span> Pre-test y Post-test<= span style=3D"font-family:'Times New Roman'">Para poder identificar como er= a el conocimiento de matem=C3=A1ticas, de los estudiantes antes y despu=C3= =A9s del uso de Polypad se realizaron pruebas estructuradas con 5 preguntas= de opci=C3=B3n m=C3=BAltiple, evaluando la identificaci=C3=B3n de t=C3=A9r= minos semejantes, suma y resta de expresiones, multiplicaci=C3=B3n algebrai= ca mediante la propiedad distributiva, y divisi=C3=B3n algebraica b=C3=A1si= ca.La es= cala de calificaci=C3=B3n fue de 0 a 10 puntos, se us=C3=B3 el mismo format= o en pre-test y post-test para garantizar comparabilidad.2.2.2.<= /span> Actividades con PolypadEl dise=C3=B1o did=C3=A1ct= ico desarrollado con Polypad se estructur=C3=B3 en una secuencia de cinco s= esiones de 45 minutos durante toda una semana de clases, las sesiones fuero= n orientadas para favorecer la transici=C3=B3n desde la manipulaci=C3=B3n c= oncreta hacia la comprensi=C3=B3n simb=C3=B3lica en el =C3=A1lgebra inicial= . Cada sesi=C3=B3n se fundament=C3=B3 en principios del aprendizaje activo,= el constructivismo y el uso de representaciones m=C3=BAltiples, aprovechan= do las caracter=C3=ADsticas interactivas del entorno digital.La sesi=C3=B3n 1 fue = =E2=80=9CIntroducci=C3=B3n al entorno Polypad=E2=80=9D, la cual estuvo neta= mente dedicada al reconocimiento de la interfaz de Polypad, en donde se pue= do explorar las principales categor=C3=ADas como bloques manipulativos, rec= t=C3=A1ngulos algebraicos, l=C3=ADneas num=C3=A9ricas y controles de edici= =C3=B3n. Se comenz=C3=B3 con una fase inicial de exploraci=C3=B3n libre, se= guida de una exploraci=C3=B3n guiada para identificar funciones clave como = arrastrar, soltar piezas, duplicar y eliminar elementos. Esta sesi=C3=B3n f= ue primordial para disminuir la ansiedad tecnol=C3=B3gica, desarrollar auto= nom=C3=ADa en el estudiante y fomentar la disposici=C3=B3n para las siguien= tes sesiones.<img src=3D"data:image/png;= base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAiCAYAAAApkEs2AAAABHNCSVQICAgIfAhkiAAA= AAlwSFlzAAAOxAAADsQBlSsOGwAAAl9JREFUWIXtlz9r6lAYxp9cuogOXYqDDv0ASgmCgyAoKPg= BXPwWDgUHO4jgVK2lXSy46OAkOOqqqO1SQWkpFJFKaVWoIKJtISXPnSoEpTfmht4/5AdZ3vc55M= fLOYdEIEn85QiCIPz40xJqMUT1xhDVG0NUb/5v0efnZ8RiMUwmE7y+viKTycDtdiMYDKJSqaxyq= VQKrVZLH1Nuyd3dHUVRZLlcpizLjMfjBKB46vU6SbLf79Pv97NUKm37GgVbi85mM3q9Xp6enpIk= Hx4eWCqV+Pb2xpubGzqdTgLg0dHRak2n0yEAXl1dfZ/o+fk5AfDx8ZEkuVgsFP2zszMCYDqdVtT= D4TBDoRA/Pj40i6reo5IkIZfL4eDgADabDQBgNpsVGVmWAQA+n09R93g8qNVq6HQ6mreoatHBYI= Db21s4HA4IgrAx0263EY1G4XK5FHW73Q4A6Ha7mkV31Aan0ykAwGKxbOxfX19jOp3i4uJirWcym= QAAo9FIs6jqiX5OcdM0F4sFjo+Pkc/nsbu7u9b/3BK/8+mrWnRvbw8AsFwuFXWSyGazSCQS2N/f= hyzLqFareHl5WWXe398BAFarVbOo6lMvSRJFUaQoiop6oVBYu0c9Ho8ic3JyQgC8vLzUfOq3up5= 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Los estudiantes visualizaron c=C3=B3mo la multiplic= aci=C3=B3n se descompone en partes, cada parte corresponde a un t=C3=A9rmin= o del desarrollo algebraico, la propiedad distributiva emerge naturalmente = del modelo. 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marg= in-left:300pt; position:absolute" />La sesi=C3=B3n 4 fue =E2=80=9CDivisi=C3=B3n algebraica median= te agrupaciones y particiones visuales=E2=80=9D, en donde los estudiantes t= rabajaron problemas de partici=C3=B3n, utilizando rect=C3=A1ngulos y bloque= s para representar divisiones como los que se observan en la Ecuaci=C3=B3n 4</s= pan>: <im= g src=3D"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAmCAYAAADJJcvs= AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAA+VJREFUSIndlrtLK1sUxr8= 94xwmxkcwmBBsJGihhaiJiGKjYGFlIWIjWClY2gSttLTwAYIIPkDs4h8QEFSiCAoSUVAbMURNIG= ggJpkwmee6hSTn3pPxXu/1VuerhrXht/f61t5rDSMiwjfFGGPcdyFFVfwaICIYhvGxWFG2/M8gI= kKhUEA6ncbFxQUURcHo6OiXYVwRkslksL29jZGRETw8PMDr9eJf2UdEJEkSLSwsUFdXFyUSCbKS= qqokSRIpikJERIZhUD6fJ1mWP3YzTZNOT0/J6/VSNBq1hOTzeTo4OKDJyUm6urqiQqFAsViMAoE= AHR4eEgBwqqpibW0NbW1tMAwDkUgE5+fneHp6gq7rICIkEgm8vr4CABYXF/H4+IhgMIiWlhbU19= cDAFgqlaK+vj709vbC7XbD7Xbj8vISyWQSS0tLaGtrg6ZpMAwDV1dXmJ2dRX9/P8bHx+H1eiEIA= hhjDPF4nBoaGmh1dZVkWSbTNOnl5YUGBgZoenq65AkRUTQaJb/fT1tbWyRJUikOABzHceB5Hs3N= zRBFEYwx1NbWwu/3I5lMQtf1opdQFAWMMYiiCEEQ/lp+u90Oj8eDWCxWCpqmCUmSUFdXB57nQUR= Ip9PY399HV1cXbm5uIEkSFEUpbVRht9sxNTWFnZ0dDA4OwuFw4P7+Hre3t5ifn0c2m8XR0RGen5= 8xPDyMh4cHbGxsIBwOAwCGhoY+zCYiymQyOD4+xt3dHTRNg8PhQHd3Nzo6OvD8/IylpSVMTEzA5= /Ph/f0dy8vLcDgcmJiYgMfjgSAIjBXN0jQN+XwehmFAFEXYbDZwHAdFUVAoFGCz2fDjxw+YpglZ= lkFEsNls4HkejLGfoO/of20jvzGoYmVl5VsAu93+Acpms98CFdvyb1x+yxGh6zpkWS51SCKCKIq= orKwEY+xrIF3XcX19jcXFRTQ2NqK6uhrhcBg+nw9zc3NwOp3WR/q10cuyTGtrazQzM0OyLJOmaX= RyckJNTU10dHREpmmWDQfLEwmCgLGxMXAcB1EUQURwOp2lbyKyTK8MxPM8XC4XiAiqqiKdTiMUC= qGzsxOtra3gOOv6WJpdbK2hUAiHh4eoqalBIBCAy+Wy9ufvyl9MqaenB4lEApubm0gmk5+PccvR= +idpmkaRSITa29tpb2+PVFW1NLvsRIZhIJVKIZfLfeReUQGPxwOn04l4PA7TNL+WmqIoWF9fRzA= YhK7rME0TmUwGsizD7/d/+ptTFuU4DjabDbu7u0in03A6nTg7O8Po6Ch8Ph94nrcElb1+0zSRy+= Xw9vYGTdNK96murg5VVVWWd4h99m7+i/4AGxehDnRcBXEAAAAASUVORK5CYII=3D" width=3D"= 18" height=3D"38" alt=3D"" style=3D"vertical-align:middle" /><img src=3D"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADYAAAAnCAYAAAB= Ez7vjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAOxAAADsQBlSsOGwAABg9JREFUaIHtmF9IVN= sXxz/nzDiHGWcMlEnE0kBImswkpSnQIMuCIAvMl4QIaiDrrUnQssgeAsOnHgqzCImeeigwKhA1x= KxByV7EqMhJscmmEZ3ROR7Ov9/DzeEnv9+9ze02dYs+j4e1917fvfdaZ68lmKZp8oshCIIg/mgn= UoU1GSPDMFBVFU3TME0TURSRJAmLxZJ6D7+SpITNz8/T3t7OyMgIq1ev5vXr1zQ3N1NSUoIo/js= PPSmvFEVhcXGR1tZWGhsbyc/P58qVKyiK8s0d0nWdWCxGOBxmenqaUCjEzMwMqqr+rXmSOjG328= 