Good morning everyone. Welcome. to the first international conference Interactive mathematics 2026 organized through the Curriculum Network of Logic, Algebra and calculation of the Formation chain Basic Sciences of the School of Basic Sciences, Technology and Engineering at the National University Open and Distance Learning UN Colombia. During We will share these two days experiences of reflections on the teaching mathematics from the gamification, digital tools and Steam applications. This event It has the support of interpreters from Colombian Sign Language throughout the day and takes place in a format 100% virtual. We begin with the acts protocol. We invite you to listen the national anthem of Colombia. Oh glory, Oh immortal joy pains from the wind There Good ends now all the pains of the sweats will be night falls sublime freedom You will pour forth dawns of its invincible light. Humanity entire between chains. Understand the words of the one who died on the cross. Glory, as immortal joy, in waves of pain the belly. will end and simple furrowed with pains queará. Next, we will speak. of institutional openness. We give him the Word to Dr. Hadiley Gabriela Leon Perez, national leader of the chain with a background in Basic Sciences. Thank you very much, Professor Alexis. Well, Good morning everyone. receive a Warm greetings. It is an honor for me. Welcome to the first congress international conferences interactive mathematics, a space academic that is born with the purpose of to strengthen logical thinking, the critical reasoning and understanding deep mathematics as universal language of knowledge. As the leader of the chain of training in basic sciences, me It is a pleasure to accompany this important meeting organized by the network curriculum of logic, algebra and calculus, whose commitment has therefore allowed consolidate innovative scenarios of learning about teaching mathematics in contexts contemporary. Well, today we are also gathered for a shared mission and is to transform the the way we approach the integrating mathematical knowledge interactive methodologies, resources digital and pedagogical experiences that promote active participation and significant. In an increasingly dynamic world and mediated also by technology, the mathematics ceases to be solely that set of abstract concepts for become an essential tool for decision-making, the solving specific problems and the innovation across multiple disciplines. This congress is part of a commitment clear for educational transformation, integrating approaches such as gamification, digital tools and the ST applications. During These academic sessions we have structured an agenda that articulates the pedagogical reflection, innovation, the research and teaching practice. TO throughout this congress also We will have prominent participants, national speakers and internationals, who will share their knowledge, experience and advances in the field of teaching and application of mathematics. To them, our most eh our sincerest thanks for their willingness and their valuable contribution to this academic space. The same way, We highlight the participation of allied universities whose Contributions reflect the work collaborative and commitment to strengthening education in mathematics in different contexts also from the country. Well, we also deeply appreciate it. Well, to each one of you, to our teachers, researchers and in a very especially to our students, who with their active participation also reaffirm the educational purpose and the transformation of this type scenarios. I invite everyone attendees to get involved in a active in each of the sessions, to to question, to reflect and also build that knowledge in a way that collective. This congress is not just a learning space, but also a opportunity to further consolidate a academic community committed to the excellence, innovation, the social transformation through the basic sciences. I wish you a day enriching, inspiring and full of meaningful learning. Be all welcome. Thank you so much. Thank you, doctor. Next, we give the floor to Dr. Daniel Steven Morán Pizarro, leader of the logic curriculum network, Algebra and Calculus at the University National Open and Distance University, UNAMP. Alexis, thank you very much. Good morning for everyone. Please also receive a warm Greetings to all our guests, speakers, colleagues, teachers, students and the entire community academic that makes this possible today space. Today, more than inaugurating a academic event that we hope can to have a much greater significance, We are creating a scenario of thought, experience, and interaction and construction of mathematical knowledge. We want to redefine the idea that the mathematics are not only taught from the perspective of how it's an aspect disciplinary, but we also want that they serve precisely to explore the impact that we we can leave in the community, that can we link them precisely with all the needs which we also have in our environment, that it be precise. Precisely the Mathematics, a bridge to power consolidate everything that is the experience, mathematics education, and the development of a community, its history and meaning in a academic community. We want precisely that to also redefine that idea that Precisely, mathematics humanizes knowledge in general and this It is the coordinated work that we have been doing doing from UNAT eh with the basic science chain and network curriculum of logic, algebra and calculus. This event has three axes fundamental. the axis of logic, in which we will be accompanied by Our speaker Eilen, who is doctor from the Autonomous University of Baja California, which will be... accompanying this thematic conference also from the algebra that accompanies us From Chile, Dr. Estefanía Bravo and from the Autonomous University of Guerrero in Mexico in the area of calculation, our doctor Magali. We hope, then, that we can learn uh also as a teaching staff and all the students present at these experiences that, well, the idea is that, uh They are international, which precisely They lead us to see mathematics as well in other contexts and that precisely eh that all this can be a space enriching. I also want to acknowledge to these speakers, uh, that we accompany you today. Also We will have a panel of experts. all that Experience and knowledge will help us enrich us as a community academic and also to our students. We firmly believe in the ability that you all have to learn from constantly question, to build and transform the environment of you based on the knowledge mathematical. Mathematics for us is a universal language and we hope it will be precisely that bridge, that bridge transformer of territories such as We conceived it here in the UNAT. We then officially open to This congress with the certainty that it that happens here today is going to to transcend in teaching practices, in the learning processes and in the the way we understand education virtual mathematics. We give you a warm welcome to our first congress of mathematical conferences interactive. Thank you, Daniel. Okay, so now then With this opening we enter fully into academic program of our congress. Our inaugural conference presents Elien Oviedo González. Dr. Oviedo González has a doctorate in management and educational policy and teacher in specialized education and training teacher with additional studies in curriculum design and school management. is member of the National System of Researchers Researchers since 2014 and certified skills assessor teachers with experience in organizations national accreditors and international. She currently serves as head of the Department of Training and Evaluation Professor at the Autonomous University of Baja California, a position from which promotes strategies for the strengthening of skills pedagogical aspects of the teaching staff university student. She is also a professor of the National Pedagogical University since eh headquarters 021 Mexicali, as well as the International University of La Rioja in Spain and the University Latin American online in Mexico. Their lines of research focus on the Teacher training, the use of ICTs, as well as in the update and in the evaluation of teacher performance. His career includes work as a teacher full-time undergraduate and postgraduate studies at the Pedagogical University Nacional CD Tijuana, where he was Coordinator of the Master's Program in Education upper average from 2015 to 2019 and of regional doctorate in development educational from 2015 to 2021. Its production The academic work comprises more than 40 articles. arbitrary and inexact, as well as participation in the publication of six books, book chapters, and numerous presentations at national conferences and international. He serves as a referee in 10 specialized journals in education in different countries. member of Mexican Council of Research Educational, from the Research Network from Chihuahua, from the network of capabilities and regional development of the College of the Northern Border and Mexican Society of Comparative Education Mexico. His lecture entitled Methodology active and universal design of learning with a pedagogical framework for the teaching mathematics in Steam environment. Doctor, this is your space. Welcome to this first interactive mathematics congress. Thanks a lot. Good morning to all, to everyone. Uh, that's very nice of me Greetings. Let me... uh present my slides. a just a second and uh and well, I would like to begin by thanking the National Open and Agrarian University Distance, the UNAT of Colombia, as well as the Curriculum Network of logic, algebra and calculation, as well as to Daniel Steven Morán the invitation to this space for to reflect, in order to have a dialogue regarding to this topic that brings us today. not today? And it's how to make them real mathematics reach our students, that is, how to achieve learning much deeper, much more representative, as I mentioned Dr. JD Lec Gabriela, uh uh how Incorporate these topics, right?, into our agenda, whether we are students, if We're teachers, uh, if the topic is about interest to us. As previously mentioned, my name It's Aile Noviedo. I am a researcher, I am also a teacher of various subjects. universities And well, my topic is teacher training and curriculum design in education Inclusive, right? In this sense, my area mathematics itself is not a discipline. I've come to speak to you from the perspective of training. teacher, eh, and I say that with all transparency, precisely seeking to provide a area, a pedagogical framework, that is, how they are taught mathematics and it's uh looking precisely Integrate this element, right?, to see if we can agree on some ideas. So, well, having said that, my The conference is called methodologies active and universal design of learning as a pedagogical framework for the teaching of mathematics in external environments OK? So, Okay, if you're all right, let's begin and I want to start with a question, uh, what I think it's strong, don't you? When my teachers use tools digital classrooms, how willing I am going to participate, and why? And about I mention all of this because in certain environments Virtual things can sometimes be a bit complex, Right?, uh, to obtain the participation of all our students. How do we know? that our students are attentive when we talk about distance education and that they are not only connected at the same time? In other words, how many of them really They are following the class, they are participating in class and especially They are paying attention to what is being taught. and therefore how many of them They are really learning. So, I ask you please, uh, if someone is in a position to Please open your microphone. If not, please Let's answer the lie meter. we can focus our phone on this Hey, check this link, and if not, give me a second to share with you the link. Sorry, I didn't consider it. before. Hey, we have it here. Ah, The screen went out. Hey, Give me the opportunity to share with you, because Please, in the link. Here it is. So, let's ask ourselves really How many of us are in this possibility of introduce. Okay, thank you very much for your answers. Hey, We're going back to the session now. There's a second slide, isn't there? In in terms of whether we don't do it or whether we almost do it We always do it. What is the reason? which is why we don't always participate? It's on the second slide. Further Go ahead, we'll go back to the other two questions, but to begin with I would like Ask them that, right? What is that? a matter that prevents us from participating not at all when our classes are on and Our teachers commenting? Of agreement? So, I ask you please Let's continue answering. Interesting, No? In my experience, the numbers are a A little different, but oh well, let's go give the opportunity to answer those questions. Let me return to my slides. Excuse me, the presentation has ended. AND So, having said that or having started this conversation in this way, Um, I'd also like to start... Commenting on something, right? as teachers, thinking about this search that we do on a daily basis about uh how to better address this concern how to better engage our students, because we have received a promise. Yes, this attractive promise of that if we incorporate technologies, if We gamify, if we use apps Interactive, learning will improve. OK? However, Is this really true, and I ask... with complete clarity and also in this reflection process that this that I I'd like us to be just getting started, wouldn't you? AND I believe it's not fake, it's not a Good promise, but it's not complete. AND It's not complete, why is that? Because the reality is that technology is a tool tool, it's not a means, but what It teaches us, or what it teaches our students is the pedagogical design, not necessarily the tool as if. In other words, if I use a Kaho, the Kaho He is not teaching. Yes, Kaho is telling me supporting. If I use tools like GeoGebra, if I use it flipped classroom, if I use any other digital tool, uh, really what I'm integrating technology, but A design is necessary. pedagogical because it can guide my student to achieve learning that I am looking for. And precisely in That, in that sense, is what the talk is about. of today. What does this mean? Well, that means we're looking that this pedagogical design framework be precisely the universal design for the learning articulated with methodologies active and therefore also with technological tools, Especially in virtual environments, right? As is the case with these of the subjects integrated into this congress. Now then, uh, if we start to analyze, well, let's think about what it is Universal design for learning. Universal design for learning, The famous DUA is a framework that is developed at the Technology Center Special Applied called Cast, Right? In the United States. eh is based on a series of investigations that They performed based on neuroscience cognitive, that is, how our The brain learns, it appropriates certain issues, right?, to achieve a learning and basically proposes something It's very simple, it's about designing experiences. learning for diversity from the beginning, not as an adaptation What are reasonable adjustments, right? EITHER curricular adaptations, but as an initial planning strategy didactics. In other words, this is not aimed at who cannot work with certain topics, No? But to all people uh with three basic principles. He First, offer multiple ways to representation in the information that we We present our students. As? Well, using graphics, audio, manipulable activities, activities in where so that the student can appropriate that information and based on that, well, uh reach the entire audience. in a second A second principle is to offer multiple ways of representing the information, that is, different ways in which the student can demonstrate what you know starting from Different ways, right? This is the text, uh, you can do it orally, You can do it digitally, through art, right? And I think this we have seen through many activities that have been integrated Lately, haven't they? Uh, it implies, by For example, if I am working in a level two of Bloom's taxonomy is that the student can present that product in different forms, always and when that second one is integrated, eh Wait a minute, right? That is, from that point on of that second level of knowledge. AND Finally, the third principle is build multiple ways to motivate and to involve, that is, uh, in what way us can we achieve that our student eh, integrate into the different activities. This is done through challenges, through games, through a A connection with reality, right? That that allows him to represent that everything he has learned It's really at stake and it can then recognize it and explain it. It is in this sense that, therefore, For example, let's put a small one Hey, a small example, isn't it? In mathematics, if I am teaching, because For example, a linear function, which does nothing I'm going to show you the equation, but... that I can explore it with a graph, with a table, with words, representing it with movement, eh is I mean, giving it different eh approximations for the student then I managed to recognize, uh, from different forms, the same content, it is say, Change the entries, right? In other words, the channels under which how do I get there? information to reach the channels that the student has more assets. Okay. In this case, uh, in the example, uh Let's say we're teaching functions. Graph and explore the function in GeoGebra or using this tool SMMOS could be a way of visual representation. Okay? This is I am giving that possibility that the student visually represent that topic. Also, obviously, because I'm going to to teach a numerical representation, No? I show them the table of values, I teach how to calculate, how to record, etc. in a third moment, which is when I am giving my verbal representation, In this case, what I'm saying is... What it does is describe the function, whether in my own words or ask the student who does it with their own words and uh from that uh or Explain it even to a colleague, right? use analogies, that is, look for that there is that possibility of, uh, description based on eh of this verbal representation. Now then, when we talk about representation physical or recreational, there I can ask the student who represents with body movements, with games of roles, which integrates this uh in a way where it implies the Body movement, right? precisely to uh search that this behavior is represented the function through the body. Now Well, it's not about choosing one adapted performance for those who cannot arrives. In other words, it's not about choosing one representation for each person, but rather integrate these activities of everyday way. Because? Because of that way uh in a lesson plan, When I design for the extremes, it's In other words, for everyone, to a greater or lesser extent, So, who does that benefit? Well benefit to all, benefit to the center. Because? The Dua is not looking to lower the level and this It is something extremely important. This quote is from David Rose, one of the founders of universal design for the learning and he said that when we design with the students with more barriers, for For example, someone who has anxiety severe mathematics, the one who is learning the content in a second language, the one that needs more times, uh, what works for this This type of student will work for all. Therefore, the multiple representations They don't just help those who have learning difficulties, but uh all students learn to despite the barriers they may have. The DUA in general is not Condescension is structural equity. What works for students with The barriers will work for everyone. Uh, in this, in the STEM context, right? It's very important because the narrative is what we hear It's not always that mathematics isn't for everyone, but the reality is that yes, Yes, they are, aren't they? Uh, even students that in very early grades, right? They are developing this skill mathematics over the years they go losing. Because? Because finally uh, it is considered, isn't it?, that the Mathematics is not for everyone, and it is They believe. Okay? Now, what are the most common barriers that we have or that We seek to attack when we talk about mathematics and when we talk about STER, No? and how can the DUA help us to tear them down, right? Hey, when we talk about math anxiety And we respond with multiple entries, huh? the student can explore visually before facing a Calculation, right? Anxiety decreases because He already has a conceptual model. and mental concept. The point here is that with a lot frequency one of the problems for That is the teaching of mathematics possibility of visualizing, right? uh this problem in terms uh abstract, aren't they? Mathematics seeks Well, actually, we're the ones looking for the teaching mathematics to overcome this problematic. Now, when We're talking about learning rhythms differentiated, eh, and we respond with activities that go uh of a difficulty from least to most difficult, right? Progressive, autonomous, each student It moves forward from where it is and So this helps with learning It looks more natural. when We're talking about language barriers, or... when there is a highly technical vocabulary and We can answer using glossaries visual, analogical, of concrete representations, we managed to the student reaches this point where This representation is easier. abstract, visualize