Table of contents

Sharing the motto "Mathematics is Everywhere" and its icon "The crane" symbolizes honesty, maturity, the judgment that ensures the growth of all in spite of unseasonable winds and integrity, the objective of the IV International Meeting on Mathematics Education (IV IMME) is to create and maintain a space that privileges and promotes the culture of mathematics, reflection, and discussion on education and the application of mathematics, statistics, its history, evolution and didactics, and its interrelationship with science. At the meeting, researchers, scientists, and mathematics teachers socialize research results, consolidate networks for the exchange of successful experiences, with the purpose of strengthening mathematics education at different educational levels, promoting innovation, and fostering the creation of educational policies, models, strategies, tools and techniques, in various areas of knowledge and encouraging students' interest in research.

List of Organizing Committee International Scientist Committee National Scientific Committee are available in the pdf.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

• Type of peer review: Single-blind

• Conference submission management system:

By email received from the organizing and editorial committee of the conference. The correspondence authors make the submission by email.

• Number of submissions received:

27

• Number of submissions sent for review:

24

• Number of submissions accepted:

20

• Acceptance Rate (Number of Submissions Accepted / Number of Submissions Received X 100):

74.07%

• Average number of reviews per paper:

2 reviews per paper

• Total number of reviewers involved:

14

• Any additional info on review process:

All papers are plagiarism checked by Turnitin software

• Contact person for queries:

Ely Dannier V. Viño

Foundation of Researchers in Science and Technology of Materials (FORISTOM)

Email: foristom@gmail.com

Physics is capable of describing, through equations, phenomena on a micro and macroscopic scale. However, most of these equations are non-linear and the identification of their roots requires the use of approximation methods, with numerical methods being a proposal based on a systematic and iterative process, that conclude only when a pre-established tolerance is satisfied. Traditional teaching of numerical methods involves the memorization of algorithms. However, this hinders student's ability to understand the important aspects and then apply them for solving applied problems in subjects such as kinematics, dynamics, electromagnetism, etc. Therefore, this work proposes the use of GeoGebra, as a didactic tool to illustrate the functioning of single root searching algorithms. By using the dynamical graphic's view of GeoGebra, a series of abstract and applied problems where solved by engineering students taking a numerical methods course. The scores of this test group was then compared to a test group, taught trough algorithm memorization. Results show can improve their understanding of how the bisection, false position, secant, and Newton-Raphson methods are able to find approximated solutions to polynomial and trigonometric equations. The results are compared against traditional learning, based on memorizing the steps of the algorithm for each method and the representation of the convergence of successive roots by numerical tables.

The calculation of variations initially it was a technique that was born in the field of physics and its great contributions have been taken advantage of by the engineering sciences in problems that involve finding a minimum trajectory that minimizes time, energy among other variables of interest. The following document will show how to find an optimal control law in order to minimize the time to bring the system that in this case is a direct current motor from a known initial state to a desired final state, using the Bang-control technique. Bang In direct current motor, the variables to be controlled are the field current, the input voltage and the angular velocity developed by the motor. For all the above, the control technique is not only innovative but also useful and practical for energy systems.

The study of efficient solution methods for mathematical models from physics is important for the purpose of making predictions. In the study of the equations of mathematical physics, the heat equation has an important place. Techniques for studying heat transfer include topics such as Fourier analysis, Bessel functions, Legendre polynomials, etc. Throughout this article we will study the heat equation from the point of view of calculating its solutions. For this reason, the solution of the heat equation is proposed by the Fourier method and the explicit numerical method. In the last part of the article studies the accuracy of the numerical method in relation to heat transfer in a spherical polymer and raises the advantage of working with numerical methods to solve mathematical models derived from conservative laws.

Conventional regulators or controllers are used regularly in control engineering, however, there are limitations to their use. In this document we develop the essential mathematical concepts and expressions in the study of adaptive control techniques. To do this, we will initially make a brief deduction of the equations that are identified in a linear regressor control system, and also for the case of the parameter identification algorithm. Next, we will apply this control technique in a non-linear state space system for a magnetic levitation system, allowing us to conclude, among other things, that this technique makes the control more robust.

