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Enseñanza, aprendizaje y enfoque de la matemática en la ingeniería

Teaching, learning and approaching to mathematics in engineering<= ![endif]>

 

= 1

Henry David Loachamín Iza

https://orcid.org/0000-0003-2573-6228

 

 

Tercer nivel: Ingeniero en Mecatrónica

Cuarto nivel: Maes= tría en Docencia Universitaria, Maestría en Ingeniería Matemática y Computació= n

Ministerio de Educación

henrydavid= loachamin@gmail.com

= 2

Álvaro Patricio Vargas Chavarrea

<= ![endif]>

https://orcid.org/0000-0001-9743-6449

 

 

 Tercer nivel: Ingeniero en Electrónica= y Computación

Cuarto nivel: Maes= tría en Tecnologías Educativas y Competencias Digitales

Instituto Superior Tecnológico Liceo Aduanero

avargas@liceoaduanero.edu.ec

= 3

Jefferson Vladimir Andrade Villarreal

<= ![endif]>

https://orcid.org/0000-0003-4302-745X

 

 

Tercer nivel: Ingeniero en Mecatrónica

Cuarto nivel: Maes= tría en Diseño Mecánico

Universidad Técnica del Norte

jvandradev= 1@utn.edu.ec

= 4

Pablo Francisco Pu= ente Ponce

<= ![endif]>

https://orcid.org/0000-0001-8884-6905

 

 

Tercer nivel: Ingeniero en Sistemas

Cuarto nivel: Maes= tría en Ingeniería de Software

Escuela Politécnica del Ejército

pfpuente@espe.edu.ec

 

 =

 

Artículo de Investigación Científica y Tecnológica

Enviado: 10/06/2023

Revisado: 25/07/2023

Aceptado: 07/08/2023

Publicado:20/09/2023

DOI: https://doi.or= g/10.33262/ap.v5i3.2.400

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

 

 

Cítese:

 

 

Loachamín Iza, H. D., Vargas Chavarrea, Álvaro P., Andr= ade Villarreal, J. V., & Puente Ponce, P. F. (2023). Enseñanza, aprendiza= je y enfoque de la matemática en la ingeniería. AlfaPubli= caciones, 5(3.2), 6–20. https://= doi.org/10.33262/ap.v5i3.2.400

 

 

 

ALFA PUBLICACIONES, es una revista multidisciplinar, trimestral, que se public= ará en soporte electrónico tiene como misión contribuir a la &nbs= p; formación de profesionales competentes con visión humanística y crítica q= ue sean capaces de exponer sus resultados investigativos y científicos en la misma medida que se promueva mediante su intervención cambios positivos e= n la sociedad. https://alfapublicaciones.= com  

3Deditorial1.pngLa revista es editada por la Editorial Ciencia Digital (Editorial de prestigio registrada en la Cámara Ecuatoria= na de Libro con No de Afiliación 663) www.celibro.org.ec<= /a>

 

 

 

Esta revista está protegida bajo una licencia Creative Common= s Attribution Non Commerci= al No Derivatives 4.0 International. Copia de la licencia: http://creativecommons.org= /licenses/by-nc-nd/4.0/

 

Pala= bras claves:=

Enseñanza, aprendizaje, enfoque, matemát= ica, ingeniería.

 

Resumen

Introducción. La ingeniería es un campo que impulsa el progr= eso y la innovación en nuestra sociedad. Desde la construcción de estructuras impresionantes hasta el desarrollo de tecnologías vanguardistas, los ingenieros desempeñan un papel crucial en dar forma al mundo que nos rode= a. Sin embargo, detrás de cada logro ingenieril se encuentra una base sólida= de conocimientos matemáticos que permite la conceptualización, el diseño y la resolución de problemas complejos. Las matemáticas son el lenguaje univer= sal que consiente la comunicación y el entendimiento de los fenómenos natural= es y las aplicaciones tecnológicas. La interacción entre las matemáticas y la ingeniería es tan profunda que se podría afirmar que la matemática es el cimiento sobre el cual se erige la ingeniería. Objetivo. Analizar y comprender cómo se aborda la enseñanza, el aprendizaje y el enfoque de las matemáticas en el contexto de la ingeniería, con el propósito de mejorar = la formación de los estudiantes y su capacidad para aplicar conceptos matemáticos en la resolución de problemas ingenieriles. Metodología. <= /b>Mediante la técnica de análisis documental, en la que se revisan diferentes fuente= s de información científica. Resultados. La enseñanza y aprendizaje de la matemática en la ingeniería debe ser relevante, activo, funcional e interdisciplinario, con una perspectiva en el desarrollo de habilidades de aplicación y pensamiento crítico. El enfoque de la matemát= ica en la ingeniería debe ser altamente direccionado a la aplicación práctica= y a superar los desafíos de la ingeniería para el siglo XXI, con una base sól= ida en conceptos matemáticos fundamentales. Conclusión. El docente debe adaptar sus métodos de enseñanza para capacitar de manera efectiva a estudiantes de ingeniería, la mayoría= de los cuales no se especializarán en matemáticas, pero usarán las matemátic= as como una herramienta esencial en sus futuras carreras. La dificultad en el aprendizaje del cálculo en ingeniería a menudo se relaciona con un enfoqu= e de enseñanza que fomenta la memorización y la aplicación mecánica en busca de respuestas finales correctas, en lugar de centrarse en un enfoque que priorice el proceso, el contexto y la comprensión con claridad y coherenc= ia.

