Characteristics of the Solution of a Certain Riccati Differential Equation Using GeoGebra in Engineering Students through a Case Study | Chapter 9 | Mathematics and Computer Science: Research Updates Vol. 6

 

The objective of this study was to explore how engineering students at the University of Sinú (Colombia) understand and solve a Riccati differential equation using GeoGebra during the first semester of 2024. A qualitative approach was adopted with a case study design, involving three students selected at the researchers’ discretion from a total of nine students in the differential equations course. Through semi-structured interviews, the study aimed to identify the usefulness of the software for visualising and verifying solutions, as well as to recognise students’ perceptions of its advantages and limitations. The results show that GeoGebra facilitated the graphical representation of the comparison between manual and computational solutions, and the analysis of conceptual errors, which strengthened the understanding of the behaviour of differential solutions. Among the advantages, participants highlighted the immediacy in verifying results and the visual clarity for the graphical interpretation of equations, while as limitations, they pointed out technological dependence and the initial difficulty in learning the digital environment. In conclusion, the use of GeoGebra not only increases students’ motivation but also constitutes a valuable pedagogical resource for improving the teaching and learning of differential equations, providing relevant implications for engineering education. Learning differential equations provides relevant implications for engineering education.

 

 

Author(s) Details

Jorge Olivares Funes
University of Antofagasta, Chile.

 

Eber Javier Lenes Puello
University of Sinú, Cartagena Section, Area of Exact Basic Sciences, Colombia.

 

Pablo Martin
University of Antofagasta, Chile.

 

Please see the book here :- https://doi.org/10.9734/bpi/mcsru/v6/6186

 

A Case Study on Exploring YOU Artificial Intelligence and GeoGebra in Learning the Method of Variation of Parameters in Second-Order Differential Equations | Chapter 3 | Mathematics and Computer Science: Research Updates Vol. 8

 

The study presents an innovative experience carried out with engineering students at the University of Antofagasta, Chile, during the first semester of 2023.

 

The main objective was to analyse how students describe their learning of the method of variation of parameters when solving a certain second-order linear differential equation, using a combination of the YOU artificial intelligence tool and GeoGebra software.

 

The research was conducted using a qualitative case study approach, which allowed for an exploration of the perceptions of three students as they used these digital tools. The results show that the integration of both technologies fostered reflection and autonomy in learning. The students evaluated the experience positively, emphasising that these tools do not replace reasoning, but rather enhance it.

 

In conclusion, the constructivist nature of this type of activity is highlighted, where knowledge is actively built through the interaction between the student and digital technologies. Additionally, YOU supported symbolic reasoning and computation, while GeoGebra provided a visual understanding of the process, turning the resolution of differential equations into a collaborative and participatory experience.

 

Author(s) Details

Jorge Olivares Funes
University of Antofagasta, Chile.

 

Pablo Martin
University of Antofagasta, Chile.

 

Please see the book here :- https://doi.org/10.9734/bpi/mcsru/v8/6572

Using GeoGebra to Solve Homogeneous Reducible Differential Equations: A Case Study with Engineering Students in Colombia |Chapter 7 | New Horizons of Science, Technology and Culture Vol. 5

Learning differential equations continues to be a challenge for engineering students, especially when it comes to solving homogeneous equations, which often generate difficulties in their understanding. This study is framed within a qualitative approach and corresponds to a case study conducted during the first semester of 2024 with students from the University of Sinú, Colombia. The main objective was to explore the analysis of the solution of a homogeneous reducible differential equation using GeoGebra, with the purpose of identifying perceptions, advantages, and limitations that emerge from its application in the classroom. The research was carried out with an initial group of 16 students from the differential equations course, of which four were selected to participate in semi-structured interviews. The results show that students positively value the use of GeoGebra, highlighting its speed, accuracy, and ability to graphically represent solutions, which favours comprehension. However, they also pointed out limitations such as the absence of a step-by-step procedure and difficulties in use from mobile devices. In conclusion, GeoGebra is presented as a relevant teaching resource to enrich learning, provided it is complemented with strategies that reinforce mathematical reasoning.

 

 

Author(s) Details

Jorge Olivares Funes
University of Antofagasta, Chile.

 

Eber Javier Lenes Puello
University of Sinú, Cartagena Section, Area of Exact Basic Sciences, Colombia.

 

Pablo Martin
University of Antofagasta, Chile.