3Zs2cBmJ6eRlEUSktLk76K8/PzWCwW7Hb7X9qZpkkwGOT8+fOsWLECj8dDX18fsizT2tpKYWEhV= mtSLid3YkvEYjGePHnC4uIiNTU12Gy2pMZdv36dhw8fftHOMAzGx8fRdZ0zZ85QX19PW1sbU1NT= dHR0EI/Hk/bVCjA7O8vIyAh2u52ysjIMwyAYDDI5OUl5eTmSJBGLxejp6aG7u5uWlhbcbnfSi4R= CIRwOxxftRFHE6/WyceNGMjMzEQQBSZJwOp04HA4EQUhswOTkJKOjoxQXF5OTk4OqqgQCAZxO5x= /CVFWlq6uLQCDA4OAg9+7dQ9M02tvbkWUZr9eLaZoMDQ1x9+5d/H4/hmHQ09NDRUUFkiQlLfBLC= IKAy+XC5XKhaRozMzP09fWRl5dHXV1dYnMikQi3bt1iYGCAgoICLly4QHd3N4FAgJKSkj+EARQV= FVFVVcXevXvp7e0lGAzi9/txuVzY7XZmZ2fp7Oxkbm6Oa9euEY1GycrKYuvWrd9U2BKyLHP79m2= ePn1KLBbj+PHj5OfnJ2Ja0zR8Ph+bN2/G7/fT29uLxWLh3LlzWK1WDh8+jLD08pBlmVOnTjE2Ns= bVq1dZu3Zt4ujj8Tjj4+OJLCgIAllZWeTm5v5PAlEUhRs3bjA6OophGAA8e/aMjIwMPB4PfL5y6= 9ato76+/v8mIEVRePXqFaFQiL6+Pl68eEFjYyNbtmxZtpHhcJjt27dTVVVFc3Nz4voKgiAkUowg= CBQWFtLf309eXl5CFIDD4WD9+vVJ7bYoihQXF7Ny5UqWXmvv378nJyeHysrKxFrZ2dnL1vhvJEl= iw4YNFBUVUVJSwrFjx7h58yYej2dZbKelpWGaJmVlZaSnpy+bz8rnYAyFQgSDQURRRJblL6bmPy= MtLY3y8vJl34aHhykoKKC2tvYvxxqGQTQaRVEU3G43oiiSkZFBQUEBExMTaJqWsNU0jfv377Np0= yZGRkbYt2/fsrnEqakpQqEQly9f5siRIwAMDQ0xPj7Omzdvvkrc16LrOl1dXbS0tBCJRACIRqO8= fPmSoqIinE4ni4uLRCIRBgYGcLlcVFdX09PTQyQS4c6dO4lwEU+fPo3P5+PEiROsWbOGPXv24Pf= 7aWtrY9WqVd9VmCiKuN1uxsbGaGho4NKlS5w8eZLS0lJ8Ph/p6elMTExQU1PD48ePqaiooLKyEp= vNRm1tLdnZ2YmYFT59+mRarVYyMjLgc6KQZRmHw4Hdbv/TOPg7dHZ2kpOTw65du75oq6oqsiyj6= /pSIsBmsyFJEqIooqoq8/Pz2Gy2RLjEYjE0TcPpdCJJEoIgCML3qMdUVUUQhKSfQ/+U7ybse/NL= F5q/hf1sWBcWFn60DynBeujQoR/tQ0oQAoHAL5cVvV7v73T/0/Fb2M/Gb2Ffg67rfPjwgY8fPya= q6Xg8zrt371LSbF2GmSJ0XTf7+/vNAwcOmNu2bTPD4bAZjUbNhoYGc//+/ebs7GyqljZJthP8NR= iGwdzcHBcvXqS6uprnz58zNjbGwYMHE33CVJKy/5hpmmiahiiK1NXVoaoqPp+PnTt3prwuS+l/T= BAE0tLSsFgs7N69m+HhYcrLy79bsZnyrBiPxxkcHMQwjGVdplSTUmGaptHR0cHRo0exWCy8ffuW= hYWFRAcqlaQkxnRdp6mpiVgslmidV1dXoygKHo+HpqYmcnNzv/WyCVLW89A0jUePHpGZmYnX68V= isRAOh3nw4AE7duxIeVvvl27m/AdkWEi9TRsBdwAAAABJRU5ErkJggg=3D=3D" width=3D"54"= height=3D"39" alt=3D"" style=3D"vertical-align:middle" /><sp= an style=3D"font-family:'Times New Roman'">Con esta manipulaci=C3=B3n digit= al se favoreci=C3=B3 la comprensi=C3=B3n intuitiva de la divisi=C3=B3n como= distribuci=C3=B3n equitativa, c=C3=A1lculo de cu=C3=A1ntas veces cabe un b= loque dentro de otro, e identificaci=C3=B3n de factores ocultos. </p= >La sesi=C3=B3n 5 f= ue =E2=80=9CSesi=C3=B3n integradora=E2=80=9D, en esta =C3=BAltima sesi=C3= =B3n se desarrollaron actividades que exig=C3=ADan mezclar operaciones. Los= estudiantes deb=C3=ADan reforzar sus estrategias, explicar los pasos reali= zados y contrastar sus modelos con los de sus compa=C3=B1eros. Esta fase co= nsolid=C3=B3 la autonom=C3=ADa en la resoluci=C3=B3n de problemas, el pensa= miento cr=C3=ADtico y la capacidad de relacionar lo concreto, lo representa= tivo y lo simb=C3=B3lico.3. Resultados<= p style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-si= ze:12pt"> <spa= n style=3D"font-family:'Times New Roman'">Los resultados obtenidos durante = la investigaci=C3=B3n permiten analizar los efectos de la implementaci=C3= =B3n de Polypad como estrategia did=C3=A1ctica para fortalecer el aprendiza= je activo de las operaciones algebraicas en estudiantes de octavo a=C3=B1o = de educaci=C3=B3n general b=C3=A1sica. La informaci=C3=B3n recopilada media= nte los instrumentos aplicados fue organizada considerando los componentes = cuantitativos y cualitativos del estudio, permitiendo establecer una compar= aci=C3=B3n entre el desempe=C3=B1o acad=C3=A9mico antes y despu=C3=A9s de l= a intervenci=C3=B3n, as=C3=AD como conocer las percepciones de los estudian= tes respecto al uso de herramientas digitales en el proceso de aprendizaje.= De esta manera, los resultados presentados permiten valorar tanto la incid= encia de la estrategia tecnol=C3=B3gica en la comprensi=C3=B3n de contenido= s matem=C3=A1ticos como los aspectos motivacionales y pedag=C3=B3gicos asoc= iados a su aplicaci=C3=B3n en el aula.3.1. Resultados del pre-test y post-test<= p style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-si= ze:12pt">El an=C3=A1lisis com= parativo entre los resultados del pre-test y post-test permiti=C3=B3 corrob= orar el impacto significativo que tuvo el uso de la herramienta digital Pol= ypad en el aprendizaje de las operaciones algebraicas en estudiantes de oct= avo a=C3=B1o de Educaci=C3=B3n General B=C3=A1sica. <s= pan style=3D"font-family:'Times New Roman'">Antes de la intervenci=C3=B3n, = los estudiantes presentaban dificultades notorias en la identificaci=C3=B3n= de t=C3=A9rminos semejantes, la aplicaci=C3=B3n de la propiedad distributi= va y la resoluci=C3=B3n de expresiones algebraicas simples, lo que coincid= =C3=ADa con las observaciones previas realizadas durante las clases tradici= onales.E= n el paralelo A, el promedio inicial fue de 5,83/10, mientras que tras la i= ntervenci=C3=B3n se alcanz=C3=B3 un promedio de 8,45/10, lo que representa = un incremento de 2,62 puntos. Este crecimiento evidencia una mejora sustanc= ial no solo en los resultados cuantitativos, sino tambi=C3=A9n en la compre= nsi=C3=B3n conceptual, ya que los estudiantes demostraron mayor seguridad a= l explicar procedimientos, justificar resultados y representar gr=C3=A1fica= mente las operaciones.Por su parte, el paralelo B mostr=C3=B3 un aumento de 1,14 pu= ntos, pasando de 5,10/10 a 6,24/10. Aunque el incremento fue menor en compa= raci=C3=B3n con el paralelo A, los datos indican una mejora positiva en la = comprensi=C3=B3n de conceptos algebraicos, especialmente en estudiantes que= al inicio presentaban mayores dificultades. Esta diferencia entre grupos puede atr= ibuirse a diferentes factores como el nivel de participaci=C3=B3n, la famil= iaridad previa con herramientas digitales y el ritmo de trabajo grupal.