 

Keywords: Teaching, learning, approaching, mathematics, engineering.

 

Abstract

Introduction. Engineering is a field that drives progress and innovation in our society. From building impressive structures to developing cutting-edge technologies, engineers play a crucial role in shaping the world around u= s. However, behind every engineering achievement lies a solid foundation of mathematical knowledge that enables the conceptualization, design, and resolution of complex problems. Mathematics is the universal language that allows communication and understanding of natural phenomena and technolog= ical applications. The interaction between mathematics and engineering is so d= eep that it could be said that mathematics is the foundation on which enginee= ring is built. Objectiv= e. Analyze and understand how the teachi= ng, learning and approach of mathematics is approached in the context of engineering, with the purpose of improving the training of students and t= heir ability to apply mathematical concepts in solving engineering problems. Methodology. Through the documentary analysis technique, in which different sources of scientific information are reviewed. Results. The teaching and learnin= g of mathematics in engineering must be relevant, active, functional and interdisciplinary, with a perspective on the development of application skills and critical thinking. The focus of mathematics in engineering mus= t be highly directed to the practical application and to overcome the challeng= es of engineering for the XXI century, with a solid foundation in fundamental mathematical concepts. Conclusion. The teacher must adapt their teaching methods to effectively train engineering students, most of whom will not major in mathematics, but will use mathematics as an essential tool in their future careers. Difficulty = in learning engineering calculus is often related to a teaching approach that encourages memorization and rote application in search of final correct answers, rather than focusing on an approach that prioritizes process, context, and understanding. clearly and coherently.

 

 

 

&n= bsp;

Introducción<= /b>

La enseñanza, aprendizaje y enfoque de las matemáticas en la ingeniería constituyen un aspecto crítico en la formación de futuros profesionales en = este campo. La habilidad de aplicar y comprender conceptos matemáticos es esenci= al para abordar con éxito los desafíos y problemas complejos que los ingenieros enfrentan en su labor diaria. En esta investigación, exploraremos cómo los métodos de enseñanza, las estrategias de aprendizaje y el enfoque de las matemáticas en la ingeniería pueden influir en la preparación de los estudiantes para enfrentar los retos tecnológicos y científicos en la indus= tria actual. Además, examinaremos cómo la adaptación de enfoques didácticos alternativos puede fomentar una comprensión más profunda y aplicada de las matemáticas, permitiendo que los futuros ingenieros utilicen estas herramie= ntas con mayor eficacia en sus campos de especialización. En última instancia, e= ste tema es fundamental para comprender cómo la integración efectiva de las matemáticas en la educación de ingeniería contribuye al desarrollo de soluciones innovadoras y al avance de la ingeniería moderna.

Metodología

La  realización  de este análisis  sistemático  de  literatura  se  basó  en la técnica de análisis documental, en la que se identifican, reco= gen y examinan escritos de orden científico, revistas de investigaciones, tesis= de grado, documentos de  organismos  internacionales  emitidos  bajo  los  más  estrictos  estándares  científicos académicos, investigaciones científicas que proporcionan la información necesaria para detallar el cont= exto estudiado.

Resultados y discusión

Enseñanza de la matemática en la ingeniería

La enseñanza de la matemática es esencial para proporcionar al estudiante universitario las habilidades y conocimientos necesarios para abordar probl= emas y desafíos en la ingeniería. Debe ir enfocada en la aplicación práctica de = los conceptos matemáticos y su integración con otras ciencias.