 

 

Please see the book here :- https://doi.org/10.9734/bpi/nhstc/v5/6417

Exploring Student Perceptions of GeoGebra Software for Learning the Parabola on the Cartesian Plane: A Study in Antofagasta, Chile, 2024 | Chapter 12 | New Horizons of Science, Technology and Culture Vol. 3

 

The use of GeoGebra software is a form of technological integration for learning mathematics. Its use provides students with more opportunities to visualize geometric concepts—particularly benefiting those who are below average in traditional learning environments. This study presents in a structured manner the core elements of qualitative research within a case study. This study is based on a general objective accompanied by two specific objectives, which guide both the design and data collection. Based on these objectives, three semi-structured interview questions were formulated, one for each objective, addressed to five secondary school students at an educational institution in the city of Antofagasta during the year 2024. The responses provided by the participants allowed us to draw three significant conclusions that reflect their perceptions, experiences, and learning related to the use of digital tools in mathematics teaching.

 

The findings indicate that the participants consider GeoGebra to be a very useful tool for learning Cartesian plane parabolas due to its creative and interactive approach, which facilitates understanding and increases engagement.

 

One of the most notable contributions of this research is the incorporation of a concrete and motivating example of the use of ChatGPT to support the learning of the parabola, an innovative content in mathematics education. This approach seeks to promote active student participation through dialogue with artificial intelligence. The study also explores how the integration of ChatGPT with GeoGebra not only fosters the conceptual understanding of mathematical content but also opens up new pedagogical possibilities. This study contributes a renewed perspective on the role of emerging technologies in mathematics instruction and promotes new directions for research and innovative classroom practice.

 

Author(s) Details

Jorge Olivares Funes

Department of Mathematics, University of Antofagasta, 1240000 Antofagasta, Chile.

 

Pablo Martin
Department of Physics, University of Antofagasta, 1240000 Antofagasta, Chile.

 

Byron Droguett
Department of Physics, University of Antofagasta, 1240000 Antofagasta, Chile.

 

Alexandra Burgos
Department of Mathematics, University of Antofagasta, 1240000 Antofagasta, Chile.

 

 

Please see the book here:- https://doi.org/10.9734/bpi/nhstc/v3/6003

 

Geogebra Applets and Gemini Artificial Intelligence in Separable Variable Differential Equations in Engineering Students of Antofagasta Chile| Chapter 8 | Mathematics and Computer Science: Contemporary Developments Vol. 5

This paper unifies the advantages of combining GeoGebra applets and Gemini AI to enhance mathematics learning for university students, specifically in the differential equations course at the University of Antofagasta, Chile. This combination of technological tools offers an innovative and effective approach to solving separable differential equations, providing students with a motivating learning experience. GeoGebra, a free dynamic geometry software, enables the creation of interactive applets that facilitate the visual and conceptual understanding of mathematics. In turn, Gemini AI complements GeoGebra applets by guiding students and adapting to their level of understanding and learning style. This integration not only improves comprehension compared to traditional methods but also fosters a more personalized and engaging learning experience. Various studies have demonstrated the benefits of using GeoGebra in mathematics teaching, and now, the inclusion of Gemini AI amplifies these advantages by offering a more adaptive learning experience. Together, this combination represents a significant advancement in the use of educational technologies to innovate mathematics learning in higher education.

 

Author (s) Details

 

Jorge Olivares Funes
Department of Mathematics. Universidad de Antofagasta, Antofagasta, Chile.

 

Byron Droguett Parada
Department of Physics, Universidad de Antofagasta, Antofagasta, Chile.

 

Pablo Martin De Julian
Department of Physics, Universidad de Antofagasta, Antofagasta, Chile.

 

Alexandra Burgos
Department of Mathematics. Universidad de Antofagasta, Antofagasta, Chile.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v5/2337

GeoGebra and ChatGPT as Support Tools to Find Particular and General Solutions in Non-homogeneous Linear Second-Order Differential Equations | Chapter 5 |Mathematics and Computer Science: Research Updates Vol. 5

This work focuses on the solution of non-homogeneous linear differential equations of second order, using technological tools such as GeoGebra and ChatGPT. These tools are especially useful in the context of the differential equations course for mathematics pedagogy students at the Universidad de Antofagasta, Chile. The use of GeoGebra, a free software, has grown in the teaching of mathematics, since it allows students to better visualise and understand mathematical concepts. On the other hand, artificial intelligence, ChatGPT, has proven to be a valuable resource in learning, providing explanations and examples that facilitate the understanding of the topics. The combination of both technological resources not only improves the learning experience but also enhances the teaching of mathematics, making students more motivated and engaged. In conclusion, this innovation in the teaching of differential equations seeks not only to solve calculations but also to foster a more dynamic and effective learning environment.

 

Author (s) Details.

Jorge Olivares
Department of Mathematics, University of Antofagasta, Chile.

 

Melissa Sanchez
Department of Mathematics, University of Antofagasta, Chile.

 

Alexandra Burgos
Department of Mathematics, University of Antofagasta, Chile.