it and then to understand her better. Also when We're talking about a lack of connection with the real life, it is answered with the problem-based learning or projects, right? From the solving specific problems and where the student can understand that there is uh that there is that possibility of resolving it, eh of a specific and practical application for problem solving. Of agreement? Now then, uh when we talk about active methodologies in this in this teaching and learning process Hmm, and we talked about... integrate, right?, uh, what is the gamification to our to our sessions. I would like to make a distinction that I It seems very important. AND when we put games in class and there are no a learning established with clear objectives, uh, the fun It is not an end in itself, but a means to an end. No? The activity is not integrated at all more to motivate the students. We lose a very important point in itself. Because? Because when we do gamification and It has an intention, the challenges for it In general, we must align them to these learning objectives. The levels of The difficulty increases as we go on increasing activities. Uh, we do offer some badges, right? AND We also provide feedback. Or, uh, this narrative provides context to the that is being addressed and those There are various participation options, Well, the learning we achieved is... much larger and the problem is not the The tool is not whether we gamify or not. Um, the situation is how we design this gamification to then achieve that my students, achieve that critical thinking that I am so much Looking, aren't you? In other words, one would have to ask ourselves once we have designed our gamification activity, which It is already complex because it requires a training process, okay? I must ask myself, what is my activity? Gamified learning leads students to think mathematically or just to respond quickly through the game? Okay. So, if the answer is this last, Yeah? If nothing else allows them, huh integrate, answer quickly, then, Do you know what the problem is? The problem It's that there's a design that isn't there Present, okay? So, uh It would be something to consider and reflect upon. on this topic. So, what happens? If I integrate gamification and universal design for the learning? In other words, if in this I integrate multiple points into gamification. To begin with, and then I create the challenge Based on what? In three levels, it's That is, the visual level, the numerical level, and the applied. Let's continue with the example of the equations. Okay? In this case, in my First level, I ask you to solve with a table of values ​​and a graph interactive using Geogeva. Okay? Uh, at this level the student construct the equation from the graph, No? Observe their behavior before enter to manipulate symbols. on a second level, which is the numerical one, I would try to resolve that there. algebraically with the support of guided steps and the digital verification. That is, that's where the student builds the equation from an interactive graph, It can also be in the same GeoGebra, and see that behavior before uh sorry, uh, now integrating this all those steps. Okay. Now, in the application level, the student poses and solves a real problem using the equation and presenting it in X. Because? because at the moment of to represent him, uh, sorry, to present him in the team allows the others students who perhaps haven't yet They manage to reach that level of learning to better understand this process. In this sense, the three levels They aim for the same objective of learning. What varies is the path to through which we arrived. Uh, none This level is for those who can't. TRUE? but they are different doors or These are different paths in which he will... achieve the learning that will Do all three, okay? But in one of all three levels, then you will achieve the learning that we are searching. And that, I think, is the most important. Now, when we talk project-based learning, huh the tool It becomes a medium, but not This is mathematics, it is a tool, not an end. In this case, uh We achieved, we can achieve it starting from of guiding questions, of research, of modeling and presentation. That is to say, how to optimize, for example, consumption about water in our school raising a project, or a very big problem concrete. And I say project or problem because it can be achieved from either of the two elements. Collect data, identify variables, Using functions would be the part that The student would investigate. Uh, in modeling you can build a mathematical model that responds to the ask and in the presentation communicate the results with tools digital. Okay? And this, uh, is what it seems to me It is important to emphasize that none of these phases mathematics They're the target, aren't they? They are a means to solve the problem or the project. And it is in this sense that it changes radically the arrangement that it will have student towards the content, that is, towards mathematics, right? He's going to look for solve the problem. Because? because It is a situation that arises in your context, but the mathematics in this In that case, they will be the vehicle that allows you to solve it. Now, when we talk about the classroom reversed in mathematics, What is the teacher doing here? Prepare a video where he briefly explains the issue. There is a reading involved, There is an exploration in some system which could be Geogebra or it could be something else. There is a verification quiz, of understanding of the contents, of the concepts, right? And questions that are They prepare to bring to the classroom. Later, back in class, the In the classroom, doubts and questions are discussed. findings. There is an activity collaborative or a challenge that poses the teacher to reinforce this content, these topics. There is feedback, There is a deeper exploration or an application and the teacher takes on a different role. In This sense becomes a facilitator and not an ah a person who is going to provide all the information in the limited class time he has. Okay? In this sense, the flipped classroom is not assumes access, connectivity eh available to devices that we have at home and this is sometimes a A little problem, okay? But if he Access is guaranteed, then We have design possibilities, alternatives, technology integration, etc. But hey, if we don't have that access, well We have a problem. Because? Because we are uh Digitizing this inequality, right? So, I assume that in the case of eh of the students in this program, because being a university, eh which is open and remote, well, They have a certain guarantee certain access, okay? Access not It has to be, always, but it must be to have that access. Okay? Now then, when we talk about a traditional class uh versus a uh class that has active design plus DUA, well, there's a small change in roles and in the activities, right? In a class traditional, the teacher is the transmitter of the content, the The student is a passive recipient and the activities are generally masterful explanations, copied from formulas, problem solving. If we're talking of a design eh under a methodology active and a DUA, here we're talking about activities that include explorations in systems or software, right? Arguments between couples. The teacher becomes a facilitator and a experience designer. The student he becomes an explorer, coconstruc builder of the of the knowledge and uh and it's also It is important to consider that the evaluation It also changes, okay? In a class traditional, generally, uh the forms, exams, and written work They are, uh, the way I evaluate in a class traditional, but if I'm talking From the DUA, I will integrate others tools such as portfolios of evidence, self-assessments, Rubrics, right? It all depends on the activity that I am proposing, But hey, when I design under these schemes there is more coherence large among the activity, the roles, the assessment. OK? And here I am I would ask another question, wouldn't I? What active methodology do they already use in your classrooms? And this could be that We would give an answer, wouldn't we? Uh, maybe. gamification, flipped classroom, problem-based learning or projects or something else. We're going to to return to the results, right?, of These questions, but I would like to ask this question. There is a question where we voted for the first three and And we asked in that specific case uh, if it's another one, right? What other one is the What is integrated there? Uh, the link is the same as this from the first talk. We can also this integrate our phone, right?, into the screen if we are seeing it on computer. Hey, and if not, let me come back to share the link to this Okay, I don't know if you can help me share this Hey the link. Okay, now uh What are the mistakes, how do they I was saying, more common when we do gamification, or how we try to integrate gamification. Hey, One of the points is that we integrated gamified challenges. Oh, we also do projects collaborative or integrate classroom inverted, but Let's think about this scenario, okay? A teacher spends 3 weeks with a learning project based on problems, very cool, this, very complete. The students integrate teams, they model, they present, okay? But So what does he do in the end? Evaluate with an exam. So what's going on? He message that I am sending as The teacher's role to the students is that the The project didn't really count. What matters, eh, will always be the memory and resolution. And well, there's going to be this a widespread discouragement on the part of our students. Because? Because then we are sending the message that the only thing that matters is is how much uh the student remembered and this was done in order to achieve the learning. Therefore, we must be consistent with what that we are designing. and We are designing an exercise where there is challenges, where there are projects, where the Collaboration matters. So, we need to integrate these elements into the evaluation and also have different ways of evaluate, yes? modify our vision towards the formative assessment. Okay? that formative assessment and asking ourselves, Right? Formative assessment really that I am proposing demonstrates that my students achieved learning. And here I present four ways to Consistent, aren't they, with the design? universal for learning and with active methodologies under which It can be evaluated. The first These would be the analytical rubrics, The second one is the digital portfolio, The third would be peer evaluation and the The last step would be self-evaluation. Each one of them, well, with criteria Clear, graduated, right? Aligned to project that we are presenting. A digital portfolio will allow me see the student's progress or that he carried out during this process project. Peer evaluation, which is evaluation between peers, where each one of We, the team members, right? visualize the other person's participation. And here's an interesting point because It is always considered that in peer evaluation it is given away qualification, But nothing could be further from the truth. The Students are very aware of time to give the grade to buddy, and that's where sometimes there are a discrepancy between what the student and what the teacher sees. So, I would tell them, peer evaluation It's a good exercise to do and especially self-assessment, Sorry, because the self-assessment is going to allow the student to reflect about his own process and that also eh reveal what the barriers are that he himself faced to achieve this learning. Okay? Now, what digital tools Can we integrate this into the evaluation? Okay, we have Desmos. Desmos is a tool that allows us to graphical exploration of functions, allows you to see different forms of representation, as we had seen, and it also allows programming immediate visual feedback. GeoGebra helps us, I think that's it He knows most of it, eh, geometry dynamics and algebra. It supports the visual learning and can also help to manipulate. We have kaho or Quisis, which are tools that allow us to uh gamify, They also allow us to program questions, answers, feedback and the reports by students. We can use a Google Forms, which These are tools that most of us have. accessible, where I can elaborate different questionnaires so that uh it may allow this point. Uh, Padlet or Jambard, which are collaborative walls for visual portfolios. All these They have free versions and they have paid versions. The free ones, therefore In general, they help us to... do most things of things without this, like teachers, No? No, it's not necessary to have light. pay. If we can have it as support The institutional aspect is great, but if not It allows us to work quite well. We also have Flip, Philip Grid, or Lo What are these video tools? that we can generate for this and there are Many others, right? But anyway, these They are the most common, the friendliest, and those that allow you to do more things with the free versions. OK? Now, if I talk about uh about rubrics and assessment tools, what would that be? interesting? Well, here, uh, the An interesting point would be Hey Let's say if I talk to someone from a rubric, because I would look for at least three achievement levels, right? One criterion, by For example, it could be the understanding of concept, the representation used, participation in the challenge and the communication of the process. And I would put three levels, initial, in process and already achieved. In the case initial, because that is where the student It's barely in its initial stages, huh? this, For example, in the case of the concepts, identify the concept with visual or guided support. process is when can explain theirs with their own words And it is achieved when he applies it and transfers in different contexts or for solving different problems. Okay? So, uh, it's a rubric simple, but that somehow makes us guide to identify at what level find our student. Now Okay, so how could we implement universal design for learning in our classes? Well, and here I propose five steps, No? Uh, the first one is the diagnosis. Who are my students who know, What do they know? Two, uh, through universal design of learning, that is, how do I eliminate the barriers from the beginning. And this is looking for the multiple ways of representation. What active methodology do I implement? projects, flipped classroom, gamification, Some other one, right? Learning, service, this, Uh, challenge-based learning, I don't know, depending on the topic that I am teaching. Um, in formative assessment, what I'm gathering evidence, that is, uh under what product am I evaluating and what Barriers remained, didn't they? that adjustments in a final moment where I reflect about the teaching process, learning that was given. And in this sense uh, we're back to the main topic, right? The tool doesn't teach, the design pedagogical, yes. Okay. So here, uh, already in the manner of It's closing, right? The DUA is the framework that guarantees that no one is left out of the STEM experience. Yes. Two, the gamification and active methodologies They are not only powerful if there is intention pedagogical. Yeah. Oh, and the evaluation must be consistent. with active design, that is, uh diverse, educational and geared towards process. And here I would ask, did anything change? the answer our initial understanding regarding this on the topic of the participation of their students or the participation of you as students within this process? And well, that's as far as my... conference. OK? It was a pleasure to have I agree with you on these points. space and uh and well, to their ready. Well, Doctor, thank you very much. Well, look, I'm looking at this chat here, I've been following the minute by minute chat and we have, uh, the participants very happy with their intervention, with everything what the knowledge it brings us. So, we have a few questions, doctor, so that the audience becomes much more motivated. Well, We have a question, it goes like this, what one way to measure knowledge of the students, uh, that it's not through from an exam or through a questionnaire? Well, I think we covered that, uh, well, We answered it there through rubrics, portfolios, through some tools such as They could be, uh The written reflections, right? Hey, problem sets are good. exercises. In other words, the issue here is not leave only one, one single means for the evaluation, but different. I mean, uh If I focus solely on the exam written, so then I'm measuring only one of the elements, which in This case is, uh, knowledge uh tacit, isn't it? But not the resolution of problems, not critical thinking necessarily We should look for the app. Ready. Yes, ma'am. Very light. Well, Here we have a very important question. Interesting, doctor. When we use games, when we use games or points in class, Sometimes we only strive for the reward, not for learning mathematics. How do they design a gamification intentional that truly makes us Understand the concepts, don't just accumulate them achievements? Okay, so the point is, uh, what it that we saw previously, right? Hey the The act of gamifying is not just about putting the exercises to get them to answer quickly or so that they participate, otherwise, I have to have very Clearly, what is the purpose of that? gamification. Two, uh, look for these levels of progressive difficulty where each level is best represented with We can even use these badges, No? like these small prizes, these small ones this Oh, I forgot the word, this those little trophies he keeps getting the student at the moment of generating Quite an achievement, isn't it? Uh, also uh to encourage reflection on the that is learned. Okay, ma'am, thank you very much. Here We have more questions, doctor. He says, "In mathematics there are "Guys?" But hey, here like We are observing before passing To this question, the students are Very active, aren't they? These are questions from students. Says, "In mathematics there are colleagues who They prefer to see graphs, others need physical manipulables or explanations step by step." In a project without how They ensure that we all have access to the same mathematical idea without feeling that some go further ahead than others. Okay, that's a good point, you see, and it's That's a very good question, but it's achieved by starting from precisely this that we were talking about. Insofar as I do not I offer a special activity for those who cannot, but from the outset I design my activities in such a way that Everyone will go through everything, Do you know what's happening? The following are achieved learning, whether through a channel or by other. and there is better utilization because there are no differences. In other words, I can't see who there is. Yes, he knows, and who doesn't know, right? But They all go at the same pace. Ready. Well, yes, ma'am. Excellent. I see That was a very good question. Well, Here we have ready. If we have to watch videos or read materials at home before going to class, what happens when we don't understand Something's wrong with our internet connection? I don't know It becomes a barrier instead of a aid? That's how it is. and it was part of what We were just talking about it a little while ago, uh, we should make sure that the student will have the access to any of these tools. And let me tell you that in For the last 3 months there has been a tool very powerful for us teachers and which is a tool of artificial intelligence called Notebook LM. It's with Google, right? AND That's where we as teachers can upload our content, that is, uh the texts or the syllabus that we are going to work and allows me to generate summaries audio, video and download them. It allows me to generate many other things, No? Uh, these are work cards, etc. So I can download them and, for example, send them via WhatsApp to my students or upload them to the educational platform. So what happens? Uh, the student can You can see them or listen to them or can you see them or read them without access to the internet, That is, simply by reproducing them. And this helps me, why? Because it's not throughout the network, but with the ecosystem of documents or resources that I provide the tool. So, that gets really cool because because there are indeed communities where the internet is bad, where the The signal is very bad, or I only have access at certain times. So, if I can generate the resources that I will be working on in class In this way, the flipped classroom becomes much more powerful. Ready? Yes, ma'am. Well, here We then continued with the session of questions. We have another question. Dr. Oviedo, Could you share a concrete example of a classroom strategy based on UDL that has had positive results? Yes of course. In fact, uh, well, a a An example of this tool is the that I saw a few minutes ago, if I allow. Uh, and sometimes we think it must be The process is very complex, but not It's so much, huh? when we implemented it in in a specific class, for example, uh I make the diagnosis based on what I want my students to learn And this applies to any topic. Two, I'm trying to figure out what the barrier is that they have the students. Maybe it could be an anxiety eh Math anxiety, that is, where the student, uh, look for this or has a lot pending perhaps the calculation or Some other topic, right? I'm looking for an active methodology To implement, for example, this could be gamification, as we were discussing. AND then I design my strategy of gamification-based learning, but