Por ejemplo, (Sold= ini y otros) exponen que la enseñanza de la Matemática no debe suponer una mera transmis= ión de conocimientos con énfasis en el desarrollo de habilidades operacionales, sino el desarrollo en el educando de habilidades templadas en una rigurosa comprensión de nociones y conceptos. Al enfocarse en el desarrollo de habilidades templadas en una rigurosa comprensión de nociones y conceptos matemáticos, se fomenta el pensamiento crítico, se genera una base sólida, = se promueve la resolución de problemas, se estimula la transferencia de conocimientos y se aumenta el interés y la motivación de los estudiantes.

(Plaza Gálvez, 2017), asegura que el docente de matemáticas en programas de ingeniería debe promover determinadas habilidades entre sus alumnos; algunas de crucial importancia son las siguientes:

= 1.      Pensamiento holístico, investigación crítica, análisis y reflexión.

= 2.      Aprendizaje activo y aplicación práctica.

= 3.      Autoconsciencia y empatía.

= 4.      Comunicación y una fuerte capacidad de escucha.

Adicionalmente, cabe destacar que el pensamiento sistémico y crítico se consideran dos competencias transversales, importantes a desarrollar por un ingeniero, ciudadano del siglo XXI.

Al utilizar el pensamiento sistémico, se busca comprender cómo los diferentes elementos interactúan y cómo los cambios en uno de ellos pueden afectar a l= os demás. Esto implica identificar las relaciones de causa y efecto, los retrocesos y los bucles de realimentación que pueden estar presentes en un sistema. Al comprender estas dinámicas, se pueden diseñar intervenciones más efectivas y soluciones más sostenibles. También  ayuda  a  ampliar  el  racionamiento  humano,  contribuye  en  la  eliminación  de  paradigmas  mentales que dificultan la comprensión de los procesos y sistemas, y fomenta la apertura  a  nuevo  conocimiento  y  a  la  práctica científica (Liévano Martínez & Enrique Londoño, 2012).

El pensamiento crítico involucra un enfoque sistemático y estructurado para analizar y evaluar la información. Esto implica ser capaz de identificar suposiciones, detectar sesgos, evaluar la validez y fiabilidad de las fuent= es de información, reconocer argumentos sólidos y fallidos, y llegar a conclusiones basadas en la evidencia y el razonamiento lógico. (Campos Fabian, 2012) concluye que un mayor o menor nivel de pensamiento crítico, se asocia con un mayor o menor aprendizaje de la matemática. Sin embargo, cabe decir que esta relación o asociación positiva es débil, lo cual significa que, un buen nivel de pensamiento crítico no asegura un buen aprendizaje del curso de matemática = en todos los casos, tampoco lo contrario; pero si se puede decir que los estudiantes que muestran un mejor nivel de pensamiento crítico tienen mayor posibilidad de alcanzar un buen aprendizaje en el curso de matemática, porq= ue en las primeras etapas de resolución de problemas matemáticos, como la comprensión e interpretación de datos, requieren de un pensamiento reflexiv= o y razonando para decidir qué hacer en las siguientes etapas.

Por otra parte, (Moreno, 2005) menciona que la enseñanza de los principios del cálculo resulta bastante problemática, y aunque seamos capac= es de enseñar a los estudiantes a resolver de forma más o menos mecánica algun= os problemas estándar, o bien a realizar algunas derivadas o integrales, tales acciones están muy lejos de lo que supondría una verdadera comprensión de l= os conceptos y métodos de pensamiento de esta parte de las matemáticas. Es dec= ir, la enseñanza de la matemática debe tener una perspectiva no solo teórica, s= ino también práctica y aplicada. Donde los estudiantes comprendan los conceptos matemáticos desde una perspectiva ingenieril y puedan aplicarlos para resol= ver problemas reales. Esto implica la utilización de ejemplos y ejercicios relacionados con situaciones y fenómenos propios de la ingeniería.

La enseñanza de la matemática en la ingeniería debe tener integración con otras disciplinas, como la física, la química, la informática, entre otras. Es co= mún que se realicen conexiones entre estos campos del conocimiento para mostrar cómo la matemática se aplica en diferentes contextos y cómo contribuye al desarrollo de soluciones ingenieriles.

En la actualidad, el uso de herramientas tecnológicas, como software de cálculo simbólico, hojas de cálculo y programas de visualización, es fundamental en= la enseñanza de la matemática en la ingeniería. Estas herramientas permiten realizar cálculos complejos de manera más eficiente y visualizar los resultados, lo cual facilita la comprensión de los conceptos y su aplicació= n en problemas de ingeniería.