</sp= an>Por lo que, = los resultados evidencian que el uso sistem=C3=A1tico de Polypad favorece l= a consolidaci=C3=B3n del aprendizaje significativo, permitiendo que los est= udiantes transiten progresivamente desde representaciones concretas hacia n= iveles m=C3=A1s abstractos del pensamiento matem=C3=A1tico.3.2. Resultados de la encuest= a sobre aprendizaje activoEl an=C3=A1lisis de los resultados obtenidos a partir de = la encuesta aplicada a los estudiantes permite comprender de manera m=C3=A1= s profunda el impacto del uso de herramientas digitales (espec=C3=ADficamen= te Polypad) en el aprendizaje activo de las matem=C3=A1ticas. Esta informac= i=C3=B3n cualitativa complementa los datos cuantitativos del pretest y post= est, permitiendo una visi=C3=B3n m=C3=A1s integra del proceso educativo des= arrollado durante la intervenci=C3=B3n.Tabla 1Inter=C3= =A9s en aprender matem=C3=A1ticas mediante herramientas tecnol=C3=B3gicas</= span><table style=3D"width:100%; margin-right:auto; margin-left:auto; m= argin-bottom:0pt; padding:0pt; border-collapse:collapse"><tr><td style=3D"w= idth:41.6%; border-top:0.75pt solid #000000; border-bottom:0.75pt solid #00= 0000; padding:0pt 5.4pt; vertical-align:top">Nivel de acuerdo</td><td style=3D"width:25.52%; border-top= :0.75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4p= t; vertical-align:top">Frecuencia</td><td style=3D"width:32.9%; border-top:0.75pt s= olid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertic= al-align:top">Porce= ntaje (%)</td></tr><tr><td style=3D"width:41.6%; border-top:0.75= pt solid #000000; padding:0pt 5.4pt; vertical-align:top">Muy de acuerdo</td><td sty= le=3D"width:25.52%; border-top:0.75pt solid #000000; padding:0pt 5.4pt; ver= tical-align:top">39= </td><td style=3D"width:32.9%; border-top:0.75pt solid #000000; = padding:0pt 5.4pt; vertical-align:top">58 %</td></tr><tr><td style=3D"width:41.6%; = padding:0pt 5.4pt; vertical-align:top">De acuerdo</td><td style=3D"width:25.52%; pa= dding:0pt 5.4pt; vertical-align:top">22</td><td style=3D"width:32.9%; padding:0pt 5= .4pt; vertical-align:top">33 %</td></tr><tr><td style=3D"width:41.6%; padding:0pt 5= .4pt; vertical-align:top">En desacuerdo</td><td style=3D"width:25.52%; padding:0pt = 5.4pt; vertical-align:top">4</td><td style=3D"width:32.9%; padding:0pt 5.4pt; verti= cal-align:top">6 %<= /span></td></tr><tr><td style=3D"width:41.6%; padding:0pt 5.4pt; vertic= al-align:top">Muy en desacuerdo<= /p></td><td style=3D"width:25.52%; padding:0pt 5.4pt; vertical-align:top"><= p style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-si= ze:10pt">3</td><td= style=3D"width:32.9%; padding:0pt 5.4pt; vertical-align:top"><sp= an style=3D"font-family:'Times New Roman'">3 %</td></tr><tr><td = style=3D"width:41.6%; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt= ; vertical-align:top">Total</td><td style=3D"width:25.52%; border-bottom:0.75pt sol= id #000000; padding:0pt 5.4pt; vertical-align:top">68</td><td style=3D"width:32.9%;= border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"= >100 %</= td></tr></table>Nota= : pregunta sobre el inter=C3=A9s y mot= ivaci=C3=B3n hacia el aprendizaje matem=C3=A1tico<span= style=3D"font-family:'Times New Roman'">Los resultados evidencian que el 9= 1% de los estudiantes manifest=C3=B3 estar muy de acuerdo o de acuerdo con = sentirse m=C3=A1s motivado al aprender matem=C3=A1ticas mediante herramient= as tecnol=C3=B3gicas. Este hallazgo confirma que la incorporaci=C3=B3n de r= ecursos digitales incrementa el inter=C3=A9s y la disposici=C3=B3n hacia el= aprendizaje, especialmente en contenidos que tradicionalmente generan rech= azo o ansiedad, como el =C3=A1lgebra.Este aumento en la motivaci=C3=B3n puede expli= carse por el car=C3=A1cter interactivo, visual y din=C3=A1mico de Polypad, = el cual transforma el aprendizaje en una experiencia activa y participativa= . Al permitir que los estudiantes manipulen objetos, observen cambios en ti= empo real y experimenten sin temor al error, generando un entorno que favor= ece la curiosidad y el compromiso cognitivo. Este resultado coincide con es= tudios previos que sostienen que las tecnolog=C3=ADas educativas bien integ= radas promueven mayor involucramiento emocional y cognitivo.Tabla 2Comprensi=C3=B3n de los contenidos mediante act= ividades interactivas<table style=3D"margin-right:auto; margin-l= eft:auto; margin-bottom:0pt; padding:0pt; border-collapse:collapse"><tr><td= style=3D"width:78.35pt; border-top:0.75pt solid #000000; border-bottom:0.7= 5pt solid #000000; padding:0pt 5.4pt; vertical-align:top">Nivel de acuerdo</td><td style=3D"width:1pt; = border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; paddin= g:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75= pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; ve= rtical-align:top">&= #xa0;</td><td style=3D"width:1pt; border-top:0.75pt solid #00000= 0; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:to= p"> </p= ></td><td style=3D"width:1pt; border-top:0.75pt solid #000000; border-botto= m:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"><s= pan style=3D"font-family:'Times New Roman'"> </td><td style= =3D"width:1pt; border-top:0.75pt solid #000000; border-bottom:0.75pt solid = #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; = border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; paddin= g:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75= pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; ve= rtical-align:top">&= #xa0;</td><td style=3D"width:1pt; border-top:0.75pt solid #00000= 0; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:to= p"> </p= ></td><td style=3D"width:47.25pt; border-top:0.75pt solid #000000; border-b= ottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top">Frecuencia</td><= td style=3D"width:1pt; border-top:0.75pt solid #000000; border-bottom:0.75p= t solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"wid= th:1pt; border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000= ; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-= top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5= .4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75pt soli= d #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-= align:top"> </= span></td><td style=3D"width:1pt; border-top:0.75pt solid #000000; bord= er-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><= td style=3D"width:1pt; border-top:0.75pt solid #000000; border-bottom:0.75p= t solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"wid= th:1pt; border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000= ; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:65.25pt; bor= der-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0= pt 5.4pt; vertical-align:top">Porcentaje (%)</td></tr><tr><td style=3D"width:78.35p= t; border-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top">= Muy de acuerdo</spa= n></td><td style=3D"width:1pt; border-top:0.75pt solid #000000; padding= :0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75p= t solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"wid= th:1pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:= top"> <= /p></td><td style=3D"width:1pt; border-top:0.75pt solid #000000; padding:0p= t 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75pt s= olid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width= :1pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:to= p"> </p= ></td><td style=3D"width:1pt; border-top:0.75pt solid #000000; padding:0pt = 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75pt sol= id #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:47= .25pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:t= op">42</= td><td style=3D"width:1pt; border-top:0.75pt solid #000000; padding:0pt 5.4= pt; vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75pt solid = #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; = border-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td>= <td style=3D"width:1pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt;= vertical-align:top"> </td><td style=3D"width:1pt; border-top:0.75pt solid #00= 0000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; bor= der-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td= style=3D"width:1pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt; ve= rtical-align:top">&= #xa0;</td><td style=3D"width:65.25pt; border-top:0.75pt solid #0= 00000; padding:0pt 5.4pt; vertical-align:top">61 %</td></tr><tr><td style=3D"width:= 78.35pt; padding:0pt 5.4pt; vertical-align:top">De acuerdo</td><td style=3D"width:1= pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; paddi= ng:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.= 4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; vert= ical-align:top">&#x= a0;</td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-alig= n:top"> </span= ></td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"><p= style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-siz= e:10pt"> </td= ><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"><= span style=3D"font-family:'Times New Roman'"> </td><td styl= e=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"widt= h:47.25pt; padding:0pt 5.4pt; vertical-align:top">22</td><td style=3D"width:1pt; pa= dding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt= 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; v= ertical-align:top">= </td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-a= lign:top"> </s= pan></td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"= > <= /td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td s= tyle=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"w= idth:65.25pt; padding:0pt 5.4pt; vertical-align:top">32 %</td></tr><tr><td style= =3D"width:78.35pt; padding:0pt 5.4pt; vertical-align:top">En desacuerdo</td><td sty= le=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"wid= th:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; p= adding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0p= t 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; = vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-= align:top"> </= span></td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top= "> = </td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td = style=3D"width:47.25pt; padding:0pt 5.4pt; vertical-align:top"><s= pan style=3D"font-family:'Times New Roman'">3</td><td style=3D"w= idth:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt;= padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:= 