oriented towards what, the design of the specific objective that I want to achieve in in learning. I align this formative assessment to starting from the choice of these eh of the activities that I am I am working on this and looking for a final reflection. about how it was achieved learning and how that was generated How did the student manage to get there? That point, right? Yes, ma'am. Thanks a lot. Well, Here's what they tell us. You say that you say the tool doesn't It teaches, but when we use simulators or math app, How do we differentiate if we are learning through the tool or through the design that you planned? Okay. Well, if we are learning from the tool That's why, because the teacher had a intention, because he designed an activity in which it was going to be represented visually the function. OK? So, there's an exercise Therefore, behind it lies a design. From another way, if I get involved, uh, in the application and only uh as student, without pedagogical knowledge, I'm starting to get into it, aren't I? Probably I learn, maybe not. But when the professor designed the activity so that I can visualize the function, I can manipulate the variables and see how they change, So there's a design there. Yeah. Then, ma'am, that's correct. Well, here already They ask us, how to articulate the duet with the problem-based learning, the Gamification and the flipped classroom sound powerful but complex. What would be the starting point? realistic? The realistic starting point for a teacher who just wants to implement this framework without overloading overloading yourself with planning. Okay. First, start with the diagnosis, second, to raise, eh two or three activities to begin with. I always say, uh, we have to plan two or three activities in one first moment, Take them to the end, right? That is to say, towards evaluation and reflection. And maybe in the next activity I complete four. I might include more in the next one. but gradually do this Exercise is not so complex now. He The point is, uh to soak ourselves a little and I think the Problem-based methodology is a good way to start. Ready. Well, yes, ma'am, very many thank you. Here we go. We have another one. The Honestly, your talk has been so It's interesting that it has generated multiple You ask questions, and everyone is interested. in which they can be resolved. Ready. Delighted and ready parent. Oh, it's not TRUE. Ready. Okay, that's it. Sure, sure. Here We'll be waiting for you at our next mathematics congress interactive. Well, Dr. Oviedo, How can DUA contribute to closing educational gaps in contexts Latin Americans? Well, at the moment when I uh I consider the different barriers that my students face them, I recognize them And I work on them, I think, in that way. We are seeking equity in the education and above all promoting the access of the students' eh, regardless of their condition cognitive, social, political. economic. I don't think that's a good way to go. They have even eh were born or we were not so much born because we already have active methodologies always had. The thing is, They regain that prominence from the integration of the four pillars of the education of the future and above all, eh of working based on methodologies competency-based, right? That That's precisely what they're looking for, huh? overcoming these gaps and inequalities that exist in these contexts Latin Americans. Okay, doctor. Thank you. We have here already another question. In gamification for educational purposes, the aforementioned comparison, the The comparison mentions the importance of pedagogical scaffolding from their experience. What is the recommended technical route? to integrate a narrative of the context real without the complexity of the history sacrifices the density of mathematical or logical content that is Are you looking to teach? Okay. Well, I think there's a A very important point is that most We teachers are the experts in the content we teach and always we recognize which application is Each piece of content that we teach in the reality. So, somehow, when We arrived at the classroom, uh, we are clear about this relationship that There is a connection between these two concepts, but We don't always communicate it to our students. So, I think a good one The strategy is to start by saying, "Ah, Okay, let's look at this topic and this topic We can see it in reality and look for it This is the most concrete example we can find. how that concept is applied on a daily basis daily. Yes, because at the moment when the student sees a direct relationship from what he will learn with the application, This is going to be better a better, a better approach to the that he is learning. Ready. Yes, ma'am. Well, here we have These are questions at a teacher level, aren't they? Also interested, very active in their chat. They ask us the following question. What pedagogical skills should... pedagogical skills must be developed a math teacher for implement this framework? Where do they fail? plus the teachers when trying to apply UDL with active methodologies? Okay. In my experience, in the I've been training for 20-22 years. teachers, I think the biggest challenge is the fear of change. That's where it all lies. Because? Because We have maybe 10 years of teaching experience, 20 years, 30 years, 40 years doing the things in the same way and it gives us a lot fear of changing the way it we do. But I think we have to understand something fundamental is that the current generations are not what It wasn't even 3 years ago. That is to say, uh, technology, the use of social media, the use of uh all the elements and even of the artificial intelligence is giving us forcing us to modify our internships, no matter what. There is no discussion. So, uh I think the most important point is in the desire or the ability to integrate these Hey These active methodologies are in search entry the different ways of teaching. That is, to think that if I am looking at a topic that maybe I've seen over the last 20 years at the level purely conceptual, because I have to understand that now I'm going to have to To present it visually, right? And to the The best thing at first is the time to recover all these elements for a class, but believe me, the medium- to long-term results There are way more of them, huh? much more fruitful. Okay, doctor, then we can consider at this point that we have past or mathematics has had a evolution of static mathematics, the traditional one, the one we always come to working on the board, on paper, New technologies are arriving and we can to say that we move on to some mathematics dynamics. That's how it is. Yes. When you spoke or gave the concept of dynamic geometry through GeoGebra, and there are many more. educational that allows us to see in a way more dynamic to see those invariants that are not We see it in a static way. So We can say or we can consider, right? I also have a degree in math and I'm here listening to your talk because everything you've said is Very interesting and very timely. education that must be imparted in the era. So, we can consider that we moved from static to dynamic and we can already be in mathematics disruptive. That's how it is. Yes. Right there where you're talking about that Change, right? That change. The disruptive word is change, isn't it? A breakup. A change. It's a breakup, yes. With what We believed, we saw, and we did. Okay, that's it. I think that, starting with the pandemic, those of us who were still a little reluctant to fully enter the more interactive part, now there are no possibilities of Wait, right? It is already necessary and also We are required to do so. Well, and this is where the invitation comes in, No? to all future educators, to those who are training to be educators, right? And not only that math, right? I think it is The invitation is open to everyone to We need to adapt to that change and Take advantage of these new technologies, right? In order to provide a quality education, What is being sought today in all universities and in all the educational contexts. Well, doctor, I I wanted to finish this last one already. question we have. they tell us Next, many teachers think that In essence, there are no digital tools. innovation. How do you convince or train your colleagues or trains his colleagues that the heart It's in the pedagogical design, not in no on an A or a platform? Okay. Well, I'm going back to my... initial thought, right? Uh, the The incorporation of technology does indeed help us It will help, it will definitely help. to engage the student, but uh the difference between engaging him and gaining knowledge That's where the answer lies. Yeah We do good design, then we will ensure that there is also the Hook, right?, of this engagement That's what the Americans call it, right? that there be deep learning, a critical thinking and reflection about teaching. Okay, Dr. Oviedo, thank you very much. Thank you from Mexico for this a conference that makes us think about what fundamental. It is not enough to have the tools, you need to know how to design the learning. A key message for everyone the teachers who are with us. So, I want to take a step in this moment to Dr. Daniel, to say goodbye. and the closing. From my side, many Thank you, doctor, and in the chat too We are very grateful for this important intervention today. Thanks a lot. Well, Dr. Eilen, thank you very much for having accepted, uh, this, uh, well, in this version, this talk. thanking him a lot because I think we get along many lessons learned. We are here from UNAT We're doing a job, uh, well articulating algebra, logic, and calculation in all our processes and It really leaves us with many challenges because assume. Uh, we appreciate all that. experience that it has given us. definitely remembering a lot of the words of a friend who is a professor at another university where I was at some point working, uh, many times we continue teaching 20th-century mathematics eh from the 19th century with professors from 20th century for 21st century students And that's precisely the challenge, uh We now have native students digital that we, well, in some the moment when we have been prepared, eh for the teaching of mathematics or for mathematics itself discipline, because perhaps we didn't learn it That way, and that puts us in that position. a double challenge, huh, both teaching how to relearn in order to teach, and that is a A constant challenge for us and we are because of that continuous learning. So, we are very grateful. And well, hoping that we can continue then in communication with the Autonomous University of Baja California. Thank you very much for accepting the invitation. Thank you for the invitation. See you later. See you later, teacher. Ready. Okay, so we took a brief technical space to give way to our next guest. Teamwork achieves great things results. We have reached more than 100,000 subscribers on YouTube obtaining the silver plate for our TV UNAT Virtual channel, thus becoming the first higher education institution in to achieve this milestone. And we're going for more. TV UNAT Virtual, institutional commitment to achieve more UNAD, more equity. Colombia is a land of landscapes vibrant from majestic mountains to the welcoming beaches. But her true The magic lies in its people. Stories woven with colors, textures and flavors. Fill yourself with an unforgettable experience of Colombia, where every corner seems like a natural altar. A journey awaits you charm and authenticity. Come and experience the magic of Colombia with Olor the region. Teamwork achieves great things results. We have reached more than 100,000 subscribers on YouTube obtaining the silver plate for our TV channel Una UNAT Virtual, thus becoming the first higher education institution in to achieve this milestone. And we're going for more. TV UNAD Virtual, institutional commitment to achieve more UNAD, more equity. Heh Ah. We continue with the area conference of mathematical logic. We present to Lady Hernandez Mesa. Dr. Lady Hernández Mesa is a professor full-time researcher at Faculty of Pedagogy and Innovation Educational Department of the Autonomous University Baja California, member of the system of researchers level one and a member of the academic body mathematics teaching. In 2024 She was awarded academic merit of the Autonomous University of Baja California California in the area of ​​education and humanities in recognition of their outstanding track record and commitment and vocation. She has a degree in education with specialization in mathematics, computing by the Enrique José Pedagogical Institute Woman from Havana, Cuba. Master in teaching at the University of Baja California and doctor in the doctor in education by the University of Tijuana. He also has a diploma international in education assessment of higher education in modality distance granted by the network consortium CREAP distance education. Is creator of the DAE method. I reveal myself, I learn, I teach. A proposal pedagogical approach focused on the didactics of mathematics and the use of technologies in teaching, from innovative approaches and inclusive. His work focuses on the teaching mathematics from real contexts, integrating the cognitive, emotional, and social aspects. serves as vice president of the Baja California delegation of the National Association of Teachers Math. She is also a member of the Cinemates networks, eh Redipe and AMED and serves as a national evaluator of evaluation and accreditation system of higher education, also participating in committees scientists from editorial journals national and international. His lecture entitled The Dade Method as interactive strategy for the development of logical thinking mathematical. Dr. Hernandez, go ahead. Uh, good morning, it's a pleasure to greet you. Me Can I hear you okay? Yes, ma'am. Clear and strong. Thank you so much. Well, good morning for everyone. Many thanks to the entire organizing committee of this first international congress of interactive mathematics lectures. Thank you so much for the invitation and I was really telling you a little while ago that For me, it's a very big thank you. that they invited me and also one day Like today, since today I'm turning 55. years and I'm very happy starting with one of the things that bring me the most joy in My daily life, besides my family, which is teaching, which is sharing, which It's about having these reflections with colleagues, with students and it's very, very nice to be here. Thanks a lot. Well, like The teacher said, "I'm in this..." moment uh uh attending to the part of the logical thematic conference. Uh, for That's it, when I'm invited, I start to to reflect and say, well, how to carry out the method, that is, the approach methodological gives me self-discovery, I learn, I teach it as a strategy interactive and how to carry it too certain exercises where, uh, although whether we are doing arithmetic or we are working in some area of ​​or other areas of mathematics, one way or another the logical process It's very strong in him, and also also how to live this moment that We're going to have it today, wherever we can, uh to reflect on how much we can through the methodological approach to develop logical mathematical thinking. So, at this moment uh I invite you all to go with me walking in these slides through various exercises that we will be doing and that This will lead us to some reflections and also to live through the three moments of This methodological approach then the method as a strategy interactive for the development of logical mathematical thinking. Thanks a lot. We discussed it there. I'm leaving my name, and I'm also leaving my email address. in case after this conference They want to write to me about this topic and we can network and keep working as eh people who dedicate themselves to teaching the area of ​​mathematics or doing mathematics. Thank you so much. Let's begin. First of all, I want to talk about the interactive strategies. In other words, in the The educational field is a set of actions, tools designed to that learning is not a process unidirectional. In other words, it's important that there be a bidirectional dynamic exchange, multidirectional. Its essence lies in the fact that the Student, stop being a spectator passive and becomes the protagonist of their own knowledge. That is very important when we use interactive strategies in the classroom class. say the active approaches to through active methodologies and everything we know that may be within those interactive strategies in the protagonist of his own knowledge and that he can also do it through active participation, reflection and action. In other words, not only make it an interactive moment that motivates the student, but within that whole moment, through that planning and it has a lot to do with it also with what Dr. Ilen said in the previous conference, that my congratulations, I have great pride and much affection for the Dr. Eilen. It has a lot to do with it also that part of how we plan the process, that is, how we guide the student not only to actively participate, but also that there be a reflection profound and evident in that action to make decisions and have a debate. So, we're going to experience all of that today. a little through the three moments and of the exercises I bring you. And here, a little before we begin... design the environment that the student does not can avoid thinking, that is, that the The student doesn't have to be thinking, no just solving something that maybe It stems from the problem-solving process, but to take the student to the student to a much more reflection deep. For that, I want us to begin with this exercise that I bring you in this moment. He says, "Let's solve an exercise that It's called the party challenge. The exercise, or rather, the problem, is that We're organizing a 60th birthday party, eh for 60 young people and we want to prepare water flavored with sachets that make 2 L each one. The glasses we have are 250 ml. The first question is, how many You need envelopes so that everyone can drink up to two glasses? If we decide To add ice, we'll need the same number of envelopes. Yes, we add the ice 5 minutes before. to hand the glass to the people that they can drink the flavored water, what Is it better? Crushed or cubed ice? Because? For this, I invite you to Let's scan the QR code that's here. screen and in less than 2 minutes we can answer these questions. We took our time, we went into the QR code. It is very important to know that although at this moment through the The methodological approach is requested of the and to the student who works in a individually, once we more or less see Let the almost 2 minutes pass, they are the 38, we will be reflecting and through the debate seeing the different answers and the reasons why. When they finish answering it in the QR code, I would greatly appreciate it if you could send me they put it in the part of uh, from the conversation here in the chat, if already He would complete it. And I would be very grateful to the people who are moderating the conference that will help me to see What were the answers, or did they They can open or they can turn on the microphone to to be able to hear how many envelopes We need it so that everyone can drink up to two glasses. How many envelopes? We need the same number of envelopes if we add ice. And what if we want to serve it? 5 minutes earlier? Remember that at this moment it is very It's important to focus on the possible answers. There will be no answer mistake. On the contrary, each answer tells us It reveals certain areas of opportunity, It lets us see that first moment in the methodology, which is finding ourselves to answer, to find each other and that can to experience a cognitive imbalance, which is very important. and is found cognitive balance in the following moment, which is the second phase of me I discover, it is this and I learn when Let's get into the debate. How are we doing? We've finished. I'll be waiting. I am entering Go to the drive to see if it's already there. We finished and a little bit to see the answers. Doctor Lady, in the chat we have an answer, if you wish to go starting. Very well, thank you very much. He says, "It's 15 envelopes and the ice in cubes." Very good. 15 sachets and the ice cubes. Very good. What other answer do we have? For the time being, doctor? As they come out, I'll keep you updated. Thank you so much. I'm also entering here to the space of the response. While he's checking, I'll tell you I'll keep you updated in the chat. We have another one answer. It says, "10 envelopes and the crushed." That is, 10 envelopes. Yes. Uh, like, uh, the part of whether we need the same number of envelopes, that is, if not We want to add ice, that would be 15 packets. Very good. I'm watching here, some people are commenting to me. that 30 envelopes. So, we are Now for the reflection part. We are currently in the part of The reflection, that is, some give me 15 envelopes, others put 30 envelopes in the first part which is without ice. TO Check and always important as to immerse ourselves in the problem, to experience it. Yeah They realize this is a problem in real-world contexts. we live and we can until working through it experience, and if we don't have experience In this, the data comes explicitly or implicitly in the problem. So, We got to 30 envelopes, uh, they can't It's because when we reach 30, it We divide by two because of the situation of Each sachet gives me up to 2 L. Uh, 2 L. Very