Por lo tanto, la enseñanza de la matemática debe incluir una planificación o di= seño curricular donde se evalué cómo se integran los contenidos matemáticos en l= os programas de estudios de ingeniería y cómo se estructuran para lograr una progresión coherente de habilidades y conocimientos. También, deben estar presentes las metodologías de enseñanza que permiten investigar las diferen= tes estrategias pedagógicas utilizadas para impartir conceptos matemáticos en contextos de ingeniería, como el aprendizaje activo, el enfoque de resoluci= ón de problemas y el uso de ejemplos prácticos. Y finalmente, nos ayuda mucho = la tecnología educativa que destaca por analizar cómo se incorporan herramient= as tecnológicas, software y simulaciones en la enseñanza de las matemáticas, y cómo estas tecnologías pueden mejorar la comprensión y la aplicación de conceptos matemáticos en situaciones ingenieriles reales.=

Aprendizaje de la matemática en la ingeniería

El aprendizaje de la matemática en la ingeniería es fundamental para el desarr= ollo de habilidades de pensamiento crítico, lógica, resolución de problemas y razonamiento abstracto, lo que permite a los ingenieros enfrentar desafíos complejos y tomar decisiones instruidas en situaciones que implican múltipl= es variables y factores. De forma similar, (Iglesias Domecq & Alonso Berenguer, 2017) mencionan que = dentro de las ciencias básicas que requiere un ingeniero, para desempeñarse eficientemente en su campo de acción, se destaca la Matemática, disciplina = que contribuye al desarrollo de su pensamiento lógico y algorítmico, aportándole los fundamentos básicos de un especialista en ciencias técnicas, dado que t= odo ingeniero realiza las representaciones técnicas y científicas en términos matemáticos, con los cuales refleja los rasgos cuantitativos y cualitativos= de los fenómenos que estudia.

Así mismo, (Contreras, 2013), plantea que el ingeniero trabaja tomando decisiones que pueden ser técnicas o de otro tipo, por lo que debe acostumbrarse a razonar en forma ordenada, y esto sólo lo logra cuando sabe Matemática; ya que es objetiva, clara y universal, como se espera que sean = las actuaciones de un ingeniero, por eso él debe nutrir su mentalidad con esta ciencia.

Varias investigaciones han detallado la importancia de aprender matemática en el inicio de una carrera de ingeniería, ya que es la base de muchas de las ciencias aplicadas y tecnologías modernas. Por ejemplo, (Zuñiga, 2007) explica que durante la formación de= los ingenieros se debe poner énfasis en desarrollar mentes maduras y educar ingenieros que puedan pensar. Identifica al uso de las técnicas matemáticas como: “un medio poderoso para lograr este objetivo sobre todo si son utiliz= adas para describir, modelar y resolver situaciones técnicas. La matemática es la herramienta más poderosa para el ingeniero y su dominio desde los principio= s de su carrera le permitirá un rápido progreso en temas específicos de su forma= ción profesional”.

En la ingeniería, el aprendizaje de la matemática comienza desde las bases, con conceptos como aritmética, álgebra, geometría y trigonometría. Luego, los estudiantes de ingeniería avanzan hacia temas más complejos como cálculo diferencial e integral, ecuaciones diferenciales, estadísticas y probabilid= ad. El estudiante de nivel superior debe concebir a que todas estas partes de la matemática vayan más allá de la aplicación de teoremas y procedimientos en problemas matemáticos.

(Ruiz Ledesma y otros, 2016), exponen que la formación de ingenieros demanda un considerable aprendizaje de las matemáti= cas que contribuyan a resolver problemas de orden técnico y tecnológico, pero s= obre todo práctico. Las matemáticas que requiere un ingeniero deben constituir recursos, herramientas e instrumentos capaces de lograr la optimización en = el uso de los recursos que la humanidad posee y requiere para su desarrollo. Un problema importante presentado en este artículo es que el conocimiento generalmente se trata fuera de contextos apropiados. Así, cuando se pretende mostrar a los estudiantes la utilidad de los contenidos que se estudian, a = lo más que se llega en un curso común de cálculo es a resolver los llamados problemas de aplicación que se proponen en los textos, que casi nunca corresponden a la realidad.

Por otra parte, (Trejo y otros, 2013) expresa que pa= rte de la problemática en ingeniería es que la matemática se encuentra totalmente desvinculada de las asignaturas de la ingeniería, y la realidad del ingenie= ro reclama esta vinculación que en materia de educación está en tierra de nadi= e. Es decir, más allá de memorizar fórmulas y procedimientos, el aprendizaje d= e la matemática en la ingeniería se centra en la comprensión conceptual. Los estudiantes deben entender los fundamentos matemáticos y las conexiones ent= re diferentes conceptos. Esto les permite aplicar principios matemáticos de ma= nera efectiva en la resolución de problemas de ingeniería.