 

Pablo Martin
Department of Physics, University of Antofagasta, Chile.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v5/5324

 

ChatGPT and GeoGebra to Support the Learning of First-Order Linear Differential Equations in Engineering Students | Chapter 4 | Mathematics and Computer Science: Research Updates Vol. 5

 

In the teaching of mathematics, and particularly of differential equations, students often face multiple difficulties in understanding abstract concepts. To address these challenges, two powerful tools, GeoGebra and ChatGPT, have been integrated to enrich the learning of engineering students at the University of Antofagasta, Chile. GeoGebra, recognised for its dynamic and interactive potential, allows the construction of graphical and animated representations that make visible the behaviour of the solutions of first-order linear differential equations, while ChatGPT acts as a guide for students in the interpretation of concepts and the resolution of doubts. This combination of interactive visualisation and conversational support allows students not only to access a mix of innovative technological resources but also to reinforce their learning and strengthen their mathematical competencies through a methodology that is accessible and adapted to their needs.

 

Author (s) Details

Jorge Olivares
Department of Mathematics, Universidad de Antofagasta, Antofagasta, Chile.

 

Melissa Sanchez
Department of Mathematics, Universidad de Antofagasta, Antofagasta, Chile.

 

Pablo Martín
Department of Mathematics, Universidad de Antofagasta, Antofagasta, Chile.

 

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v5/5176

Incorporation of GeoGebra Applets and ChatGPT to Strengthen the Learning of Exact Equations in Engineering Students | Chapter 8 | Mathematics and Computer Science: Contemporary Developments Vol. 7

This paper presents the integration of GeoGebra applets and ChatGPT artificial intelligence in the learning of exact differential equations in the university context. GeoGebra has established itself as a powerful tool in teaching mathematical concepts, thanks to its ability to dynamically visualize and model, which facilitates deeper understanding and motivates the students. Meanwhile, ChatGPT provides detailed solutions, and step-by-step explanations that complement autonomous learning and reinforce mathematical problem-solving.

The combination of GeoGebra and ChatGPT creates a dynamic learning environment that not only supports the visualization and experimentation of complex concepts, but also promotes interaction, offering an alternative to the traditional pencil-and-paper approach. This integration is especially relevant for engineering students in differential equations and multivariable calculus courses, as it provides a more comprehensive and effective learning experience, enhancing both their theoretical and practical skills.

 

Author (s) Details

Jorge Olivares Funes
Department of Mathematics, University of Antofagasta, 1240000 Antofagasta, Chile.

 

Byron Droguett Parada
Department of Physics, University of Antofagasta, 1240000 Antofagasta, Chile.

 

Pablo Martin de Julian
Department of Physics, University of Antofagasta, 1240000 Antofagasta, Chile.

 

Alexandra Burgos Villegas
Department of Mathematics, University of Antofagasta, 1240000 Antofagasta, Chile.

 

Pablo Martin de Julian

Department of Physics, University of Antofagasta, 1240000 Antofagasta, Chile.

 

 

Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v7/2443

 

Understanding Special Cases in the Method of Undetermined Coefficients with GeoGebra and DeepSeek in Non-Homogeneous Linear Differential Equations of Third Order | Chapter 3 | Mathematics and Computer Science: Research Updates Vol. 4

 Over the years, the teaching of differential equations in the engineering programs at the University of Antofagasta, Chile, has faced various challenges, particularly regarding the learning of the method of undetermined coefficients. This method, used to find particular solutions in third-order linear differential equations, has been identified as one of the most complex topics for students. The difficulty lies primarily in determining the general solution of these equations, which requires a high level of understanding and advanced mathematical skills.

To address these challenges and improve the learning process, innovative technological tools such as GeoGebra applets have been developed. These applications allow students to interact dynamically with the concepts and procedures of the method of undetermined coefficients, facilitating their understanding and application. The results obtained after implementing these tools have been highly positive, showing a significant improvement in students' learning and motivation. Additionally, this work incorporates the use of artificial intelligence, specifically through DeepSeek. This AI has proven to be an effective tool for assisting in the determination of particular solutions, which not only simplifies the resolution process but also fosters students' interest and active participation in their tasks and studies. The integration of these technologies not only strengthens learning but also modernizes the teaching of differential equations, aligning it with the current demands of engineering education.

 

Author (s) Details

 

Jorge Olivares
Department of Mathematics, University of Antofagasta, Antofagasta, Chile.

 

Carlos Portillo
University of Antofagasta, Antofagasta, Chile.

 

Byron Droguett
Department of Physics, University of Antofagasta, Antofagasta, Chile.