good. When we go to the part with ice, Some tell me that 12 envelopes. In other words, some people tell me that 12 envelopes. Because? Because when you throw the ice passes this part of the displacement when pouring the ice, cover a volume and the water is displaced. Excellent. Very good. And that they prefer pour it into buckets. And I would appreciate it if someone could say Why not give the answer? Cubes and not crushed ice? Could someone help me with that? Although I have some answers here and could in cubes to avoid loss of flavor, because if it defrosts too much The flavor is quickly lost. Very good. Some call me crushed, most They call me a cube, since it can be kept longer cold weather. Yes, and with the flavor. Very good. Excellent. In other words, we arrived here in a cube Because how are we going to serve it in 5 minutes? Before handing over the glass, we run the risk because the crushed ice is very fine or very, very crushed, as it has, uh, as It is more on the side of it is more surrounded of liquid, he immediately lies down to defrost much faster than the cube that is a little bit bigger. EITHER That is, the cubes are always more larger than that crushed ice. This, At this moment, the crushed ice as It has more, uh, and is wider within That volume of liquid will... help it melt less quickly. Very good. Excellent. Thank you so much. So how do the three of us live? moments? Well, I'm revealing my age, which is the first moment, is when we activate prior knowledge and We generated debate with this challenge of the party. In other words, when we say that We're organizing a party, 60 young people, that is, we give the data, We are looking for previous data. Because? Because if I don't know how much it is, uh How many milliliters, huh? Or how many glasses? They fit inside 1 L, maybe then I can't move forward anymore because they are... giving a very important piece of information which is 250 ml per glass. Therefore, if I don't I have the knowledge that within 1 L There are four times that type of glass, then I have trouble getting to the conclusion that each envelope gives me eight glasses. Okay, now let's do the calculations. That makes sense. How many envelopes do we need? so that everyone can drink up to two glasses? In other words, two glasses is the maximum. It may be that there are people who are not going to drink both glasses, but we have to Make two glasses and that's how we connect them As we said before, how 2 L, the ratio with 250 ml and we begin. But also within the logical part the physical variable is activated, which if we decided to add ice, we need the same number of envelopes. There that The question helps me, and there's a decision to be made. The strategy you take, if you go Add the ice 5 minutes beforehand, So what happens? If I'm going to use crushed ice or ice cubes and the because. Therefore, there is one reflection in which you will better through analysis, already After the debate, they begin to realize What is the ratio of crushed ice? when we put it in the water and the time, what is the cube relationship as a form of ice, uh, I mean, ice in cube shape and they begin to look certain some x number of variables entering from that within that decision-making process decisions that we have to make in a problem that might seem that we only add, subtract, that is, in a arithmetic process. There is an analysis of the imbalance cognitive. Because? When we see that It's not just a division operation 60* 0.250 / 2, We see how the Alchemist principle. Right now when we are talking about volume displacement, or In other words, there is a volume displacement when we add the ice. That's why You decide and make a decision that We're not going to buy anymore, or we're not going to instead of using 15 envelopes, we're going to Use 12 sachets. or it could be that Let's also use 11. Therefore, there Maybe if we already have some experience Beforehand we can start measuring the quantity of the volume of ice that we are going to add. AND If you notice, we've already taken up to the decision that we're going to put it the cube, that is, ice in cubes, what's it about to go for 5 minutes, I mean, maybe that question in the problem of mathematics at the end of life everyday life already gives me a volume process and that displacement that may occur. In other words, if the ice occupies space in the in a glass, less liquid is required, therefore so much, less about. And there is a reflection Very, very important is that the ice crushed material has a larger surface area The surface melts faster drink, while the cube preserves better flavor concentration because It melts less quickly in those 5 minutes. Sure, if I'm going to put it on more Even in 5 minutes, I'm already taking a risk here. So I have to use more envelope so that I have a little more The flavor is strong and the ice doesn't affect me. spoiled. Or I make a decision that I made the ice and immediately I made uh uh the soft drink, I mean, the water of flavor. So, phase one, I'm revealing myself, you guys They identified areas of opportunity and prior knowledge. Because? Because in this moment when we are entering This reflection that if we were with open microphone or we were in a living room, I'd rather explain it to him than anyone else, were you telling me why They made each decision, and explained why. result, what would happen and even us we realized that maybe, uh, when We put in the ice, some will use it More or fewer envelopes, but always There will be fewer than 15 and they are starting to occur different answers depending on the the what quantity of ice, that is, what is the volume, displacement and how many minutes before or if they want change the problem strategy to to be able to live an experience with a lot Take more care and don't waste the water the taste. We also see in that first phase of discovering the imbalance cognitive, such as the ice dilemma, the emotion, because it is curiosity as Front door, what am I going to do? Because? That? In other words, in that first one phase I am discovering myself in personal because I work in the individual. In the second phase I learn, I see an active construction process through inquiry and debate. By that? Because it's possible that the student Lady said, "Ah, I wouldn't use two 12s envelopes, I would use 13 because I'm going to throw less ice or because, uh, the ice that I'm going to throw them out, they're smaller because "I don't have any ice cubes." a very reflective process begins to emerge profound, not only in the answer that It has the problem, which is very important give them, but also in those things that can happen when we throw the ice, the amount of ice. there is one interaction because learning doesn't happen alone, We reflect with other people and There is an aspect of logical thinking. because there is a modeling of solutions based on the evidence of ice. Uh, the teaching phase that the student socializes and re-signifies, that It is the third phase of self-discovery. I learn, I teach. I mean, he socialized his In response, he explained the whys and redefines. In other words, it's possible that when Initially she gave it correctly, but then one way or another to enter the second phase, when the debate begins, it says, "Wow, I hadn't thought about that." "My partner, my partner," he said. Therefore Therefore, there is growth. Although that maybe my answer is the one I was looking for the problem, but it can also Perhaps my answer wasn't entirely the one who was looking for the problem and in the second phase I am able to find and work on those areas of opportunity, analyze the whys and in that third when I am able to socialize why my answer to a reinterpretation and I also become aware of my own learning and enter into a metacognitive process. Therefore, the methodology is a strategy metacognitive also within the process of teaching, learning. So far we've seen how the three of them lived moments. I would be very grateful if you could put me If not, quickly here in the messages. were able to see these three moments in you right now when They were answering the exercise. Thank you very much. If they say yes, then... They experienced those three moments. Remember, the first one doesn't have to we don't have to have wrong, because finding our areas of opportunity are not only because We made mistakes, but also because we find certain things that we They grew beyond experience we have within the process. I would really appreciate it if you could tell me. Yes or no, did they experience those three moments? in the message. Doctor, here in the chat have Hey Yes, yes, yes, yes, yes. We already have more than 10. Yes, and then some more. Yes sir. That's how it is. Yes, yes, doctor. Everyone is saying at this moment in the chat that Yeah. Thank you very much, teacher Alex. Yes, many thank you. So let's think about it. Wow, how interesting. If we take this to 50 minutes, that is, virtually in the teaching or also in person, so that we can open up the space much more. for reflection or until we can In other words, if we are at home, Let's look for such a thing, let's look for ice or Let's look for something else if we don't have ice. It looks like ice and we see how the displacement then becomes more interactive. But if they realize, even at this moment, which is much more Quickly, there has already been an analysis process, of reflection, of development of that logical thinking. Thank you so much. We continue. And the impact part, which is the application of logic in environments real, such as the organization of those resources and that it is a problem in real-world contexts. Therefore, also We are teaching for life. Okay, we've reached this point and I I am very grateful to be with that dynamism up to this moment and I tell them I kindly ask that we enter this code QR code that I'm leaving here on the screen and in in less than 2 minutes can they add me the answer to this exercise that follows here on this screen. Remember, everything What we do at this moment is excellent. Because? because there will be a learning very good. I'm looking at it on my drive that I have here. from my cell phone so I don't have to move around in the display your response and in advance I appreciate your participation. Very good. How are we doing? How are we doing? I have it now, I see an answer. I see an answer. Very good. Remember that This whole process, and even more so when it is taught It is virtually very important your participation, that motivation. Excellent. How are we doing? If they notice, the They don't have to put their name in the answer. It's completely anonymous and also not We have to be afraid of to make mistakes. On the contrary, when we make a mistake, whether minor or Great, we'll always learn something new. that we understand, that we reflect on, that we enter into that metacognitive process and sometimes much greater growth. By that? Because maybe we think that We're doing well, and since we haven't stopped... to reflect deeply, then It accumulates and that's when it costs us a lot. more work. Excellent. I already have many answers. Thank you so much. Many answers. Thank you so much. They are very active. Well, I I'm going to read some of the replies. says Some say it's 20, others tell me it's 4. Others tell me it's 26/12, which is 13, which is 7.12. Uh, others tell me it's 20, others tell me They say it's 26, they say it's 4. Okay, we're almost ready to wrap up. Post your answer. Very good, I have about 28 replies, 26 replies, 25. Sorry, I have a... Very good, very good. grateful, grateful. How wonderful! stake. Excellent. Many Congratulations to the whole team. Excellent. Your participation was very good because this It also enriches the process of teaching, learning in spaces interactive. Excellent. There are 2.16 62 / 12 20. Very good. So I'll give it a few minutes, a few seconds. Countdown 36/6. The possible answers. Okay, then. So, I ask you that before Let's analyze what the answer is, let's go Now, to this exercise that I'm putting in this moment. Here's another code. QR code, please. We're going to enjoy it a lot. Here we have another QR code. Let's enjoy it a lot and you'll see that this moment of solution to the exercise, which can be maybe a little bit for some of motivating, it has a super purpose excellent. Very good. Remember that I changed the screen and I put another QR code where They have another exercise. Very well, I'm starting to get this QR code answers. It is very important That they do it is very important. Observe the exercise. Look closely at how the exercise is performed right now. Excellent. Very good. Come on, come on. We're almost at the second stage of which is learning. In other words, when we started to reflect on what the answer is, why? We got there. Very good, very good. I see that the response began to change things up a bit. Very good. I see that the The answers began to change a little. An example. Those who already put the answer and saw that their answer It changed from the previous exercise to this one, can quickly put in the area message explaining why he changed his answer. Be very brief. Very good. Someone who has changed the initial response. Why did he change his What is the answer at this time? Very good. I see many responses changed. Can someone put me in the chat? of this space, uh, why your The answer changed. Very briefly. Excellent. Very good. Thank you so much. Let's move on to reflection. Okay, before pass the reflection and put the slide, can someone put it like this for me? briefly in the chat, uh, why your Did the answer change? Since I see there were more than 12 replies changed, which is very good and those that are They also maintained that it was very good. Yes, Master Alexis, is there anyone who Are you typing in the chat? if me If you could help, I would be very grateful. Uh, they're writing right now. The results are 28, 20. Most agree with 20 as result. Yes, I also did it here on the drive. I have. Thanks a lot. Now I see that Some changed their answer from first exercise to second. Can someone tell me can briefly put in the chat by Why did they change their answer? There's a reply in the chat that says My answer was the same, since I only I changed the way I represented the division. Excellent. Excellent. Another one says, "I changed my answer because I considered the dividend before. In it I considered the previous one later." Very good. Excellent. Excellent. So, let's quickly take a look here... slide. I mean, I'm putting Thank you very much, teacher Alexis. I to him I am putting the first exercise. Yes, remember that it was 10 - 2 which multiplies to 1 + 3 + 24 2. 4 parentheses 2 + 1 close parentheses. This exercise has, as you yourselves have. They said they changed because of the way in which who saw the dividend. This exercise, although it is an exercise in arithmetic, It has a very important logical process. In other words, if we put it on, we put this exercise as it appears on screen, we are developing much more the logical, mathematical thinking, the critical thinking to the students or the person who gives a in one way or another has interaction with this exercise. Because? Because the Students study the hierarchy of operations. And when we study the hierarchy of operations tells us, First, what's inside is done. from the parentheses, subsequently eliminates exponent, then multiplies or It is divided because it is at the same level and then it is added and subtracted because it is at the same level. What's happening? Many Students go and do the process like this. Let's think, what is going on in my mind? mind as a teacher when I generate the exercise? as it appears on screen with the two points of division, beyond put a fraction. What's happening to me? Mind as master? It happens that I say, Well, I want the student to reflect on that moment and when I finished this very simple exercise, no. only has solved the exercise and has not only has it reached 20, but it has also have realized how to apply the hierarchy of operation. How to apply that operational hierarchy? For example, If I start doing the exercise and I say 10, I say, what is he doing? 10 with -2? Ah, subtracting. But what Is he doing the 2 with the 1 + 3? Ah, multiplying. Therefore, here the The hierarchy of operations tells me that solve what's inside the parentheses or that multiplies -2 * 1 and by 3. So, I have two ways to do it. Multiply -2 * 1 and -2 * 3 or Saying 1 + 3 is 4. That is, I'm in the blue part. Yes, 1 + 3 is 4. And I say, Ah, -2 * 4 is 8. Those two out of 10 men 8 a It doesn't affect me to do it. because up until that moment the hierarchy of operations are going very well. What is it that I can't do anything after I get the eight? I can't say eight and then add six, sorry, uh, add 24, because at that moment the 24th is dividing and the hierarchy of operations It tells me to divide first and not to add. But Okay, let's start with the first one. Sorry, to the first part, to the first eh, in line we reached 24 2.4 and between parentheses 2 + 1. I first have to solve the 2 + 1 because the hierarchy me He says, well, what's inside the excellent parenthesis. But although the hierarchy tells me, I eliminate power, that Apparently it's removing parentheses, I I cannot remove the parentheses because the thing about eliminating power, that is, How many times do I have to multiply the three by itself. In this case, the power is one. But when I go to remove parentheses, I am not eliminating power. What I'm doing is that moment is multiplying By whom? For the fourth. I am in the first row. We're ok? I'm multiplying by four. So, At that moment I have to say, "Ah, What is inside the parentheses is multiplying by four, but the "Four is dividing with 24." So, the hierarchy of operations... says how to multiply and divide are in the same order. It is done from left to right. But, Why is it done from left to right? For the previous exercise I changed the slide because 24, that is, it Violet, 24/4 is as if we had Ranked 24th out of 4. Why? Because the division is a fraction at that moment. 24/4 is the same as 24/4. Therefore So, who is it that is multiplying what is inside the parenthesis? The 24th. And what is he doing? the four with what is inside the parenthesis? Dividing. So what Does this happen? If I had put the exercise for you from the beginning, as it is currently displayed on screen, the process of reflection, of analysis, no would have been so profound that with the initial exercise that I put here colors. So, what is the answer? 20. Why? Because he four is not multiplying the three that It's inside the parentheses, the fourth one It is dividing. Because? Because for that I could first multiply four by so It's inside the parentheses, I would have to have a mattress after the two-point division, that would tell me. If I had a bracket after the colon of division, would indicate to me that all 4 that multiply 2 + 1, it's all dividing a 24. But at this moment, since I don't have the rocket, I have to analyze that 24 2.4 is a fraction that is 24/4 as proposed in this exercise. AND To close this part, if I had I started the exercise from the beginning, so as it is currently displayed on screen, The reflection, I repeat, would have been very mild and the learning would not have occurred to such depth in a single exercise, where through age in the debate, which is the second part in I learn, we begin to reflect on in depth the whys we see all the answers, all of which are heard because nobody made a mistake until here, even though we've put another piece of information It's not 20. Why? Because it Reflection is important with Tolerance, respect so that we can later to build individually and in collective and get to the real why The answer is 20, and in a way like this. to reach that third stage of life that It is the process of raising awareness, of analysis, to see what my areas are opportunities, how I worked them and what give a knowledge construction much stronger. So far, how are we doing? We're doing well. So we'll wrap this up. slide. We'll close with this slide. Thank you for scanning the QR code and In less than a minute, please give me the answer to these four exercises. Remember that all the answers are correct and the important thing is the reflection and analysis that we do in the individual and the group. I'll read them to you on the drive. There you have it the QR code. Here I am opening to see the answers. I see there's already an answer. Remember It's important that they do it because if They solve it, then we can when we enter the second moment to really enter into that reflection, to what It becomes much more interactive, so that it that we are doing has a purpose much larger. How are we doing? I'm already seeing the answers. Very good. Excellent. Very good. Very good. We're coming. Already 21. Excellent. Very good. I would appreciate it if the More than 30, please give your answer so that we can finish this session super happy with a broad reflection on how in three exercises we have experienced the process of age in an interactive way, of a the way in which we develop thought logical-mathematical thinking critical at the moment when I am able capable of making decisions and knowing why I took them. to substantiate it, not only from an empirical standpoint, which is when in the formal logic and informal logic, When we say, "I'm being logical informal because I think that's how it is, but I can't go into details with you one uh this scientific part with a a very fundamental explanation. So, One of the things we want today is That's it, and experiencing it too. How do I get to that formal logic when I am also capable not only to know what the result is, but why? Not just from my experience, but from a foundation, in this case mathematical, scientific, physical, etc., etc. all those things that may come. So, here I see excellent, excellent. Thank you so much, I love it. Wow, 59. Excellent. Very good. Excellent. Then, immediately We'll move on now We're not going to see the answers because we already... I'm seeing them here. So, We'll stop answering now and look into it. the next slide. What is 24 / 6? If they want that, if they They realize, I don't put a QR code on their notebook. What is 24 / 6? When you say 24 / 6 = 4. If you They realize, I put 24 in red, six as one in a light green and four in blue. And why Should I put them in the three colors? First, because we are in a process virtual. If we were in person, The best part is there's not so much of a problem. By that? Because we are there, we are watching, we are observing as an observer external observer watching how the student progresses responding. In this case, I'll put them on. in colors because that's where I want it To arrive is, observe what I just did put the last part on the slide down. Why is 24 / 6 = 4? We could think in many ways. And in They're going to tell me in the debate, "Ah, because the Six fits four times into 24. Ah, because uh 24 / 6 is 4 because uh equals four, but I also have to go looking for her answer, although at that moment what I've been told it's not incorrect, that their The answer I came up with is that 24 / 6 is 4. Because if I pick up number four, which is the quotient, which is the result of the division, when I multiply that cu Because of the denominator, which is 6, I will obtain the numerator which is 24. or Okay, I'll come back again, I'll grab the I multiply the result by the denominator and it will give me the numerator which is 24. It's like saying a For example, what number multiplied by the Does 6 give me 24? So let's go here to this previous slide, to this one. He doesn't anymore I'm going to put another QR code so you can see their answers, otherwise we'll go to this slide and now let's think What is 0/5? What number Multiplied by 5 gives me 0? Ah, 0. Very good. 0/5 gives me 0. Why? that? Because 0 multiplied by 5, which It's the denominator, it gives me the numerator. Now I'm going to the second one, which is 5 out of 0. I wonder, what number multiplied because of the zero in the denominator Can I have five? Is there a number that multiplied by zero equals five? I mean, there is no number that multiplied by the denominator 0 gives me five. Therefore Therefore, there is no solution. is indeterminate, indefinite, we could put many things. In this case there is no solution, no There is no number that multiplied by cer me c Now we're going to 6 out of 6 And he said to me, what number multiplied by The six in the denominator gives me the six in the numerator? Wow, one. Excellent. 