La resolución de problemas desempeña un papel central en el aprendizaje de la matemática en la ingeniería. Los estudiantes deben enfrentarse a situaciones desafiantes y aplicar sus conocimientos matemáticos para analizar y resolver problemas prácticos. Esto implica la identificación de variables relevantes= , la formulación de ecuaciones o modelos matemáticos apropiados, y la interpreta= ción y comunicación de los resultados obtenidos.

El aprendizaje de la matemática en la ingeniería se beneficia al relacionar los conceptos matemáticos con situaciones y problemas reales, ya que los educan= dos deben comprender cómo la matemática se aplica en el mundo de la ingeniería y cómo contribuye a la toma de decisiones fundamentadas. Esto se logra a trav= és de la resolución de ejercicios y proyectos prácticos que reflejen situacion= es de ingeniería realistas.

En la actualidad, el uso de la tecnología es enriquecedor para aprender matemática, no solo en ingeniería sino en cualquier nivel educativo. Los estudiantes deben familiarizarse con software especializado, como paquetes = de cálculo numérico, software de simulación y programación, que les permiten resolver problemas complejos y explorar conceptos matemáticos en un entorno virtual. Además, el uso de calculadoras gráficas y software de visualización ayuda a comprender y comunicar resultados de manera más efectiva.

En la ingeniería, el aprendizaje de la matemática a menudo se realiza en un contexto colaborativo, ya que los universitarios trabajan en equipos para abordar problemas complejos, discutir ideas y compartir soluciones. Esto fomenta el intercambio de conocimientos, la resolución de problemas desde diferentes perspectivas y el desarrollo de habilidades de comunicación y trabajo en equipo, que son esenciales en el ámbito ingenieril.

Finalmente, debemos considerar la valoración del aprendizaje donde exploremos métodos de evaluación que permi= tan medir de manera efectiva la comprensión de los estudiantes en relación con = los conceptos matemáticos y su capacidad para aplicarlos en la resolución de problemas prácticos. Es muy importante también la motivación y percepción de los estudiantes, donde se puede investigar cómo se fomenta el interés de los educandos por las matemáticas en el contexto de la ingeniería y cómo se abo= rdan posibles obstáculos o desafíos que puedan surgir. Igualmente, la interdisciplinariedad es muy transcendental debido a que nos permite conect= ar las matemáticas con otras disciplinas dentro de la ingeniería y examinar es= ta integración tanto en el enriquecimiento del aprendizaje de las matemáticas = como en la formación de la ingeniería en general.

Enfoque de la matemática en la ingeniería

El estudiante de ingeniería, si bien requiere de la matemática pura para su formación científica, en la práctica está ligado a la matemática aplicada. Diferenciar entre las dos es primordial en la capacitación del futuro ingeniero, ya que la primera es el análisis de las concepciones básicas que subyacen a la matemática, y su objeto es buscar una comprensión más profund= a y un conocimiento más amplio de la misma; mientras que en su forma aplicada se utiliza para solucionar problemas ingenieriles utilizando herramientas, estrategias y métodos matemáticos donde se combinan dos o más ramas de la matemática pura.

(Blum & Niss, 1991), explican que = la forma de describir la interacción entre el mundo real y las matemáticas es = bien conocida y de ninguna manera es nuestra invención. El punto de partida es un problema aplicado o, como también lo llamamos, una situación problema real. Esta situación tiene que ser simplificada, idealizada, estructurada, sujeta= a condiciones y supuestos apropiados. Esto conduce a un modelo real de la situación original que, por un lado, todavía contiene características esenciales de la situación original, pero por otro lado ya está tan esquema= tizado que (si es posible) permite un enfoque con medios matemáticos. Tomando en cuenta lo anterior se puede mencionar que en la ingeniería, el enfoque de la matemática se centra en la aplicación práctica= de los conceptos matemáticos para resolver problemas reales. Los ingenieros utilizan las matemáticas para analizar y diseñar sistemas, construir modelo= s y realizar cálculos para optimizar la eficiencia y la seguridad en una varied= ad de procesos.

Por su parte, (Chatterjee, 2005) considera que la Ingeniería se desarrolla en función de mejorar las condiciones de la vida humana por medio del uso deliberado de las leyes de la naturaleza para poder explotar sus recursos de forma óptima, lo que implica que su interés está más en lograr aplicaciones prácticas (es decir, en resolver problemas), donde para lograr esto hace uso de las matemáticas y particularmente del cálculo.<= /span>

La matemática y la ingeniería desde sus inicios han establecido una dupla que = ha coexistido para el beneficio y el progreso de ambas disciplinas; la ingenie= ría proporciona problemas de fenómenos auténticos a la matemática que le ha permitido tener un instrumento con la cual ha experimentado un desarrollo f= irme en la solución de muchas dificultades técnicas que se han presentado (Giler-Velásquez, 2020).