 

Pablo Martin
Department of Physics, University of Antofagasta, Antofagasta, Chile.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v4/4552

Use of GeoGebra in High School Mathematics: A Case of Geometric Transformation for Teaching and Learning| Chapter 6 | Recent Progress in Science and Technology Vol. 1

 This stage discusses how GeoGebra is secondhand in high school arithmetic classes to teach and learn lines transformations. GeoGebra is an common geometry, algebra, enumerations, and calculus use of mathematical software that is to say very important from simple to university levels to foster numerical experiments and discoveries. Similarly, this chapter's gift included various specific illustrations of renewal, including idea, rotation, translation, and distention, for teaching arithmetic to sixteen students in one of the subordinate schools in Kathmandu Valley, Nepal. This chapter examines the use of GeoGebra in eleven episodes by subscribing to the teaching experiment as the subjective research methodology. To help the student appreciate abstract concepts of renewal, we used adequate drawings, pictures, and animations with the help of GeoGebra. The experiment's consequence in a classroom demonstrates the profit of GeoGebra in instructing and learning about life-changing ideas. The results of this study display that if GeoGebra is used in arithmetic classes, students may start to assemble their own knowledge actively. In these classes, pupils co-operate in a group, illustrate transformational ideas, and take pride in their authority in the hall. The traditional lecture method of education mathematics, that moves the focus of education from the teacher to the trainee, is supported by this critical visualizing tool.

Author(s) Details:

Niroj Dahal,
Department of STEAM Education, Kathmandu University School of Education, Hattiban, Nepal.

Binod Prasad Pant,
Department of STEAM Education, Kathmandu University School of Education, Hattiban, Nepal.

Indra Mani Shrestha,
Department of STEAM Education, Kathmandu University School of Education, Hattiban, Nepal.

Netra Kumar Manandhar,
Department of STEAM Education, Kathmandu University School of Education, Hattiban, Nepal.

Please see the link here: https://stm.bookpi.org/RPST-V1/article/view/9092

Use of GeoGebra in High School Mathematics: A Case of Geometric Transformation for Teaching and Learning| Chapter 6 | Recent Progress in Science and Technology Vol. 1

 This part discusses by means of what GeoGebra is secondhand in high school mathematics classes to teach and discover lines transformations. GeoGebra is an shared geometry, arithmetic, enumerations, and calculus request of mathematical program namely very main from basic to academy levels to foster examining experiments and discoveries. Similarly, this chapter's contribution included differing specific exemplifications of shift, including hope, rotation, translation, and inflation, for teaching mathematics to sixteen students in individual of the subordinate schools in Kathmandu Valley, Nepal. This chapter awards the use of GeoGebra in eleven episodes by subscribing to the teaching experiment as the emotional research methodology. To help the junior learn abstract ideas of conversion, we secondhand adequate exemplifications, pictures, and animations with the help of GeoGebra. The experiment's effect in a study hall demonstrates the profit of GeoGebra in instructing and education about life-changing plans. The results of this study display that if GeoGebra is secondhand in arithmetic classes, students concede possibility start to build their own knowledge energetically. In these classes, pupils co-operate as one, illustrate transformative ideas, and take pride in their authority in the students that study together. The traditional lecture arrangement of education arithmetic, that moves the focus of education from the coach to the pupil, is supported by this detracting visualizing tool.

Author(s) Details:

Niroj Dahal,
Department of STEAM Education, Kathmandu University School of Education, Hattiban, Nepal.

Binod Prasad Pant,
Department of STEAM Education, Kathmandu University School of Education, Hattiban, Nepal.

Indra Mani Shrestha,
Department of STEAM Education, Kathmandu University School of Education, Hattiban, Nepal.

Netra Kumar Manandhar,
Department of STEAM Education, Kathmandu University School of Education, Hattiban, Nepal.

Please see the link here: https://stm.bookpi.org/RPST-V1/article/view/9092

Papert's Microworld and Geogebra: A Proposal for Enhancing Functional Teaching | Chapter 1 | Modern Perspectives in Language, Literature and Education Vol. 5

 This paper discusses how to improve mathematics teaching in Brazilian schools using Seymour Papert's Constructionism and information technology tools. This work, in particular, introduces the constructionist microworld, a digital environment in which students can build their knowledge interactively, in this case using the dynamic mathematics software GeoGebra. Papert's constructionism provides a flexible framework for implementing pedagogical models with computers.

Author (S) Details

Carlos Vitor De Alencar Carvalho
State University Center of Western, Rio de Janeiro, RJ, Brazil and CEFET/RJ, Valença, RJ, Brazil.

Lícia Giesta Ferreira De Medeiros
Rio de Janeiro Federal Institute (IFRJ), Pinheiral, RJ, Brazil.

Antonio Paulo Muccillo De Medeiros
Vassouras University, Vassouras, RJ, Brazil.

Ricardo Marinho Santos
CEFET/RJ, Valença, RJ, Brazil.

View Book :-  https://stm.bookpi.org/MPLLE-V5/article/view/1630