1 * 6 equals 6. And now I'm leaving. On the fourth one, I say, what number multiplied by the zero that is in the denominator, that is, at the bottom of the fraction? What number multiplied because of that zero in the denominator Does it give me zero in the numerator? And some Some can tell me zero, some will tell me to be able to say 1, 4, 5. That is, there is only one answer. My question is, we found only one answer. We are in the room. In other words, what is 0 divided by C? Is there any number that multiplied by zero in the denominator, a single number Give me zero in the numerator? They don't exist. many numbers. Because? Because 0 * 0 gives me 0, 1 * 0 gives me 0, -4 * 0 gives me 0. In other words, there are countless numbers that multiplied by zero of the denominator me gives the numerator. That's why it's said that 0 / 0 is indefinite, indeterminate, infinity, tends towards infinity, all those things. Because? Because I'm not going to I'm going to have only one answer. infinite answers. I have nothing to do with it. exact number. It gives me 0 out of 10. And in At this moment we not only reached 0 about 0 is neither one, nor a zero, nor It's not even three, it's infinity, which is also we can call it indefinite, indeterminate. Now, what else can we build in Let's close this moment? Because? Because if we look at 6 over 6, it's 1 and 0 over 0, wow, what do we see there? which is the division of a number by itself. So, there is a theorem that many Sometimes as teachers we give it, that today it is It takes as an axiom, it does not need proof, which says that every number divided by itself gives me one. But it is that theorem says, every number divided by itself is one, except the zero. And what is one of the answers? Why except for zero? This is one of the answers, but there may be many which I invite you to look for in the Internet. There are many other ways to explain why 0 over 0 is indefinite, indeterminate, tends to infinity. So, analyze what your answer is They put it on and see what happened to you when we started analyzing those four previous exercises through this that I just put on the slide. EITHER So, how do I handle them? Instead of giving it The answer, I'll take you to this slide that they have displayed now with an exercise that's in your zone comfort and I take it to be analyzed. Because? Because 4 * 6 is 24. So that you know that do the process carefully in these four and immediately tell me in the eh in the chat, please, if doing that Did the process change any of the things you did? answers, especially the last one, cer upon cer. I would greatly appreciate it if you could tell me if... Do this process 24 over 6 and see the answer by the denominator and Do it in these four exercises if That helped them think that the answer that they were able to put be modified. Apologies. But, Thank you very much. Teacher Ley, can you help me? Yes they put, please. Yes, ma'am, of course. Thank you. I'm going to Okay, let's wait a moment, Let them load the questions. In other words, the question is what if after that We saw this here in the slide, that is, after we did the four exercises, before watching the The answer is, we look for why 24 / 6 is = 4 and we analyze that because 4 * 6 24 e We did the same process in these exercises. So, what number Multiplied by 5 gives me 0? What number multiplied by 0 gives me five? That number multiplied by 6 gives me 6? and number multiplied by the zero of the The denominator gives me the zero of the numerator. If that process of analysis that we are experiencing, for reflection, seeking that you They built, it helped them modify the the answer they had given at the beginning, mainly in the fourth. Ready. Here we have Gisette Rodriguez says that my perception. We have Walter Gaviria. Walter says, "Yes, Madam, it provided more clarity on the thought." César Camacho says, "Yes, better, better "Analysis of the response." It says there was a better analysis. He says that later he says Caesar, he says Caesar Parra says yes, he did help him remember properties of division. Excellent. "We have Wilmer Velázquez," he says. that did change my way of thinking. I did the exercise mechanically without analysis what the doctor analyzed. Darwin also says, he says, "Yes, it We think, only one wants to respond faster only wants to answer with zero, believing that It is the most accurate. Excellent response. Very good. Excellent response. Many Thank you, teacher Alexi. Thank you so much Thank you for your support. Very good. Excellent answer. So, how? Did you see? Here we work individually These exercises are done using QR codes. as if we were in a class in person, I would be observing externally. What does that mean? No I would tell him what the answer is. Snap Well, if it's wrong, if not only I would observe. We enter the second Wait a minute, but what's happening? As already I'm seeing the response, I'm seeing them I'm taking this slide from 246, seeking a modification, a change in you before entering that second moment of the debate that brings eh the methodological approach gives. So, in I also observe how at that moment You modify that answer that We saw better, as in the second one, that we didn't It was the solution it was, it doesn't have The solution is either indeterminate or undefined and we see in the fourth. Therefore, already In my planning, I already have those things that I would like to happen and that The fact that they happen is not bad, on the contrary, but because when it happens, one enters a process of cognitive imbalance where that cognitive balance is found at through guided, well-conducted and we enter a very metacognitive process strong through the analysis itself of the construction of 246 that again it This takes you to this slide and you just They build that knowledge and that makes much stronger because of the process Much more has been experienced than if I were alone I would have told them, "Ah, look, the The answer is this." Even though he has Having explained why, the process of The construction is not as strong as the that you experienced a moment ago. So, this is a little bit of what I I wanted with this thematic conference and so that you could see how it is bidirectional and dialogue. It's not just about to speak, but to create spaces where the student questions, debates and propose. is reflected in the phase of I learn, where inquiry and debate with others they are engines of construction logic. learning by doing, which Interaction is not only social, but also with the object of study. I mean, The student, the female student, an apology there, because it manipulates data, experiments, He observes the results, and that's when he student or the student or the pupil and the student takes the data and processes it actively to see what happens, if it changes a variable, what happens. And not only We are teaching mathematics in the classroom, but we are also teaching for the life. Because? Because many times When we are in the classroom we think that We have only one answer, and when We're doing math in life everyday life, because we are applying the Mathematics in everyday life, sometimes We have more than one answer, and also That's within the methodologies. active. When we use the problem-based learning, we seek that the student reflects a lot older and often we have more than one answer thus leading us to the problem, to the project where we can to generate, for example, ice, do it as a classroom experiment. So, when we take the student out from that math classroom and we took it to that he/she learns for life through a problem in context, but not only has to add or subtract, but There is also a logical process of analysis, reflection, inquiry. AND now to wrap up the use of the metacognition, which is a strategy that It is interactive when it forces the subject to interact with your own thinking. That internal interaction that is in the I realize that the phrase is a strategy. interactive self-awareness where the student identifies their own cognitive processes and that in the The third phase is capable of working on it. There is technological or social mediation can be interactive through work collaborative, peer tutoring, Educational software, simulators, gamification, community projects, physical experimentation, a physical conditioning, a little like that and a And finally, I'd like to mention that... Interactive is not just about using the technology, but it's also that part that we have just experienced in this moment, as if through an exercise, From a problem, we can generate a thought analysis process critical, logical thinker, mathematical, in a way that motivates and that make us grow. Sometimes even in a Through our own practice we grow much more than Maybe do 10 or 20 exercises. AND With that, I'll call it a day. This part of the session thanking one Once again the invitation and also, uh, the that you three were able to experience moments of the methodological approach gives me I discover, I learn, I teach, and let them see. how this becomes interactive through of the problems, not by itself, and that We will also analyze certain things today. processes of logical thought mathematical, critical thinking, Thank you so much. I'll be waiting. Some ask? Thank you very much, Doctor Lady Hernández Mesa. I really want to go closing before reaching the questions. Uh, I want to read one Some comments from the participants in our chat, in our channel YouTube institutional. I think it's It is very important to highlight that we have students who say excellent exercise from logic and analysis of each operation. Also excellent exercise, teacher. They also tell us, excellent, a new way to find results. Very good. They also tell us, "I did it like the teacher and improved a lot analysis." Excellent. They also tell us Here, "My analysis changed a lot as The teacher did it." Yes, very good. Improve the analysis. The teacher gave a good explanation. Ready. Uh, Doctor Lady, look, I think The objective of your talk was achieved. hey you gave that parameter, that that tip to the students so that through your Hey, DAE project, well, go too. learning that way of seeing the exercises and how to face them in a different, doctor. So, uh, that's why I wanted to read those messages, because that's where I found out evidence of everything that it all the The lesson you taught us in this in this short time and We hope you will join us later. so that you continue showing us this experience. Well, time has passed. It's urgent, so I have a few. There aren't many questions. Here they tell us, right?, they tell us from The teaching role tells us the following. Can you describe a detailed example of a logic class with the dae method, for example, to teach tree felling truth or fallacies. What activity How do I discover myself in a concrete way? That input in learning? And how How do I organize and teach in the classroom? Very good, very good question. Give the It was a coincidence that I was going to put a I exercised on it, but I said no more We would spend a lot of time together. Uh, for example, a I love it when we see the charts of truth, uh, beyond whether it's true, No, why does this happen? I tell them, "Let's see, Where does this part of the logic?" And then we're in the living room In class, the students tell me, "No, teacher, no, I don't know." And then I I put, uh, I start asking him, there We are in the first part, that is, Where can we apply the tables of TRUE? Where do we see it in life? everyday life? There is already a first part where I get the student to think about the individual, not to be sought in the internet, not to look at the in the notebook or ask others. That It is important in the first part of Dad immediately in the dark because there he We give the minutes depending on the problem or exercise. Immediately, I begin to ask them what they thought, what their answer was They did, what they said. Then they begin to give me different answers and has past because I have lived it in which I They say, "No, Lady Teacher, no no "We know." Then I stand up immediately on the switch that He's in the classroom and I turn on the light. I turn off the lights and say, "How "Is the room there?" And they tell me, "Doctor "Lady, she turned off the lights." And I tell her, "Wow." So, let's see what it is. whether we're at zero, at one, whether it's is it true or false? And the truth, how It has to do with the one and the false one with Zero? Ah, but I'll take them. Remember Computers, remember that now They are younger, but before there were some computers where I had, like, uh I had a back there to put if it was at zero. No electricity was coming in, if it was in One of them was getting electricity and then he I say, "Ah, we see that here too. The Zero is false, which is one. Uh, zero is off and the one is true, which is on. So, how is it right now? the living room? I turn on a light and silent The other one is not in true or false and Silencing the two is true true and we've already started through there And now, what did they learn? And how What do you think? Can you give me more? answer? We're already on the third one moment and through that curiosity that It was formed there and from that analysis, in the In the second part, things start to flow in her mind and they're already starting to give me other ones answers they didn't have at the beginning. That It's an example where I can take cape. I don't know if that answered him. Wonderful, truly wonderful. What a way eh so clear of showing how one He teaches Boliana algera, doesn't he? In two states, true and false. And so it was It is strongly anchored in the context of logic mathematics. They come to me in the head one the concept of the gates logics. Okay, then that's it. to finish, doctor, Okay, so with this last question. Says, "Regarding the evidence of meaningful learning, What instrument is used to verify that the learning meaningful and not just me? How do you evaluate the transference of thought logical to new problems in non-contexts mathematicians?" Very good. The same approach Methodologically, it helps me because if they occur Tell me about what we experienced, I'm going Observing, you gave me an answer in the forms. If we were in a face-to-face classroom, I was observing. So, it has a very strong observation of being observing. So, the process is dialectical, it is growing constant. And I'm starting to realize what How far did they advance from what point? both enter into the debate process in the second moment of the of the methodology and in the third moment when they are able to open up. I have students who perhaps in the first They are not able to say, whether they are first or second class. "Oh, I learned this from my partner, from my "Partner, or am I mistaken?" But how? The same methodology, as it is a form that we create a space for it to happen meaningful, healthy learning, Careful, responsible, it makes the student or the student go interacting. So, that's exactly what I'm going for. helping me see how much it's growing. But for that, I also need to have Take great care in planning. that I'm in the process, not in terms of topics because Separately, I'm putting things together, in addition to to use a rubric, which is a rubric that I am carrying where I too I am analyzing individual growth of each student And that helps me to know how much They grew beyond simply giving him a test. only. Thank you very much, Dr. Hernández Table. Thank you very much from Mexico for Share with us the DAE method, discover, Learn, teach. The idea that the The student not only learns, but also It also teaches as a way to consolidate Knowledge is a proposal that invites us to rethink everyone's role in the classroom. Okay, so now to do the I will now give way to the respective closure. Dr. Daniel Esive Moral to do the doctor's respective farewell Lady Hernandez Mesa. Thank you very much, Alexis. Doctor Lady, Well, to thank you very much for, uh, your presentation, for having accepted the invitation to our event also for Wishing you a happy birthday, wishing you a great day and well Thank you so much for sharing your experience and knowledge in our event, uh, hoping that this will be the beginning of an alliance with the University Autonomous University of Baja California so that Let's continue working on everything that we convenes from the point of view of mathematics education and mathematics. So, thank you very much for your uh acceptance. Thank you very much. Thank you so much to everyone and to all. Hey, have a great day! Thank you, and I'm leaving very happy. A gift very large. Thank you for your participation. And yes, we will continue with this linkage. Thank you and best of luck in these two days and forever for everyone. To you, Dr. Lady Hernández Mesa, Thank you very much for your participation. Thank you. Have a nice day. Bye. Likewise. Okay, then we're done. with this presentation. We continue with the first congress of Interactive mathematics 2026 led through the basic sciences chain, eh a through the logic curriculum network, algebra and calculus. Okay, next we move on to one of the most enriching moments of this day, our panel of experts in education and Steam applications with participation in Colombia, Mexico, Chile, moderated by Dr. Daniel Steven Morales. Then, in a few moments Let's begin this panel of experts. and Good morning everyone. Welcome to this panel. Them We present the four experts who... accompany today. Lina María Toro Quintero from Colombia. Lina María Toro Quintero holds a master's degree in computer science applied to education and systems engineering with more than 14 years of teaching experience in information technology. Currently it is works as a teacher at the institution educational Ciudadela del Sur, where leads training processes in programming, software development and educational robotics. He is the team leader institutional robotics and creator of departmental robotics meeting, Ender, an initiative that has impacted hundreds of students in the SIM skills strengthening. ha led training programs in computational thinking and empowerment of girls in science and technologies, consolidating as regional leader in STEAM education. Their teams have participated and featured in settings such as Markerlap, Fars, Lego and Lap and Hakaton nationals. His work has been recognized with multiple distinctions, among them the medal for teaching excellence and the order Etelmina López. His work focuses on the integration of robotics, the programming, pedagogical innovation to enhance logical thinking and the training of new