En este mismo contexto, Iriarte Balderrama expone que “la ingeniería no existi= ría sin las matemáticas. A la inversa, la sentencia podría ser falsa, las matemáticas existen, independientemente de la ingeniería. Sin embargo, para= los ingenieros, lo importante es convencerse, no de las matemáticas en sí misma= s, sino de la aplicación de ellas. Las matemáticas aplicadas son las que han permitido lograr el desarrollo que ha alcanzado la ingeniería”.<= /span>

La matemática es una herramienta imprescindible en la ingeniería, ya que permi= te modelar y resolver problemas complejos que se presentan en el diseño, análi= sis y optimización de sistemas y procesos. En general, el enfoque de la matemát= ica en la ingeniería se centra en dos áreas principales: el cálculo y el álgebra lineal.

El cálculo infinitesimal es una de las "herramientas matemáticas" más potentes que utiliza la ciencia en el estudio del mundo físico y sus leyes.= En el estudio del mundo natural hay que medir con la mayor precisión posible, = las múltiples formas geométricas que existen en él, y que en muchos casos son m= uy irregulares, y no se pueden hacer tales mediciones con fórmulas sencillas de geometría elemental. También acontecen en él muchos procesos de cambio, cuyo estudio preciso, requiere conocer las "tasas de variación instantáneas", de los cambios que ocurren en tales procesos a medida q= ue transcurre el tiempo (Villalba, 2020). El cálculo es fundamental para la ingeniería porque proporciona los conocimientos para modelar y analizar sistemas dinámicos. Permite determinar cómo cambian las variables con respecto al tiempo, lo que es fundamental para la comprensión= de sistemas físicos como el movimiento de un objeto, el flujo de un fluido o la propagación de ondas. Además, el cálculo es utilizado en la ingeniería para optimizar sistemas, por ejemplo, para encontrar la máxima eficiencia en la producción de energía o en la utilización de recursos.

El álgebra lineal es otra área importante de la matemática en la ingeniería, q= ue se centra en el estudio de sistemas de ecuaciones lineales y sus propiedade= s. Esta área se utiliza en la ingeniería para modelar y resolver problemas que implican la manipulación de grandes cantidades de datos, como el análisis de señales, la compresión de imágenes y la resolución de sistemas de ecuaciones diferenciales. Además, el álgebra lineal es esencial en el diseño de sistem= as de control, ya que permite modelar la dinámica de los sistemas y diseñar controladores que los estabilicen. Considerando lo antepuesto (Costa & Rossignoli, 2017), explica que e= stos conceptos, tienen conexión y utilidad para la resolución de diversos proble= mas en muchas áreas dentro de la matemática y también en otra ciencias e ingeniería. Por ejemplo, los sistemas de ecuaciones lineales, permiten mode= lar infinidad de problemas reales. Los valores y vectores propios asociados a u= na matriz o a una transformación lineal, poseen varias aplicaciones prácticas = en la ingeniería. Entre ellas, podemos mencionar el estudio de la estabilidad = de una estructura y sus frecuencias y modos naturales de vibración, el análisi= s de la convergencia de métodos numéricos para resolver sistemas de ecuaciones l= ineales algebraicas, la determinación de los ejes principales de inercia de un cuer= po rígido (Thomson, 1993), la resolución de sistemas de ecuaciones diferenciales lineales y el estudio de la estabilidad de sistema= s de ecuaciones diferenciales generales = (Penney & Edwards, 2008). También tienen aplicación para el estudio de las formas bilineales y cuadráticas y aplicaciones en el Cálculo Infinitesimal como la optimización de funciones = de varias variables. Además los conceptos del Algebra Lineal son esenciales en= la teoría de Control Moderno (Amato, 2006).