0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt= ; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; vertica= l-align:top"> = </td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:t= op"> </= p></td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><t= d style=3D"width:65.25pt; padding:0pt 5.4pt; vertical-align:top">5 %</td></tr><tr= ><td style=3D"width:78.35pt; padding:0pt 5.4pt; vertical-align:top">Muy en desacuerdo</td><td style=3D"= width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt= ; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding= :0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4p= t; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; vertic= al-align:top"> = ;</td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:= top"> <= /p></td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><= td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"><sp= an style=3D"font-family:'Times New Roman'"> </td><td style= =3D"width:47.25pt; padding:0pt 5.4pt; vertical-align:top">1</td><td style=3D"width:= 1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padd= ing:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5= .4pt; vertical-align:top"> </td><td style=3D"width:1pt; padding:0pt 5.4pt; ver= tical-align:top">&#= xa0;</td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-ali= gn:top"> </spa= n></td><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"><= p style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-si= ze:10pt"> </t= d><td style=3D"width:1pt; padding:0pt 5.4pt; vertical-align:top"> </td><td s= tyle=3D"width:65.25pt; padding:0pt 5.4pt; vertical-align:top"><sp= an style=3D"font-family:'Times New Roman'">2 %</td></tr><tr><td = style=3D"width:78.35pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4= pt; vertical-align:top">Total</td><td style=3D"width:1pt; border-bottom:0.75pt soli= d #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt= ; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top= "> = </td><td style=3D"width:1pt; border-bottom:0.75pt solid #000000; padding:0p= t 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-bottom:0.75p= t solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"wid= th:1pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-ali= gn:top"> </spa= n></td><td style=3D"width:1pt; border-bottom:0.75pt solid #000000; padd= ing:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-bottom= :0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"><sp= an style=3D"font-family:'Times New Roman'"> </td><td style= =3D"width:1pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; verti= cal-align:top"> = 0;</td><td style=3D"width:47.25pt; border-bottom:0.75pt solid #0= 00000; padding:0pt 5.4pt; vertical-align:top">68</td><td style=3D"width:1pt; border= -bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td= style=3D"width:1pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt;= vertical-align:top"> </td><td style=3D"width:1pt; border-bottom:0.75pt solid = #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; = border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top">= </= td><td style=3D"width:1pt; border-bottom:0.75pt solid #000000; padding:0pt = 5.4pt; vertical-align:top"> </td><td style=3D"width:1pt; border-bottom:0.75pt = solid #000000; padding:0pt 5.4pt; vertical-align:top"> </td><td style=3D"width= :1pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align= :top"> = </td><td style=3D"width:65.25pt; border-bottom:0.75pt solid #000000; pa= dding:0pt 5.4pt; vertical-align:top">100 %</td></tr></table> En relaci=C3=B3n con la comprensi=C3=B3n= de los contenidos matem=C3=A1ticos, el 93% de los estudiantes indic=C3=B3 = que las actividades interactivas facilitaron la comprensi=C3=B3n de los con= ceptos abordados. Este dato evidencia que el uso de representaciones visual= es y manipulativas permiti=C3=B3 superar barreras asociadas al aprendizaje = abstracto, especialmente en temas como la suma y resta de expresiones algeb= raicas, productos notables y factorizaci=C3=B3n.El uso de Polypad permiti=C3=B3 a l= os estudiantes observar relaciones matem=C3=A1ticas de manera simult=C3=A1n= ea desde diferentes perspectivas: simb=C3=B3lica, gr=C3=A1fica y espacial. = Este enfoque favorece a la construcci=C3=B3n de significados y fortalece la= comprensi=C3=B3n profunda, afirmando que el aprendizaje matem=C3=A1tico se= consolida cuando los estudiantes pueden transitar entre diferentes formas = de representaci=C3=B3n.Adem=C3=A1s, los estudiantes demostraron mayor capacidad par= a explicar sus procedimientos, justificar resultados y corregir errores de = forma aut=C3=B3noma, lo que evidencia un avance hacia niveles superiores de= pensamiento matem=C3=A1tico.Tabla 3<p= style=3D"margin-bottom:0pt; text-align:center; line-height:115%; font-size= :12pt">Uso= frecuente de tecnolog=C3=ADa en las clases de matem=C3=A1ticas<= table style=3D"margin-right:auto; margin-left:auto; margin-bottom:0pt; padd= ing:0pt; border-collapse:collapse"><tr><td style=3D"width:142.65pt; border-= top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5= .4pt; vertical-align:top">Nivel de acuerdo</td><td style=3D"width:147.6pt; border-top= :0.75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4p= t; vertical-align:top">Frecuencia</td><td style=3D"width:88.45pt;= border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; paddi= ng:0pt 5.4pt; vertical-align:top">Porcentaje (%)</td></tr><tr><td= style=3D"width:142.65pt; border-top:0.75pt solid #000000; padding:0pt 5.4p= t; vertical-align:top">Muy de acuerdo</td><td style=3D"width:147.6pt; border-top:0.