generations in areas. We also have this event panel with Jorge Octavio Mata Ramírez from Mexico. Dr. Jorge Octavio Mata Ramírez has a degree in physics from the University of Guadalajara, Master in solid state physics sciences and PhD in crystallography The University of Barcelona, ​​Spain. is a member of the National System of Researchers and Investigators of Mexico and has the RODEP profile. His Postdoctoral training comprises three stays, three stays in institutions of excellence. The Optics Department in In 2002, the Department of Christology from the University of Barcelona in 2003 and from the Center for Matter Sciences Condensed version of the UNAN 2004-2005. Their main areas of expertise These are their main areas of specializations are the physics of materials, nanotechnology and solid state with emphasis on design of the creation and analysis of crystalline materials nanostructured, ferroelectrics and semiconductors. From In 2011 he worked as a professor Senior Researcher C (Full Time) completed at the Faculty of Engineering, Architecture and Design, FIA, and the University of Baja California, campus Taught, where she participates in the undergraduate and graduate programs science and engineering. His career Previous experience includes work as a researcher at the Center for Matter Sciences condensed, professor at the Faculty of Sciences of the University of Baja California and research professor at the University of Baja California website. His academic production undertakes more than 40 articles in indexed journals, eight books, 10 book chapters and numerous contributions at conferences national and international. Also in This panel of experts is with us Marta Cecilia Mosquera Urrutia. From Colombia, Dr. Marta Cecilia Mosquera Urrutia holds a degree in mathematics by the University Pedagogical, specialist in pedagogy in the development of autonomous learning and Master's degree in education from the University of La Sabana. he got his PhD in Didactics of mathematics at the Institute of Mathematics of the Pontificate Catholic University of Valparaíso, Chile, with the thesis critical points in the teaching the concept of the area of flat regions that constitute obstacles to understanding the definite integral. It also has certifications in studies Afro-Latin Americans and Caribbean students from the University of Harvard and in law promotion policies for Afro-descendant peoples by The University of the African Diaspora. Currently part of Brazil's CNP, a transformer anti-racism, intersectionality and social justice in Latin America and serves as head of the bachelor's degree program in mathematics at the University South Colombian. And our last eh eh Estefanía Bravo is the guest on this panel. Blond. Hey, we're joined from Chile by... Dr. Estefanía Bravo Rubio is graduate in mathematics and teacher of mathematics for secondary education. Both titles obtained in the Pontifical Catholic University of Valparaíso. He obtained his doctorate in sciences with mathematical mentions in the University of Chile in March 2022 with the thesis Isogenius Jocavian variants via intermediat convers Dr. Anita Rojas. His lines of Research is marked in algebra and geometry with special interest in Jacobi varieties, surfaces of Reayan surfaces and shares of group on algebraic structures complete. His teaching career includes tasks at the University of Chile, the University from Santiago de Chile and the University Federico Santa María Technical School, where She currently serves as manager outreach and dissemination on campus San Joaquín, Department of Math. She is a co-founder of science outreach project I'll tell you in 5 minutes. teacher of the ESMA student initiative Meeting of Women Mathematicians and founder mathematical explorer's explorer, from where it promotes access to the mathematics and the visualization of women in science. The dynamics of The panel will be presented shortly by each criminal lawyer. eh debate among peers, questions from the audience via chat Zoom is part of our platform YouTube. Then I give the go-ahead to doctor eh Daniel. Thank you so much, Alexis. Very good Good morning to all our invited panelists, thanking them uh By accepting this invitation, this conversation we will have about the virtual mathematics education, artificial intelligence and education mathematics. Uh, thank you very much for accept the invitation. Okay, let's go So, let's begin with a question. general. Each one comes from a different field different, advanced materials, teaching of calculus, algebra and outreach, educational robotics, but Today the four of them share this space interactive mathematics. I would like that each one would tell us from their own perspective briefly what my own experience is What does the intersection mean to you? between mathematics and education Steam. Uh, one minute, please, every one. Doctor Mata, then doctor Mosquera, later Dr. Bravo and Finally, our Master Polo. How are you? Okay, can you hear me? Yes, yes. Well, thanks for the invitation. Hey, Regarding the question, Uh, sometimes I think that we don't It's not that we dissociate or separate, no, almost Everything is together. In this case, the math, Materials, science. In the end the Mathematics is a language that is associated with all trends technological technologies that we use today, No? Mathematics, well yes, sometimes They are a more complicated language, but There are people who are in charge of some way of conveying it, translating it and above all, apply it. So, I I think they go hand in hand. Now, with the advent of infinity of technologies, I think it's very easy sharing knowledge and above all to understand it and apply it in some way in pedagogical matters, matters didactic and above all, to solve that kind of gap of ignorance that you have and look for with the support of new technologies new knowledge and new transmission of them. Yes, thanks. Uh, well, uh, good morning everyone. It's great that you're here connected in This chat. Uh, it seems to me that I need to answer the ask that connect or the connection that exists between mathematics and steaming areas It gives or shows that I am capable of using mathematics. In other words, let's say the mathematics, some, as the Doctor, that's right, who came before me, eh, One could consider them as a language, could, well, everything that I'm talking about mathematics, but let's say that when I manage to put those mathematical knowledge at stake for solve my problems everyday life or the problems of science or the problems of science mathematics, that I can articulate and see, let's say, the mathematics in all its dimensions. Thank you. Hello everyone. Uh, many Thank you first of all for the invitation, for to be here. Uh, regarding the question, I agree with much of what my friends have said here. colleagues, especially the part that is a language, eh, but I also see it as a superpower. For me, mathematics is It's super and we've actually used it as is the case in many of our activities because math tells you It teaches you to think, it teaches you to reason and Furthermore, this universal language is not It only allows us to communicate with each other us, but also in understanding the universe and in particular, for example, artificial intelligence, the machines. So, mathematics tells us They transform into who we want to be, do we want to be a user or do we want to be a creator. Good morning to everyone. Hot weather out in Armenia Quindío. Thank you very much for the invitation. Well, uh, the Steam areas, Basically, they put the math in. There you go, right? are are fundamentally four areas, but as I confirm what my colleagues were saying. colleagues, because they are like a language universal, but above all I believe that They are a connector between what we see Theoretically, what those concepts are that we have and bring them to reality. AND That is precisely what allows us to Steam approach, as they were saying in Special Estefanía, uh we applied, TRUE? to problems in our environment, to our realities, but that we apply all those concepts that we have we have been building, that we have been obtaining and especially the mathematics, because when we We put everything to the test, according to our own standards. It has mathematics all around it. Without It must be as from this awareness and this approach to be able to be visualized and be something that gradually becoming tangible, something that is so intangible, we can go seeing tangible. Well, thank you very much for this first impression about what It means for each of us the Steam education. Uh, I'll continue with uh one Question for Dr. Mata. I'd like to begin with you. Uh, you investigate nanostructured materials and at the same time time trains engineers at Fiat. How has she lived that double life? researcher and teacher? Do you feel that your laboratory findings end transforming the way teaching is done or consider that they are two worlds that Is it hard to make someone talk? H, Well, the truth is that it's very simple. Normally the investigation is associate to universities, to education. Is It's true that there are filters. It is true that regardless of what investigate, well Not all students participate in that investigation in preparation for the the mathematical part or the teaching part or the part of physics. because they are required prior knowledge, but often the laboratory is a kind of manager of Ideas condense, they become glimpsed concepts, innovation takes place. In fact, many of the discoveries that have been made, Well, they happen in laboratories, right? By conducting an experiment, searching for such one thing, well, find another, but they go from the hand. definitely teaching and the research are compatible, of in fact they are complementary Thanks to intelligence artificial, to the use of computers, processors, uh technology, We can do better experiments, We can replicate experiments, we can innovate. For example, we simulated in computers, We teach students to program, the We teach them how to simulate, we teach them, Let's say, to create on the computer and Then we went to the laboratory. So, the teaching aspect, let's say, It has weight, it has support, it is a arrow that somehow guides them. The fact that they work processing, programming, developing, generating code and subsequently developing it in the laboratory, because it is very satisfactory, but it goes hand in hand. So, To recap, I think these are things that go hand in hand. Do nanomaterials, well, it's a matter of vanguard. which are done in many laboratories and universities around the world and teaching Well, it's part of the foundation, it's support, but above all it is complement, is part. Yes, thanks. Thank you very much, Dr. Mata. And for take advantage, eh, so that all our connected students are also interacting through our chat YouTube. We currently have 450 connected students, teachers, so that they can exchange their impressions with our panel of experts, so they can tell us. also how they have integrated that part of research, education, and learning at our university. Hey, Dr. Mosquera, we are still with you. His The research comes from a very different, but equally exciting. His doctoral research got into background in something that many teachers They have an intuition, but few have studied it. systematically. Why do students fail to achieve understand the definite integral, although Do they know how to calculate it? What surprised them most about it? that he found and what has changed in his your own way of teaching? From those findings The microphone, teacher. Yes, thanks for the question. And it was saying that it's a question that I I like it a lot because you almost never see it. They formulate, not even you as a teacher, eh? the formula. I always in all the spaces I remember that I am a teacher and that I have had the good fortune for more than 20 years of training teachers math. So, uh, let's say with the mathematics teaching sometimes Something happens, let's say, to the teachers and to the students when we study mathematics, and suddenly that structure that mathematics has We didn't connect it. When I I started, let's say, to look at this... problem that I wanted to address from my This thesis, which is not new to me, because I I've been working on this issue in the area since I've seen it from many angles, Several years ago, uh, because always, well It caught my attention, let's say. that. So, uh, let's say that among the things that we say are like much more One important thing to keep in mind is the fact that when we started, because For example, at school to work, for to say something, the fractions, then we never connected those fractions, for example, with the area, TRUE? although generally We use rectangles for our work, Let's say, the area. So let's say one Then we'll see how we progress and what happens always the area as a formula. He even asks a person who It's the area of ​​a rectangle, it says base By height, yes? Or the area of ​​a triangle, right? Base times height above Two, but it is the area, right? So we go, let's say, like growing in that disconnection. where suddenly, as teachers of In mathematics, there's something we don't have. taking into account, and let's say that the teaching or development of Mathematical competence reduces five processes between what are, let's say, processes between what are, well, let's say. Those general processes, right? That They are, let's say, formulating and solving issues. As for that, well usually in the class the one who formulates The problem is the teacher and the one who... The student solves it. So we are, let's say, losing that ability of the student to formulate, Let him tell us, right? And that he may do that. There is another one, which is the modeling processes. So we don't We work on that modeling of process, but generally the teachers, we teach the concept and We delivered the formula. So h We were left wondering where it came from This formula, to say it like this. The other one is Let's say, uh, communicate, and then that Mathematical communication is something that is fundamental and I found it when We were looking for the background information, Let's say, from the thesis, even for a question that comes later, when I I specialized in pedagogy for the development of learning self-employed, then one found that distance learning students, because The biggest problem one has is achieving to understand what you read and more in mathematics So, develop those four skills they work on, for For example, from the perspective of communication, which are speaking, listening, reading and writing, mathematical language, the use of symbols. So we realized that too including higher levels, by For example, when students enter the university, because we in the We don't have it in the first semesters. account. The other one, then, has to do with with reasoning and then there are many ways of reasoning in mathematics and So there is a part that is central to My thesis is, uh, let's say, when you You read the full title, then the One of the frames I used is the framework of modes of thought. So, one, let's say the objects Mathematicians have different ways of to be represented and we then We are generally representing them to through symbols. So, because For example, one finds that from age Early childhood does not have that access, for example, to geometry, to the spatial location, to all this that It has to do with understanding the world and how mathematics helps me to to describe and understand that world. AND Finally, then there's that one of formulate, compare, practice procedures and algorithms. Because Let's say that when I put the problematic, then one finds that Students generally know you solve the operations. The children They know how to add, subtract, multiply, split. In the case of calculation, the boys solve integrals, they handle methods. But, for example, when one is working, let's say, a student that I've always had a problem with fractions, then one gives a integral by substitution in a polynomial of the form P over Q and uh with that already because the student, upon seeing the The fraction will be limited from the start. So, we have, let's say, that idea of to check, to estimate, uh we stayed a little without that. So that seems to me So, let's just say that was the discovery. bigger, let's say, like I said, I've been doing this for a long time and trying to study, to see how the People think about that. Uh, what Did we achieve it? What have I achieved? and it has allowed a lot eh eh how to improve the the way I communicate with the students and teachers in training and It is the fact that those procedures They are not old because we are accustomed, then, as Viayer said that then, uh, that the children that the stages that first algebra then such things. So, let's see how the children from a young age with questions appropriate, with appropriate procedures, They manage to get to issues like, uh very good at mathematics, such as for example the development of thought variational estimation and the prediction. Thanks a lot. Thanks a lot. Furthermore, it is a theme that in the I personally like it a lot too the research, the development epistemological of the mathematical integral and its history. And how cool! We are counting on you, teacher, because we are in some related areas. Hey, We continue. Uh, Dr. Bravo, you This afternoon he's going to show us something that Personally, it generates a lot of... curiosity. This afternoon he's going to show us how paper folding can be a Introduction to algebraic thinking. I'm curious to know how you got here to that idea. Was it something that came to you in the classroom, in research, or some other way unexpected moment? And from his experience, in what type of student has seen that that strategy really It motivates him and ignites that spark in him. Algebraic curiosity? Thank you very much, Daniel, for your question. Well, ever since I was very little I've always I really enjoyed making paper figures. Hey, She was one of those girls who, when she arrived at a restaurant with a napkin started to make the little boats, a lot of figures figuring out how to build new figures and but I never connected it With mathematics, he was always more of a hobby, a more artistic side of me, even that I once arrived at a workshop when I was an undergraduate student and a professor from My undergraduate studies taught me precisely about the Sound module B, yes?, which is this piece that is here. Well, precisely this piece e constitutes a piece of paper that It is folded in such a way that it can to combine with others and assemble figures, beautiful figures like these. And that's when two things happened things in me. The first one was like, "Wow, this thing that I've always liked, that I It's striking, it's clearly there connected with mathematics and never it "I had seen it like that." And that's when It was established as a mental bridge of the connection between this art and the mathematics. And from then on I began to study it, how to be able to use it as tool to explain certain things both algebra and geometry. And well, it was also very significant because many times at conferences We discussed tools such as Lego was very useful for developing biospatial skills of structure, certainly, of construction and which were very, very related to everything that was the STEM area, that is, people who played these games When they were little, uh, then they developed greater capacity in these STEM areas and But Lego is an expensive piece, Not everyone has access. So there Another very different part of me was also activated social, because these pieces work like Legos, because they fit together. Same idea, it's also a game of construction So it's easily accessible because it's paper. So from there we started doing many recycling workshops as well were associated with these constructions geometric and at the same time We learned algebra and geometry. In general, I have these activities done in many audiences. Uh, we've gone to schools with younger children, with high school students, that is, between 12 and 15 years old and I have also done workshops for older adults and the The truth is that it has always been very successful. At science fairs, when We presented that stand; in general, it's the most popular, it always gets very crowded people because it gives us a tool Besides being very pretty, right? uh that It allows us to create things and create from the mathematics, understanding how angles They have to fit together for these things to work. to fit together, to understand what they are edges, what are faces, how many I need to fill some pieces and the truth is that That has been very successful within the motivation for students and good, For people in general, as I mentioned, We have also done it with adults. older people. The real challenge is ensuring the activity is designed to ensure that the objectives, because where are they There are many people who are entertained, then is lost in this construction and So the challenge is in designing a an activity that specifically addresses a specific objective and that it is not lost in the beautiful, the artistic, but be rather a bridge, a complement and a very useful tool in the classroom. Okay, thank you very much. And in the chat You can also give us feedback, Dear students, if in any at this time have they had interaction with these folding tools that are very interesting to awaken this algebraic thinking. Thank you so much, doctor. Uh, we continue with our