Según la National Academy= of Engineering, los principales desafíos de la ingenierí= a para el siglo XXI se dividen en cuatro temas transversales: sostenibilidad, salu= d, seguridad y placer de vivir. A continuación, se enlistan los 14 desafíos sugeridos por líderes tecnológicos: 

·      =    Aprendizaje personalizado avanzado

·      =    Hacer económica la energía solar<= /o:p>

·      =    Mejorar la realidad virtual=

·      =    Ingeniería inversa del cerebro

·      =    Diseñar mejores medicamentos

·      =    Informática sanitaria avanzada

·      =    Restaurar y mejorar la infraestructura urbana

·      =    Ciberespacio seguro<= /p>

·      =    Proporcionar acceso a agua limpia=

·      =    Proveer energía desde la fusión

·      =    Prevenir el terror nuclear<= /span>

·      =    Gestionar el ciclo del nitrógeno<= /o:p>

·      =    Desarrollar métodos de captura de carb= ono

·      =    Diseñar herramientas para el descubrimiento científico (National Academy of Engineering, 2023)

Los desafíos de la ingeniería que = se relacionan con la matemática son diversos y requieren del uso de herramient= as matemáticas avanzadas y del conocimiento profundo de las matemáticas aplica= das a la técnica para encontrar soluciones óptimas y eficientes a los problemas prácticos que se presentan en distintas áreas de la ingeniería y que abarqu= en a los cuatro ejes transversales que me permitan mejorar la vida del ser human= o en el planeta. De manera general se pueden señalar algunos de los desafíos de = la ingeniería que se relacionan con la matemática:                   

1.&n= bsp;     Modelado matemático: Uno de los principales desafío= s de la ingeniería es la creación de modelos matemáticos precisos y realistas de= los sistemas y procesos que se desean analizar y diseñar. Estos modelos deben s= er capaces de representar de manera adecuada el comportamiento de los sistemas= , lo que puede requerir el uso de herramientas matemáticas avanzadas.

2.&n= bsp;     Optimización: La optimización es un área de las matemáticas que tiene una gran aplicación en la ingeniería. Los ingenieros deben encontrar las mejores soluciones posibles a los problemas de diseño, producción y operación, lo que implica la maximización o minimización de ciertas variables. Para ello, deben utilizar técnicas de optimización matemática para encontrar la solución más óptima.

3.&n= bsp;     Análisis numérico: La resolución de ecuaciones y sistemas de ecuaciones es una tarea fundamental en la ingeniería. Los ingenieros utilizan herramientas de análisis numérico para realizar cálculos complejos y resolver ecuaciones que no tienen solución analítica.

4.&n= bsp;     Simulación: La simulación es una técnica que permite prever el comportamiento de un sistema o proceso en un entorno virtual ante= s de implementarlo en la vida real. Para realizar simulaciones precisas, los ingenieros deben utilizar modelos matemáticos complejos y herramientas de análisis numérico avanzadas.

5.      Control automático: Los sistemas de control automático son fundamentales en la ingeniería, especialmente en la industria y la robótica. Estos sistemas utilizan algoritmos matemáticos para controlar el comportamiento de un sist= ema en tiempo real. Los ingenieros deben ser capaces de diseñar y programar est= os sistemas utilizando herramientas matemáticas avanzadas.

La ingeniería es una disciplina qu= e se basa en la aplicación de la matemática para resolver problemas prácticos en diversos campos, como la mecánica, la electrónica, la robótica, la informát= ica, la agricultura, entre otros. Los desafíos de la ingeniería que se relacionan con la matemática son diversos y requieren del uso de herramientas matemáti= cas avanzadas y del conocimiento profundo de las matemáticas aplicadas a la ingeniería para encontrar soluciones óptimas y eficientes a los problemas prácticos que se presentan en distintas áreas de la ingeniería.

Conclusiones

·      =    El docente debe meditar sobre sus méto= dos de enseñanza para brindar una instrucción efectiva a una población estudian= til que, en su mayoría, no se especializará en matemáticas, pero que empleará l= as matemáticas como una herramienta fundamental en su futura carrera de ingeniería.

·      =    Es factible argumentar que la dificult= ad en el proceso de aprender cálculo en el campo de la Ingeniería está estrechamente relacionada con la forma en que se imparte. Con frecuencia, la enseñanza tiende a promover un enfoque de memorización y aplicación mecánic= a, orientado principalmente a obtener respuestas finales, de preferencia correctas. Esto contrasta con un enfoque de aprendizaje que da mayor importancia al proceso= , al contexto y a la comprensión, con claridad y coherencia.

·      =    Para abordar las dificultades en la en= señanza y el aprendizaje de las matemáticas en programas de ingeniería, es esencial desarrollar enfoques didácticos alternativos que permitan una mejor compren= sión y que estén relacionados con las aplicaciones prácticas; esto hará que el estudio del cálculo tenga significado en los contextos ingenieriles y sea de interés para los estudiantes.