= 75pt solid #000000; padding:0pt 5.4pt; vertical-align:top">37</td><td style=3D"widt= h:88.45pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-ali= gn:top">55 %= </td></tr><tr><td style=3D"width:142.65pt; padding:0pt 5.4pt; vertical-= align:top">De acuer= do</td><td style=3D"width:147.6pt; padding:0pt 5.4pt; vertical-a= lign:top">25= </td><td style=3D"width:88.45pt; padding:0pt 5.4pt; vertical-align:top"= >37 %</t= d></tr><tr><td style=3D"width:142.65pt; padding:0pt 5.4pt; vertical-align:t= op">En desacuerdo</= span></td><td style=3D"width:147.6pt; padding:0pt 5.4pt; vertical-align= :top">4<= /td><td style=3D"width:88.45pt; padding:0pt 5.4pt; vertical-align:top">6 %</td></tr= ><tr><td style=3D"width:142.65pt; padding:0pt 5.4pt; vertical-align:top"><p= style=3D"margin-bottom:0pt; line-height:115%; font-size:10pt">Muy en desacuerdo</td><td sty= le=3D"width:147.6pt; padding:0pt 5.4pt; vertical-align:top"><span= style=3D"font-family:'Times New Roman'">2</td><td style=3D"widt= h:88.45pt; padding:0pt 5.4pt; vertical-align:top">2 %</td></tr><tr><td style=3D"wid= th:142.65pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertica= l-align:top">Total</td><td style=3D"width:147.6pt; border-bottom:= 0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"><spa= n style=3D"font-family:'Times New Roman'; font-weight:bold">68</= td><td style=3D"width:88.45pt; border-bottom:0.75pt solid #000000; padding:= 0pt 5.4pt; vertical-align:top">100 %</td></tr></table><= span style=3D"font-family:'Times New Roman'"> <sp= an style=3D"font-family:'Times New Roman'">El 92% de los estudiantes manife= st=C3=B3 a favor con que la tecnolog=C3=ADa deber=C3=ADa emplearse con mayo= r frecuencia en las clases de matem=C3=A1ticas. Este resultado refleja una = aceptaci=C3=B3n generalizada de los entornos digitales como aliados del apr= endizaje, y sugiere que los estudiantes perciben estas herramientas como re= cursos leg=C3=ADtimos y efectivos para comprender contenidos complejos.</sp= an>La aceptaci= =C3=B3n positiva de la tecnolog=C3=ADa se asocia con la posibilidad de apre= nder a un ritmo propio, recibir retroalimentaci=C3=B3n inmediata y experime= ntar diferentes formas de resoluci=C3=B3n sin la presi=C3=B3n del error. Es= tas caracter=C3=ADsticas fortalecen la autonom=C3=ADa del estudiante y favo= recen la autorregulaci=C3=B3n del aprendizaje.Tab= la 4Trabajo colaborativo mediante herramientas tecnol=C3=B3gicas<= /span><table style=3D"margin-right:auto; margin-left:auto; margin-botto= m:0pt; padding:0pt; border-collapse:collapse"><tr><td style=3D"width:167.8p= t; border-top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; pad= ding:0pt 5.4pt; vertical-align:top">Niv= el de acuerdo</td><td style=3D"width:113.9pt; border-top:0.75pt = solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; verti= cal-align:top">Frec= uencia</td><td style=3D"width:74.25pt; border-top:0.75pt solid #= 000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-ali= gn:top">Porcentaje = (%)</td></tr><tr><td style=3D"width:167.8pt; border-top:0.75pt s= olid #000000; padding:0pt 5.4pt; vertical-align:top">Muy de acuerdo</td><td style= =3D"width:113.9pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt; vert= ical-align:top">39<= /span></td><td style=3D"width:74.25pt; border-top:0.75pt solid #000000;= padding:0pt 5.4pt; vertical-align:top">57 %</td></tr><tr><td style=3D"width:167.8p= t; padding:0pt 5.4pt; vertical-align:top">De acuerdo</td><td style=3D"width:113.9pt= ; padding:0pt 5.4pt; vertical-align:top">23</td><td style=3D"width:74.25pt; padding= :0pt 5.4pt; vertical-align:top">34 %</td></tr><tr><td style=3D"width:167.8pt; paddi= ng:0pt 5.4pt; vertical-align:top">En desacuerdo</td><td style=3D"width:113.9pt; pad= ding:0pt 5.4pt; vertical-align:top">5</td><td style=3D"width:74.25pt; padding:0pt 5= .4pt; vertical-align:top">7 %</td></tr><tr><td style=3D"width:167.8pt; padding:0pt = 5.4pt; vertical-align:top">Muy en desac= uerdo</td><td style=3D"width:113.9pt; padding:0pt 5.4pt; vertica= l-align:top">1</spa= n></td><td style=3D"width:74.25pt; padding:0pt 5.4pt; vertical-align:to= p">2 %</= td></tr><tr><td style=3D"width:167.8pt; border-bottom:0.75pt solid #000000;= padding:0pt 5.4pt; vertical-align:top">Total</td><td style=3D"width:113.9pt; borde= r-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top">68</td><td st= yle=3D"width:74.25pt; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt= ; vertical-align:top">100 %</td></tr></table> En cuanto al trabajo colaborativo, el 91% de los estudiante= s afirm=C3=B3 que el uso de herramientas digitales favorece el trabajo en e= quipo y el intercambio de ideas. Durante las sesiones, se observ=C3=B3 que = los estudiantes discut=C3=ADan estrategias, comparaban resultados y justifi= caban procedimientos, lo que promovi=C3=B3 un aprendizaje socialmente const= ruido.El= entorno digital facilit=C3=B3 la comunicaci=C3=B3n entre pares y permiti= =C3=B3 que los estudiantes aprendieran unos de otros, fortaleciendo habilid= ades sociales, argumentativas y comunicativas. Este resultado se alinea con= los principios del aprendizaje socio-constructivista, donde el conocimient= o se construye mediante la interacci=C3=B3n y el di=C3=A1logo guiado.