Professor Lina María Toro. Uh, you then comes from a place closer to the day our students' daily lives. Uh, and we It seems very interesting that you created the robotics meeting from a public educational institution. That's not most common. How did that idea come about? And what did he have to move inside the institution, within yourself? for that all of this would become a reality. And what has surprised you the most? of what that space has awakened in The students? Well, Daniel, let me tell you that uh I I started with educational robotics, with some formations that we could access. Uh, a lab arrived. small with some Lego imitations, no They weren't even Legos, with just a few pieces, a few microbits, eh, and we started to explore with the children. Yes. Uh, I already had done the Steam girls process where it was therefore a process focused on girls who also had something to do with the electronics, some robotics and It so happened that at that same moment my son joined a robotics training program at the school he is part of. So I, precisely in the conversations with my son, he spoke like What were they doing in their seedbed, what I used to do that with my boys. I started watching that we were not very far apart. Both I began interacting with another entity which is the Technocademy that belongs to DINNER, where they came to support us in some processes. And then I saw that in these dimensions we had connections, that we weren't, eh of soon at the same levels, but yes So we had, as it were, an interest, a passion, and from there the idea arose to meet, to meet Tell us what we were up to and what We were kind of doing and working from these different institutions, But there was the coma, how did we get together and We told each other that. So, that's where it came from the idea that there were teams interinstitutional cones of different levels of knowledge and therefore because of our realities were also different socioeconomic levels and then what One way I thought of to share was that we would have some challenges within the Steam's approach to solving. Thus The first meeting is born, this idea, uh because it was told with the support of some colleagues, specifically the one from Tecnoacademia and the professor of contemporary gym, which was the teacher of my son at that moment. And then They were motivated, they liked it a lot The idea came to us and we had our first meeting. For us it was absolutely amazing, it was like, "Wow, what we experienced there." In addition, we invited a colleague who was doing robotics with electronic recycling from a municipality near the city where I am. I am in a apartment that is very small, that is Quindío here in Colombia. And what What we saw there is that there is an interaction between the boys when they are passionate, when they are creating ideas, watching how something develops. Of In fact, that day was a great one learning because we had programming disconnected, Uh, another part of a hand with sticks, part with Legos, uh, well, that's it with Lego robots that already some The institution had it and we didn't manage to rotate through all the stations, but yes We saw how the children interacted, how They wanted to solve that challenge together, no It mattered that they didn't know each other and that They were friends for that day. So, uh, we already made one more proposal ambitious that we were fortunate enough to He was welcomed by various institutions, between those two universities We started to get more support interinstitutional and four-team that we participated for the first time in the The second time there were 16 teams. we have grown exponentially by the fifth that version we are already preparing, We expect to have more than 30 teams and and it kept expanding. And I feel that it that you say is most surprising is something that became the philosophy of our meeting, and it is from those different levels of knowledge there All boys are equal for one day. So we have kids from rural areas, They are no longer just from the department of Quindío, we have from Caldas, Risaralda and North of the Valley and also come from rural areas, public and private. And how we managed to get there with their different levels in all this that I have counted, they will be equal for one day, equals sharing, equals developing. And I have experienced how My students are friends with others students and then by competencies, For example, what they do and what we're going to do to be. Then they tell me what they're doing doing, what they've talked about and it's Amazing, amazing to see how They can break down those barriers, because We especially find those barriers in the imaginary. So I think that It has therefore been very motivating and It was surprising what I thought you were asking. Thank you so much, Professor Lina. Hey, Okay, I'm going to ask a question. Hey, I propose that he answer it for us. First Dr. Mosquera, then the Dr. Bravo, uh, and she's next. This congress is committed to gamification and the tools digital, but today we heard about origami, drawing integrals, laboratories physical, robots that teach and that students They assemble with their own hands. Do you think there is something in teaching of mathematics and science that It simply shouldn't be digitized or do they think it's more a question of how technology is used Is it used? First the teacher and then me, right? Yeah. you as profequera. Okay, fine, but... You had told her first, well, I think there is something non-negotiable. which is, uh, the reality for people, the context in which we operate and using math for that. But then, uh, I would say, well, So, what do we use the artificial intelligence, for example? either so that we say that, for example, the Professors, we have that access, uh... find the examples, to help organize the spaces for the students. So, for example, to One, there was a question that You had placed that it has to do with Someone who doesn't know how we work, for example For example, social justice in the classroom. So, to me, intelligence artificial if it could work for me, because For example, to find out how is it that the definite integral, by For example, it is used to work on the equity in the mathematics classroom. Yeah See? And then I'll say like Professor, I have used technology to that. Students can use it to lower figures, eh compute data. Uh, by For example, when we work on everything This business of large numbers, let them do it. their accounts, but then lower the graphs and interpret them. So, if For example, one almost always the Examples he finds are from the United States United States, in the United States, such a thing occurred thing, well, and what does that have to do with it? see in our reality. So, because For example, the boys can use the technology and now all these pages that there is to enter to consult, for For example, the DANE data, to enter to look, let's say, like many things. It Another one that I also defend, absolutely fed up. It is the fact that the students can learn to use software. And then there's some software which we hardly use, because For example, dynamic geometry. Today in Well, they even say that on this day... Economic factors suggest it's better. use geobra. And then the children They study, and young people often... We as professionals use the GeoGebra, but there are some software programs before the GeoGebra, such as Cabri, TRUE? the 3D cable, the express cable that since the pandemic, it was put free of charge and that leaves us, therefore For example, guardaro lets us do everything the same thing that, let's say, a cable does, a what other function it cannot perform. So, the advantage that has software is what I need to know how to do the procedures and what helps me The software is designed to optimize that. So, Why do we sometimes see, for example, The students using geogem, then Do you give them the role? Then they They arrive and write the formula, the The program graphs them It delivers the graph, the cut points, If you hover your cursor over a point, he gives you the coordinates. So I feel like, for example, uh, if I'm going to use technology for that. Well, I'd better not use it. So, the Technology always has to be there for to help us optimize processes, to to help to know that which we do not we know. For example, right now one a I don't know how to use software or a program. like Google Earth, for example, so that I can enter, let's say, distance to a laboratory, right? a Steam lab, where I have a simulator, where I have something or go to look at my house from the air, because I because I've never had the opportunity to ride in an airplane. So, they are issues that I have to bring to the classroom to discuss with students and that I might suddenly be able to do many things with the kids connected, the disconnected children, because sometimes one And with this I want to finish so as not to To elaborate, sometimes one says, "No, But those children who are in In rural areas, for example, they don't They have, there's no internet there, there's no There's no light, no water, but the teacher... can carry the computer, the glass wine, the tablet, and projecting it to the children, that has decreased or to work, Let's say, a series of activities that These are activities where children are disconnected. I, Professor Lina, the Professor Estefanía, uh, they're talking about these elements that one can touch, use, that help him develop that creativity and that are maximums that to Sometimes we end up leaving them side and so that's why we saw each other complaining, for example, right now that with artificial intelligence, which the guys who do the rehearsal, who They command all those things, but well if we continue assigning the same tasks From 15 years ago, well, right now, let's say that you writing an essay You were taking, I don't know, 8 or 10 days if you were going Okay, because you had to read, you had to all those things and right now the Artificial intelligence will give it to you in 5 minutes if you ask him the questions appropriate. So, if I put that same task, since it wasn't even a boy, right? Don't let me submit the assignment like this. So, Thank you very much, Dr. Bravo. No, I share many things that Marta shared this with us, because currently artificial intelligence and The digital age, well, that's something. reversible, it's already here, it's something that We can't deny that, even though we know which is something that's here to stay, There are still many teachers who They are somewhat resistant to this change and that It has to do with the same thing I was saying Marta, we can no longer do the Same questions, uh, the same ones tests, the same evaluations. ones, we can no longer occupy the same things than before because, well, it has already progressed. It's a The challenge is to adapt to these new technologies, this digital age. Uh, but I want to see it as such a revolution as it was at some point, probably the calculator. Perhaps when the calculator arrived massively into classrooms, there was a at which point it was said, "Well then, that's it We're not going to teach them how to add anymore. students, multiply because we have calculator. Somehow I want Let's understand these new tools digital as something complementary, something which will help us move forward from one a different way, to have more tools in order to answer new questions. Uh, but clearly there are things that aren't We will be able to digitize because there are experiences when one does mathematics which has to do with the sensory and even with the affective aspect, in how I I relate it to mathematics, in how I experience mathematics itself, how I manipulate, how I play with numbers, how I play with papers, with the geometry and that, uh, is not something that we can digitize. Uh, so I want to see rather not something as something that competes like it digital with this type of tools such as origami, but as something that complements, to give us more tools, more perspectives, new ways of approaching It's a problem, huh, but they can't to compete because they don't deliver what same, because they don't give us that sensory experience. We used to talk a lot, a long time ago, Right?, from the representations of Well, not so much Dubal's, right? Of how could we see from those of the algebraic, graphical, among others things and now we're talking about more things complex as well as complete systems semioticians that have to do with also the physical aspect, with its manipulative nature and how all of that does indeed cause a a different experience in how I learn and how I understand mathematics. It's because That is to say, there are many things that, of course, We can digitize it to complement and have many more tools visualization or representation, but there are things like that have to do with experimental, with the sensory and also with the affective that cannot digitize. Thanks a lot. Thank you for both. answers. Uh, I'll continue with Dr. Mata again. Hey, Dr. Mata, the physics of solid state requires students an important domain of algebra linear, calculus, equations differentials. From what you have observed over the years From a teaching perspective, how do you perceive that relationship? between students and mathematics? Do you think the problem is fundamental, of motivation? Or is there something more that isn't what do we usually name? Well, it's a bit of a question Difficult, isn't it? But, for example, well, I am a physicist and the people who study physics, because in some way it has a attachment to mathematics, then already There is no rejection. I think the rejection that exists is more of the engineering people, but because has a mistaken concept of the math. It is often seen as a obstacle more than as an application, but the mathematics understand, mathematics They can be transmitted. Most of the students that I have are students of, for for example, from engineering nanotechnology. So, they already They are initially looking for a more advanced application. scientific, more technological, more avant-garde and therefore, let's say, the aversion to mathematics is not such. There is a certain genuine curiosity, there is a kind of of let's say interest wanting to know more, etc., right? By For example, some people asked me which ones were the current orbits of trip to the moon, what are the orbits like, how the mechanics work and what the equations. So, we can write. This is classical mechanics, not It's very complicated mathematics, it's a math that works. If we transfer that to the solid state, because the solid state is ours phones are our computers, They are all artificial intelligence physics, right? Alexa is solid state. To the The final is a sensor, it's a sensor, it's a device that receives a mechanical wave which is the voice and let's say translates it. It has an electric foot translator and the associates it with a program, searches for it in the The web generates a response and sends it. No? Ultimately it's a solid state, a state solid combined with intelligence artificial, but I insist, it's like Music and mathematics are a language and we can use it to our Please, we can pass it on to the students. There are engineering degrees which are more relaxed, or simpler in the sense that They intend to do without mathematics. In the case of the areas that I in the I'm a teacher, no, mathematics It's part of what we normally use. as support, it's the pyramid base, right? After mathematics comes physics and then chemistry in pure sciences And these are methods that we We applied them and managed to transmit them Curiosity arises. Most of Our students, most of them seek somehow do a postgraduate degree and the Postgraduate studies require mathematics. Yes, to know That mathematics makes them more robust, It makes them safer, it makes them better professionals, that's what they are We search because in the end the investigation It is nothing more than adaptation. of knowledge for a state of well-being. Yeah. Thank you. Thanks a lot. Thanks a lot, Dr. Mat. Okay, let's continue with the teacher Lina María Toro. Uh, you have led specific programs to empower girls in science and technology. What have you found in that job that has made you has changed your perspective on How do we teach this topic? Do you think the problem lies in how you... We get to the girls or how is it? Was the curriculum planned from the beginning? Hey, It's quite a challenge. Yes, because it goes beyond that. Exactly what you're saying. Hey, within all the gender-related issues we see, that has been explored, we found that there are narratives that we have been hearing that probably the doctors who we They accompanied what they heard in their moments and us, right? Somewhere At one point they told us that men were more logical, and we women were more emotional and this paradigm is It extended, it extended until the day of today. But I feel that now we have challenges that are immensely large, It's that we compete against what they They consume it all day long. So, the Boys and girls consume all day long Well, social media, and if we go to This, the impact on appearance, towards worrying about image, has grown in girls and adolescents through social media. So, that's it. a very important challenge that I have we have been able to identify that we are facing When we have interested girls, passionate about science and technology, which we saw with a program which was called Steam Girls, uh, it They connect, they do things, they begin to explore and to break down those barriers, but there is a moment when there is a breaking point precisely because of its development and They're going more towards that, more towards what they're doing inviting the world. Of course, we can do that from the curriculum to do, of course, through education we can do it. However, I believe that That's a challenge we should take on. everyone in society. First, we need to realize what's happening, what aggravating factors are different from what I initially spoke to them about dialogue, rather than the speech we came from listening to many generations reality we face today. From the curriculum, one must do from the education that needs to be done, from to realize that from our language must include that precisely within the Steam's focus and what we have I've been talking today, the questions focused on gender, the roles assigned, eh, so that the girls participate, all of that makes us Let's get involved, but I think in The challenge is for all of us to be there, to be everyone aware and including it from different points and factors. I feel that the curriculum must change, that Education in that sense must advance more, but it is clear that also We must have policies We must also have within what They see and consume, precisely the visibility of all women that are currently in science and the technology of this Steam approach which allows us to internalize sciences as they have shared my colleagues, especially the mathematics, which is what makes us find today and that everyone From where we are we have the responsibility to act because nothing we We benefit from having curricula, resumes, classroom plans where we include TOC and if No, if we're not seeing the problem and all that part that prevents us from being able to get there. So, I think the challenge It's quite large, and the challenge is for... all. But when we have these programs, when we had these spaces that I am excited that we have Three women sitting here And what's visible, we put it there and we go inviting them and seeing how they They can be part of all that, then We started to break down these barriers. Excellent. Thanks a lot. In addition to which is a reflection that we as educators call us and within our university as agents of in change, our students who we want them to be precisely these transformative leaders of territories. Um, having this sensitivity to everything These topics are very important because These are often the kinds of conversations that come about. which we often don't have. And to connect with what we have just... If Professor Lina answers, I would like talk to teacher Estefanía. You have built several spaces, mathematical explorers, EMA, to bring young women closer to the math. What motivated her to do that? beyond the academic? And from what Having lived in these spaces, what do you think? that we still need to understand about why how many talented young women are leaving of pure mathematics? Thank you very much for the question. I feel that in these spaces it is necessary to speak precisely about gender because still The figures are very low, especially in as we progress in the academic spaces of hierarchy taller, uh, there are fewer and fewer women the present ones. So, this isn't It only influences the fact that there aren't that many. girls interested in science, but that there aren't that many academics scientists, there aren't that many directors of department, there aren't that many female rectors, deans of faculty with according to our country, whatever it's called, right? And how as we progress in academic careers are losing presence. Well, first explain a a little bit, what does EMA and explorers mean? math. EMA is an initiative student that was created by the civil engineering students mathematics from here at the University Federico Santa María Technical and That's precisely what it aims to be: a network support for them, for women mathematics of the degree, because the The figures are very low compared to income. We are always around each other 20 to 30% of students. By 2025 we