·      =    El enfoque de la matemática en la ingeniería se centra en el uso de herramientas matemáticas para modelar, analizar y optimizar sistemas y procesos complejos en diversas áreas ingenieriles, como: industria, agricultura, genética, mecánica, electrónica, software, entre otras; lo que a su vez contribuye al desarrollo de tecnolog= ías innovadoras y soluciones eficientes. El cálculo y el álgebra lineal son áre= as esenciales de la matemática, que se utilizan ampliamente en la mayoría de l= as disciplinas técnicas para la innovación y el avance en la ingeniería modern= a.

Referencias<= /i> bibliográficas

<= w:sdtPr>

Amato, F. (2006). Robust con= trol of linear systems subject to uncertain time-varying parameters (Vol. 325)= . Berlin: Springer.

Blum, W= ., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects — State, trends and issues in mathematics instruction. Educational Studies in Mathematics volume, 37-68.

Campos Fabian, D. R. (2012). Pensamiento crítico y aprendizaje del curso de Matemática en estudiantes ingresantes a dos universidades peruanas – Lima, 2019. Universidad Nacional Mayor de San Marcos : http://cybertesis.unmsm.edu.pe/handle/20.500.12672/18244

Chatter= jee, A. (2005). Mathematics in Engineering. Cu= rrent Science, 88(3), 405-414.<= /o:p>

Contreras, M. (2013). UNIVERSIDAD DE CHILE. Ingeniería Civil Matemática: https://www.uchile.cl/carreras/4974/ingenieria-civil-matematica

Costa, V. A., & Rossignoli, R. (2017). Enseñanza del algebra lineal en una facultad de ingeniería: Aspectos metodológicos y didácticos. Educación en Ingeniería, 12(23), 49-55.

Giler-Velásquez, L. E. (2020). Estrategias de enseñanza= de la matemática en la formación de profesionales de la ingeniería. Domin= io de las Ciencias, 273-285.

Iglesias Domecq, N., & Alonso Berenguer, I. (2017). ESTUDIO EXPLORATORIO SOBRE LA IMPORTANCIA DE LA MATEMÁTICA PARA LA CARRER= A DE INGENIERÍA CIVIL EN LA UNIVERSIDAD DE ORIENTE. Revista Electrónica Formación y Calidad Educativa (REFCalE) ISSN 1390-9010, 5(1), 45-62.<= o:p>

Liévano Martínez, F., & Enrique Londoño, J. (2012).= El pensamiento sistémico como herramienta metodológica para la resolución de problemas. Revista Soluciones de Postgrado, 4(8), 43-65.

Moreno, M. d. (2005). El papel de la didáctica en la enseñanza del cálculo: evolución, estado actual y retos futuros. Noveno Simposio de la Sociedad Española de Educación Matemática SEIEM, 81-96= .

National Academy of Engineering. (2023). 14 Grand Challenges for Engineering in= the 21st Century. http://www.engineeringchallenges.org/8996.aspx

Penney,= D. E., & Edwards, C. H. (2008). Ec= uaciones Diferenciales. Pearson Educación.=

Plaza Gálvez, L. F. (2017). Modelación matemática en ingeniería. IE Revista de investigación educativa de la REDIECH, 7= (13), 47-57.

Ruiz Ledesma, E. F., Carmona García, E. A., & Salva= dor Montiel, Á. (2016). IMPORTANCIA DEL CÁLCULO EN EL DESARROLLO ACADÉMICO DEL INGENIERO. Pistas educativas, 38(120), 402-420.<= /p>

Soldini= , M. J., Gaitán, M. M., & Klimovsky, E. (s.f.). Enseñar Matemática en Carreras de Ingeniería: reflexion= es sobre la práctica. https://www.aidu-asociacion.org/wp-content/uploads/2020/02/CIDU-Rosario-3= 68.pdf

Thomson= , W. T. (1993). Theory of vibration with applications. NASA STI/Recon Technical Report A.

Trejo, E., Patricia, C., & Trejo, N. (2013). Las matemáticas en la formación de un ingeniero: la matemática en contexto co= mo propuesta metodológica. REDU Revista de Docencia Universitaria, 11= (1), 397-424.

Villalba, J. (2020). Matemáticas para la Universidad= , 5. Independently Published.

Zuñiga, L. (2007). El cálculo en carreras de ingeniería= : un estudio cognitivo. Revista latinoamericana de investigación en matemát= ica educativa, 145-175.

 

Conflicto de intereses

Los autores deben declarar si existe o no conflicto de intereses en relación co= n el artículo presentado.

3Dedito=

 =

 

 

 

 

 

 

 

 

 

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

 

3Dedito=

El artículo queda en propiedad de la revista y, por tanto, su publicaci= ón parcial y/o total en otro medio tiene que ser autorizado por el director de= la Revista Alfa Publicaciones.<= /o:p>

 

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