</span= >Tabla 5Acceso a dispositivos tecnol=C3=B3gico= s en el hogar<table style=3D"margin-right:auto; margin-left:auto= ; margin-bottom:0pt; padding:0pt; border-collapse:collapse"><tr><td style= =3D"width:116.75pt; border-top:0.75pt solid #000000; border-bottom:0.75pt s= olid #000000; padding:0pt 5.4pt; vertical-align:top">Respuesta</td><td style=3D"width:116.75pt; border-= top:0.75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5= .4pt; vertical-align:top">Frecuencia</td><td style=3D"width:116.75pt; border-top:0.= 75pt solid #000000; border-bottom:0.75pt solid #000000; padding:0pt 5.4pt; = vertical-align:top">Porcentaje (%)</td></tr><tr><td style=3D"width:116.75pt; border= -top:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top">S=C3=AD</td><td = style=3D"width:116.75pt; border-top:0.75pt solid #000000; padding:0pt 5.4pt= ; vertical-align:top">47</td><td style=3D"width:116.75pt; border-top:0.75pt solid #= 000000; padding:0pt 5.4pt; vertical-align:top">69 %</td></tr><tr><td style=3D"width= :116.75pt; padding:0pt 5.4pt; vertical-align:top">No</td><td style=3D"width:116.75p= t; padding:0pt 5.4pt; vertical-align:top">21</td><td style=3D"width:116.75pt; paddi= ng:0pt 5.4pt; vertical-align:top">31 %</td></tr><tr><td style=3D"width:116.75pt; bo= rder-bottom:0.75pt solid #000000; padding:0pt 5.4pt; vertical-align:top"><p= style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-siz= e:10pt">Total</td>= <td style=3D"width:116.75pt; border-bottom:0.75pt solid #000000; padding:0p= t 5.4pt; vertical-align:top">68</td><td style=3D"width:116.75pt; border-bottom:0.75= pt solid #000000; padding:0pt 5.4pt; vertical-align:top">100 %</td></tr></table> Finalmente, el 69% de lo= s estudiantes report=C3=B3 contar con acceso a dispositivos tecnol=C3=B3gic= os en el hogar, mientras que el 31% indic=C3=B3 no disponer de ellos. Este = resultado evidencia que, aunque el acceso ha mejorado, a=C3=BAn persisten b= rechas digitales que influyen en las oportunidades de aprendizaje.</= p>No obstante, la i= mplementaci=C3=B3n de Polypad demostr=C3=B3 que, incluso en situaciones con= limitaciones tecnol=C3=B3gicas, es posible generar experiencias educativas= significativas si se cuenta con planificaci=C3=B3n pedag=C3=B3gica adecuad= a y uso estrat=C3=A9gico del tiempo y los recursos disponibles. Esto refuer= za la necesidad de pol=C3=ADticas educativas orientadas a garantizar condic= iones de equidad tecnol=C3=B3gica, especialmente en espacios rurales.</span= >3.3.<sp= an style=3D"font-family:'Times New Roman'; font-weight:bold"> An=C3=A1lisis in= tegral de los resultadosLos resultados obtenidos confirman que la implementaci=C3= =B3n de Polypad favorece significativamente el aprendizaje activo, la compr= ensi=C3=B3n conceptual y la motivaci=C3=B3n estudiantil. La mejora en el re= ndimiento acad=C3=A9mico no se limita a la memorizaci=C3=B3n de procedimien= tos, sino que se refleja en la capacidad de los estudiantes para razonar, e= xplicar y transferir conocimientos a nuevas situaciones.El uso de representaciones = visuales permiti=C3=B3 que los estudiantes comprendieran relaciones algebra= icas complejas mediante procesos intuitivos, reduciendo la ansiedad matem= =C3=A1tica y fortaleciendo la autoconfianza. Asimismo, la interacci=C3=B3n = constante con los recursos digitales promovi=C3=B3 un ambiente de aprendiza= je colaborativo, donde el error fue asumido como parte del proceso formativ= o.Estos = resultados confirman que la tecnolog=C3=ADa, cuando es utilizada de manera = planificada y con intencionalidad pedag=C3=B3gica, se convierte en un recur= so poderoso para mejorar la calidad educativa, especialmente en situaciones= donde se cuente con limitaciones estructurales.4. = 0; D= iscusi=C3=B3nLos resultados obtenidos en esta investigaci=C3=B3n confirman que la i= ntegraci=C3=B3n de herramientas digitales, espec=C3=ADficamente Polypad, co= nstituye una estrategia pedag=C3=B3gica efectiva para fortalecer el aprendi= zaje activo en matem=C3=A1ticas dentro de la Educaci=C3=B3n General B=C3=A1= sica. La mejora observada en el rendimiento acad=C3=A9mico, la motivaci=C3= =B3n estudiantil y la comprensi=C3=B3n conceptual coincide con los hallazgo= s reportados por diversas investigaciones recientes.<s= pan style=3D"font-family:'Times New Roman'">Uno de los principales aportes = de este estudio radica en evidenciar c=C3=B3mo el uso de representaciones v= isuales y manipulativas facilita la transici=C3=B3n desde un pensamiento ar= itm=C3=A9tico hacia un pensamiento algebraico m=C3=A1s estructurado. A dife= rencia de los enfoques tradicionales, que se centran en la memorizaci=C3=B3= n de procedimientos, la intervenci=C3=B3n realizada permiti=C3=B3 que los e= studiantes comprendieran el significado subyacente de las operaciones algeb= raicas, favoreciendo la construcci=C3=B3n de aprendizajes duraderos.= Asimismo, los r= esultados confirman que el aprendizaje activo no solo mejora el desempe=C3= =B1o acad=C3=A9mico, sino que tambi=C3=A9n impacta positivamente en factore= s emocionales como la motivaci=C3=B3n, la confianza y la reducci=C3=B3n de = la ansiedad matem=C3=A1tica. Los entornos digitales interactivos reducen el= miedo al error y promueven una actitud positiva hacia el aprendizaje, lo c= ual se evidenci=C3=B3 claramente durante las sesiones desarrolladas.= Otro aspecto re= levante es el papel del docente como mediador del aprendizaje. Los resultad= os indican que la tecnolog=C3=ADa no reemplaza la labor pedag=C3=B3gica, si= no que la potencia cuando se utiliza con intencionalidad did=C3=A1ctica. La= planificaci=C3=B3n de actividades, la formulaci=C3=B3n de preguntas orient= adoras y la retroalimentaci=C3=B3n constante fueron factores clave para que= los estudiantes aprovecharan al m=C3=A1ximo el entorno digital.