had around for the civil engineering degree in mathematics the university close to 30% and this year In 2026 we went down again, we were more close to 20% this time. Then it goes fluctuating in this interval that is much smaller compared to the gender representativeness within the race. So, that's where this comes from We are worried that there are so few of us. We will take care of things within this environment. AND On the other hand, what happened was that precisely in these conversations of how they had gotten here civil engineering degree and mathematics or mathematics, Things started to emerge that I had a friend who also liked the math, but this happened and she didn't want to to study, she went to another career. Then we began to detect that there was many things along the way that also were happening. And despite the fact that here in Chile There are many initiatives, both from the university as well as at the national level, as public income policy differentiated for women in careers STEM, uh, even so, the income is If they're short, then the problem isn't in the income, but the problem is experienced It started long before and it's systematic. I mean, they're little things that will... increasingly stating where you belong and where not. So, that's exactly what we It makes you say, as if there isn't a reason. why the students don't get in either because they don't like this career or because they don't like it mathematics, quotation marks, and it's because systematically throughout his life Even the toys are telling him what These are appropriate things for women and What a thing! Uh, actually I remember it very well nostalgia a congress that was only of female researchers in STEM and One of the speakers told us, "Raise the Hey, all of you who played some once with Leo, just returning to Lego." And I think more than 80% of the The audience raised their hands and that showed us It also shows how the fact of what The game makes the difference. They teach me So let's play with the dolls because I have a caregiving role in this society or I can also be someone that creates things, that makes relationships mathematics, which makes relationships spatial. That's where they begin precisely the problems. And well, to As we move forward, Of course, many more arise, because I usually ask the question that a which mathematician(s) do you know and who are the people who say Pythagoras, Oiler, Gauss, always male role models and makes us think So, well, the woman hasn't been present in the history of mathematics And no, that also shows us how the mathematics has been counted most of the time from a single perspective, how it has been told by men, given that there are many women who They did different things, and those were already They were silenced, they were robbed their work was not made visible or They basically had to publish under a male pseudonym such as Sophigerme. So it's a recurring story that It's telling you where you belong and where not. I also remember when I I started studying for the degree and when She said she was a mathematician, the first thing. They were telling me something like, "But you don't "You seem like a mathematician." And I didn't know whether to take it as an offense. and a compliment. I think that until the day of Today, I don't know. And that answers how there are stereotypes of how someone should look who studies mathematics. So, it's constantly a struggle to This is your space, you can do mathematics and also mathematics is very diverse. It's a speech that even the Today I've even heard it in colleagues, such as mathematicians We think more or less the same, the We mathematicians look more or less the same. So, in a way, these spaces They show us that mathematics has many ways of telling oneself and also It can be counted in many ways. Yeah, from the perspective of gender, from the perspective of the community, from the work teams, from female leadership too. And that's why which is precisely what's important to talk about these things and see how we can from small tasks delete these systematic, uh, like a block that we This leads precisely to the students don't get to study mathematics. And for For example, having references like here on this panel and that's why too I am very grateful to Daniel for this organization because it is necessary to show precisely because there are women who are doing math. Thanks a lot. Uh, a lot Thank you, Dr. Estefanía. Hey, I continue with Dr. Marta Mosquera. Uh, you're part of a network of research on anti-racism and intersectionality in education Latin American. For many, it may sound far removed from a calculus class. How would you explain that connection to a colleague who still doesn't see that relationship? What have you found in your practice that... convinces that that perspective does matters within a classroom of math? all. I, for example, was just listening Estefanía and I were saying, "Yes, of course, that's it." Yes, she is answering my questions. Uh, you don't seem like math, you don't do, no, But I feel that goes a little further over there, I mean, I think it's like that knowledge that we lack us from our area. I wanted To add to something you just said, Estefanía, and it's the mathematicians or what whoever they are, they are our role models. but they are never close. So, Pythagoras, Satya, Ada, Lovl, well, all that stuff, but my teacher, my classmate, my neighbor, my cousin. So I think two things, In other words, two things. Uh, we say that on the network when one works the social justice, because in some way It's that I understand, and I was saying in the first one ask how I use math and Really, what is the role of the mathematics in that matter, because for example, of justice or of racism, uh, when, for example, and as These things, almost all of them, uh, let's say Its beginning is a little... well Let's say with movements in States United, in Europe, right?, which has that has to do with, for example, people migrants. So, like me, because For example, as a math teacher from someone who doesn't speak my language, So, uh, I don't allow it, let's say, show that understanding that she has of mathematics in their native language and later when she goes, uh understanding the language that she can to make progress on that. The other thing, well, suddenly, like To put it generally, many things that have to do with that, it's when a custom that almost always I feel like we had the teachers of mathematics that is hardly seen anymore and is the first five, that I finish I'll give you the grade for the exercise. So, one is prioritizing that work Individually, that speed and suddenly There is a person who has, let's say, a slightly different learning pace and so I end up not having it take into account because for me they are always the first five or the one who sounds exactly like me, who repeats what I say. And there are Another thing, we've already been here. several years working, let's say, with people from the deaf community, trying to understand them as, let's say they develop their mathematical thinking as a way of also challenging These inclusion policies that occur at a good level at all levels, in the sense that we, well Lately we've been, let's say, uh We proclaim that, for example, we include to people, right? In our spaces, our classrooms, a child with Asperger's, a child with, well, what So, we included it in our classroom, but Well, actually, when we We are not, let's say, trained For that. Not even I have one a deaf person, for example, in the classroom and I don't even know how to greet her. So, I have to have the interpreter so that the interpreter I contacted her and, uh, then what happens? that the interpreter reproduces it that's what I'm saying. He plays that for the deaf person question, but never, for example, the The interpreter tells me, as a teacher, For example, what is he talking about or what that deaf person is thinking. And another Which I want to say in closing, in in terms of the fact that we sometimes don't We know our area, I had, you me You asked something about what it had to do see with the integral. Because, well generally when we talk about math or all that stuff or that mathematics in real life and all, So, if you go to the market, Buy five loaves of bread and all those things and often not even the children They never go to the market, they don't know how much it costs Dad earns, they don't know how much the earns. Mom, with all these speeches mathematically grounded that we They maintain it, and we believe it to be so. We close our eyes because we don't understand it. So I wanted to, like, give a example. I said, "I'm going to find him the "For example, and I'm going to give it to you." Then I'll go to say a name that you have never I heard that it's Dr. Catherine Nacalembe. Dr. Cerina Nacalembe She is an African mathematician. She is not, Deep down, let's just say it's not She's a mathematician, an astronomer, and works currently at NASA. So right now with this whole issue of the artificial intelligence, well you They know that most of those Concepts are produced there in the United States United, the programs, all that stuff. And then she somehow has sitting down to work on how those models NASA mathematicians, right?, are designed for large fields of crops in the United States, but they fail in Africa. And then somehow I I could handle my students, right? use one of these functions, one of These applications that have been over there scheduled, for example, so as not to to go so far away, that they have been scheduled there for Bogotá, right? AND Come and see how it works here. Neiva, yes? In other words, the physics pressure plate, For example, when working on the point of reference, then the point of The reference is not the same, because For example, for a heat function. No It's the same to take it in Neiva, as We're here right now in the shade, almost... 40 gr, which in Bogotá where in this at the moment they may be at 13 or 14 gr. Then it's very different. Then she Let's say he has focused all his research into reaching Africa, to reach their land and that they teachers, people start taking out, to provide those measurements that are given in the land to send them to wherever There are the machines that make the calculations and that those machines give me solutions to cultivation problems that is in the African territory. So, for example, if I say no I haven't realized it, because many teachers, well, we haven't given ourselves account, then I feel that it implies, In other words, this issue of the Artificial intelligence implies that I sit down every day study, to see how. I am the calculus teacher, I said, uh, with the question you asked me, I asked the artificial intelligence, I mean, I am the calculus teacher and I need To work, for example, with the integral, right? And then I have that example in an article that hopefully will be published soon go out because the magazine has put them all. the world's problems. So, Let's say how to teach the integral defined in grade 11 under an approach of equity and social justice, right? Further Or less would be the question. So He says, well, the idea is to move beyond calculation. abstract of areas under the curve to the measurement of the accumulation of inequalities. How do they accumulate? inequalities? Then, suddenly Many of us have solved integrals like the one for x - f(x), for example, in a any interval between 0 and 1, without to know that, for example, that integral Well, it measures my Guini index. AND Let's say that curve it gives me, which is The Lawrence curve talks about how measuring economic inequality. And today in That curve is used a lot, huh? for example, by the Bank's technicians World Cup for all those figures that we They say every day that this country is more unequal, that this one is less unequal, that this I don't know what. And then one I could, for example, use two variables, I don't know, the minimum wage, that is, two variables, those that were for working with the students, how is that calculated? that, let's say, that variable or that issue with the 20 students who are in the lounge. And then one would already have as his question of suddenly even to be criticizing These, let's say models that sometimes we delivered by the Ministry of Education, from Education Secretariats in the textbooks that come with those problems that, well, definitely one He doesn't know what it's for. And another area that should not be neglected when we We're working on that, right? is that part about throwing a pencil, because one He says, let's say, for example, that practice of solving, for example, of Add quickly, multiply, uh well, no I know, from doing accounts of all those things, we have to work on them because, well, somehow, once I know the problem, I have, Let's say, the model, I can make my own. modeling work, because I have to solve, find the figures and interpret them. So, that one doesn't... can set aside, let's say, that writing and doing practice. So, that's my answer. For the who hasn't realized it, we have to Study hard, you have to know that context where we live and we must have I'll finish by mentioning two things. The first is that, uh, suddenly we, Many people say, "No, I am not racist." Sometimes racism has nothing to do with it. It doesn't have to do with skin color, either. It has to do with, let's say, because For example, sometimes one attacks against the other people and it turns out that we are all subjects of policies, all those things and Then suddenly we attacked We don't attack people, but we don't attack them. systems. Then we suddenly Sometimes we don't realize that we constantly for 1000 reasons We exclude. We exclude the and we are excluded by, that is, by the that include it here, exclude it here And those included here are excluded. over there. So, somehow, the The message this gives is that we We must therefore understand, that is, the Mathematics is not a neutral field and We work with human beings, We are people who need affection, that we need to be recognized our emotions, which we need from soon from a hug, from some matter So, that's what I feel like right now Estefanía was saying a little while ago that I also heard something very similar. Tell Alina, right? In the sense of that suddenly these things that always They've saddled women with a bit of it, Uh, it would have to become the universe of all. And the day we understand It's like this is a matter of humanity, most certainly because we are going to understand that the task of eliminating those Things from classrooms and life are from all. Thanks a lot. Fascinating, huh? reflection. Hey, Dr. Musquera, thanks a lot. Uh, I wish uh Bring a question that we are asked from the chat, uh, our students and I would like Dr. Jorge Mata to tell us Share your thoughts on the matter. The The question states the following. Although the Mathematics is exact, yet the Artificial intelligence makes mistakes. Do you think AI will evolve in the future? and can become perfect replacing humans and their studies? What is your perception, doctor? Does it kill? From their discipline. Yes, definitely. Intelligence artificial, it is self, Let's say, it self-evaluates, it improves. Yes. For example, I think Antropic included your code within Antropic for Improve it, right? So, the mathematics are They are numbers, they are ideas, they are concepts and Therefore they are wrong, aren't they? I mean, We can actually program it so that it may be systematic. Yes, we can make mistakes in programming, but mathematics They are not wrong. indeed They refine, they perfect, they evolve, They will be part of us, no matter what. Uh, I think we haven't managed still understand the power of artificial intelligence because We kind of use it for very... things. Simple, right? There are even people who He asks them, I don't know, it's a horoscope, I don't know, they're asking. anything, but the reality is If one asks about processes, systems, evaluates the response and monitors it and perfects it, definitely artificial intelligence is a a truthful, reliable, trustworthy tool. Yes, it depends on us. Uh, like In conclusion, I can say that hardly, We will hardly stop using it now. It's embedded in our daily lives and not We've noticed. But it's not Telling her to do my homework is to combine processes, to combine ideas, to combine concepts and above all to generate one's own criteria and somehow keep iterating, keep iterating and seeking that evolution. I don't want to talk. of a perfection, but rather we are looking for innovation, future. The future is now and it depends on us, and here we are. Yes, thanks. Thank you very much, Dr. Mata. Excellent reflection. Okay, let's go our penultimate question of our panel of experts. Uh, I want to... This penultimate question for our Professor Lina María Toro. Uh, robotics, programming, jacatones to an educational institution public? It has its own tensions. Budget, curriculum, time. How does pedagogical innovation coexist? in these realities? What would you say to a teacher who Want to do something similar? but that He feels that the system doesn't give him space. Well, thank you very much. Hey, what I can conclude from my experience is that a fundamental part of the scope that we have where we arrive part of the wills, mainly Well, starting with ourselves, the will suitable for the processes that I have Done, as you correctly listed, right? It is in addition to the curriculum, it is in addition to class hours, without However, it is motivated by my will, because of my passion, because of my desires. Hey, So what I would tell him is that When you want something, you find the form, it begins to mobilize. Therefore, if we... we go to We're going to find many barriers, and The system has them and our surroundings He has them. As you said, from since From a public school there are some limitations. However, when We began to mobilize, to want it, to to give part of our time, our own resources, which are mainly the ideas, talk about it, discuss it, uh, it They can keep adding them up, which is what has past in my own experience, and it It can move forward and we can get to to have unimaginable reach. So, uh, that's my recommendation. First, one's own will. when When you really want to, you find a way and When you start doing it, everything goes Adding it all up, everything falls into place. And us we find precisely part of what They were talking about something very nice, eh here with Our comrades, humanity, right? AND However perfect it may be, as it is saying Dr. Mata, be the intelligence artificial, that we do not doubt everything What's there? Well, behind it there were some programmers programming cycles, TRUE? If else many eh and behind There are always humanities, don't abandon us that humanity, uh, to have a look with hope in all these processes, in what which results from what we can do and we can give. And I think that the way of that we can make our The world can be a better place, because it is by doing so that the world can be better. little piece that we have around us. So, with that little bit, with my 40 students of a group, my 30, the the Managing it is difficult, it's a challenge. Uh, I'm not going to say no, but I know can. Can. So it is will, the desire, uh, not to abandon that dream or that passion and it is for what it is find the resources and the forms. Thank you so much, Dr. Lina. Hey, thank you so much. And well, that's the last one final question. I want to finish Well, first of all, thanking the Dr. Jorge Mata, Dr. Mosquera, my profeina, for all the eh for all the disposition, some answers that of The truth is, it has given us all a gift A very important, very big reflection, huh? of equity, of social justice, that We, as educators, always students, leaders, transformers of territory, we must always carry as a flag I want to finish with our teacher Estefanía Bravo. Uh, and I'm going to give it a question that we were just asked as well in the chat, uh, what's the public doing? And it is the following. What could be some strategies? functional to achieve the contemporary generations fall in love of mathematics considering its universality? I want to ask this question and I want to that also, uh, uh, gives us one final reflection to close our panel of experts, given that the truth Well, I'm contacting everyone. profiles, we have some profiles, uh supremely luxurious at this event. The I really enjoyed this of this discussion. Hopefully we can to have spaces, like, let's say, where Let's share these ideas, let's discuss a bit. There is something that seems very fascinating about her profile, and that's because You work with Jacobi varieties, Riman surfaces, you are one is PhD in mathematics, but at the same time You also explain mathematics. in 5 minutes for the general public. In other words, there's also a part of one there. social responsibility and there is a part that we often have to get off those abstractions of these objects pure of thought, that precisely those ideas we can share with all our students. So, I would like to To answer this question, which one do you think What could those strategies be? functional and that gives us that final reflection on motivation for our students who are They are connected in our panel of experts? Well, thank you very much for the question. Very interesting. I truly believe that there are There's a lot to say there regarding the science communication, the dissemination and also education, how These are intercepted in order to be able to talk about mathematics. And well, mathematics