= Esta investigaci=C3= =B3n aporta evidencia relevante para el sistema educativo ecuatoriano, espe= cialmente en zonas rurales donde existen limitaciones de infraestructura. L= os resultados demuestran que, aun en escenarios con recursos limitados, es = posible generar experiencias de aprendizaje significativas mediante el uso = estrat=C3=A9gico de herramientas digitales accesibles, como Polypad. Esto c= oincide con lo planteado por (Albuja et al. 2023) respecto a la necesidad d= e reducir las brechas educativas mediante propuestas pedag=C3=B3gicas innov= adoras.A= simismo, los hallazgos refuerzan la importancia de promover el pensamiento = matem=C3=A1tico temprano, tal como lo plantean Candela-Mu=C3=B1oz & Rod= r=C3=ADguez-G=C3=A1mez (2023) y Jimpikit et al. (2024) quienes destacan que= el desarrollo temprano de habilidades algebraicas facilita la transici=C3= =B3n hacia contenidos m=C3=A1s complejos en niveles superiores.<= p style=3D"margin-bottom:0pt; text-align:justify; line-height:115%; font-si= ze:12pt">Finalmente, los resu= ltados de esta investigaci=C3=B3n confirman que la integraci=C3=B3n de tecn= olog=C3=ADas educativas no debe entenderse como una moda pedag=C3=B3gica, s= ino como una estrategia fundamentada en evidencia cient=C3=ADfica que contr= ibuye al fortalecimiento de competencias matem=C3=A1ticas, cognitivas y soc= ioemocionales. La implementaci=C3=B3n de Polypad no solo mejora el rendimie= nto acad=C3=A9mico, sino que transforma la experiencia de aprendizaje, haci= =C3=A9ndola m=C3=A1s significativa, inclusiva y sostenible en el tiempo.</s= pan>5.<span= style=3D"width:9pt; font:7pt 'Times New Roman'; display:inline-block"> = 0; ConclusionesEl uso de Polypad como herramienta did=C3=A1ctic= a contribuye de manera significativa al fortalecimiento del aprendizaje act= ivo en matem=C3=A1ticas, especialmente en la comprensi=C3=B3n de operacione= s algebraicas.La implementaci=C3=B3n de estrategias basadas en herramientas digital= es permiti=C3=B3 mejorar el rendimiento acad=C3=A9mico, la motivaci=C3=B3n = y la participaci=C3=B3n estudiantil, evidenciando un impacto positivo tanto= cognitivo como emocional.El uso de representaciones visuales favoreci=C3=B3 la com= prensi=C3=B3n de conceptos abstractos como productos notables, t=C3=A9rmino= s semejantes y propiedades algebraicas, reduciendo errores frecuentes y for= taleciendo el razonamiento matem=C3=A1tico.La mediaci=C3=B3n docente desempe=C3=B1= =C3=B3 un rol fundamental en el =C3=A9xito de la intervenci=C3=B3n, confirm= ando que la tecnolog=C3=ADa debe ser utilizada como un medio pedag=C3=B3gic= o y no como un fin en s=C3=AD mismo.A pesar de las limitaciones de infraestructura,= el uso estrat=C3=A9gico de herramientas digitales demostr=C3=B3 ser viable= y eficaz en zonas educativas rurales.&= #xa0;6.</= span> Conflicto de InteresesLos autores declaran que no= existe conflicto de intereses en relaci=C3=B3n con el art=C3=ADculo presen= tado.= 7. Derechos de autor (copyri= gth) Los autores son los titulares de los derechos = de autor (patrimoniales y/= o de explotaci=C3=B3n) de los contenidos de la revista (copyright<span= style=3D"font-family:'Times New Roman'">).8. &#= xa0; Declaraci=C3=B3n de contribuci=C3=B3n de los autores</p= >Los autores declar= an haber participado de manera equitativa y sustancial en la realizaci=C3= =B3n de esta investigaci=C3=B3n, bajo las responsabilidades seg=C3=BAn la <= /span><a href=3D"https://credit.niso.org/" style=3D"text-decoration:none"><= span class=3D"Hyperlink" style=3D"font-family:'Times New Roman'">Taxonom=C3= =ADa CRediT</a> para d= escribir las contribuciones individuales de cada autor al trabajo. <= /p>Enrique Marcelo = Bustamante Salda=C3=B1a realiz=C3=B3 la conceptualizaci=C3=B3n de la invest= igaci=C3=B3n, organizaci=C3=B3n y ejecuci=C3=B3n del ensayo, recopilaci=C3= =B3n y curaci=C3=B3n de los datos, revisi=C3=B3n del an=C3=A1lisis estad=C3= =ADstico, interpretaci=C3=B3n de los resultados, elaboraci=C3=B3n del borra= dor original, preparaci=C3=B3n de tablas y figuras, revisi=C3=B3n cr=C3=ADt= ica del contenido y aprobaci=C3=B3n de la versi=C3=B3n final del manuscrito= .Divulgaci=C3=B3n de la delegaci=C3=B3n a la IA generativa</span= >Los autores de= claran que no se emplearon herramientas de apoyo para la elaboraci=C3=B3n d= e la presente investigaci=C3=B3n.Declaraci=C3=B3n presentada por: Enrique Marcelo Bustamante Salda=C3= =B1a. 9. 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Educational Ps= ychology Review, 36(1), 29. <a href=3D"https://link.springer.com/article/10.10= 07/s10648-024-09864-3%20%20" style=3D"text-decoration:none">https://link.springer.com/art= icle/10.1007/s10648-024-09864-3 </a> </spa= n><s= pan style=3D"font-family:'Times New Roman'"> <div style=3D"clear:both"><img src=3D"da= ta:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAuQAAAABCAYAAACWsrt9AAAABHNCSVQ= ICAgIfAhkiAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABxJREFUSIntwTEBAAAIwKDZP7TG8AGm2g= AAgA9zmTsBAl+AgmQAAAAASUVORK5CYII=3D" width=3D"740" height=3D"1" alt=3D"" s= tyle=3D"margin-top:-37.82pt; margin-left:-63.3pt; position:absolute" /></sp= an> = 0; = Nombre<span= style=3D"width:141.26pt; letter-spacing:3pt; display:inline-block"> <= /span> 1 </div></div> <div class=3D"Section_4"> = <spa= n style=3D"font-family:'Times New Roman'"> <= p style=3D"margin-bottom:0pt; line-height:normal; font-size:12pt"> </div></body></html>