This article presents a computer tool that allows to carry out a mathematical analysis of the physical stability of the bipolar transistor in the design of amplifiers. The tool allows to introduce the values of voltage gain, output impedance and input impedance, current gain of transistors and power supplies, to give as a result the values of the resistances. It also allows modifying the transistor operating point and graphing in real time the behavior of the load line and the output signal of the amplifier. Different designs were made with the tool and the results obtained were compared with academic software approved by the scientific community. The errors in all variables evaluated were less than 1.5%. The results are important for semiconductor physics, taking into account that they reaffirmed the directly proportional relationship between the stability of the transistor in its amplification state and the power required to operate. Finally, we conclude that the computer tool allows us to design amplifiers with bipolar transistors with precision and, depending on the need or application of the amplifier, the operating point Q is located in the load line to obtain an output signal without distortion and with the least power dissipation.

In recent years, the consumption of electrical energy in the world has increased, increasing the construction of power plants that operate with fossil fuels, which emit a large amount of CO₂. Due to this polluting process, it is important to generate efficient alternatives. In this work the model of the double-feed induction generator for a wind turbine is exposed, to which the control by second order sliding modes will be applied to its state variables and these results will be compared with the classic proportional-integral-derivative technique of control. In this work it was found that the responses of the system with a second order sliding mode control compared to a control of the proportional-integral-derivative type, have a shorter establishment time and a slower behavior over time; in some cases the waveforms of the signals have a vibration effect at the moment of the response, but despite this, the response is not affected due to the wind speed to which the turbine is subjected, and reduces quickly system error at any instant of time. Whereas with a proportional-integral-derivative controller, some state variables can be highly dependent on wind speed.

In this work, a process for the assembly of a standard triple Gas Electron Multiplier detector and the study of the main variables was made at the Universidad Antonio Nariño, Colombia, detectors laboratory. The triple gas electron multiplier was tested with Ar/CO₂ mixtures in proportions of 70/30%, 80/20% and 90/10% using a ⁵⁵Fe X-ray source (5.9 keV). The energy spectrum, energy resolution, effective gain and ionization rate were analyzed according to the applied voltage and the Ar/CO₂ gas mixture. The Universidad Antonio Nariño, Colombia, triple gas electron multiplier detector obtained an energy resolution of up to 19% and an effective gain close to 10⁴; where the detection efficiency is approximately 95%. These results were compared with other studies to check the triple gas electron multiplier performance.

From the study of nonlinear dynamics, the study of chaotic dynamics in deterministic systems has been developed. If a system is deterministic, its behavior would be easy to predict. However, there are systems in which their behavior seems to be unpredictable due to the complexity of the dynamics of the system, which is reflected in an aperiodic behavior. This article presents the application of parameter exploration techniques for the study of aperiodic deterministic systems using time constraint estimation through the calculation of the Lyapunov exponent in order to estimate future system values. This technique is developed on a part of the energy matrix of the Colombian system, especially with hydroelectric production.

A growing number of experiments with particle detectors using liquid argon are currently being carried out, as this is an excellent means of detecting neutrinos. These experiments develop different capture and measurement systems of the photons generated by the excitation of the argon atoms when a charged particle passes. New low-cost technologies, more sensitive and efficient detection methods, hardware and electronics, optimize and take advantage of the characteristics of the processes involved. This minireview presents the main characteristics of photodetection systems used in some of the most important experiments for the finding of neutrinos, particularly those that use liquid argon at cryogenic temperatures (-186 °C), such as Deep Underground Neutrino Experiment and the Micro Booster Neutrino Experiment. In addition, this article presents a comparison of the advances of each cryogenic photodetection system with the aim of promoting the use of this technology in new research fields.

In recent years, the popular term "polymer-drug conjugate" has been introduced to describe new drug targets to combat diseases such as cancer. Due to its potential benefits in terms of human health, this concept has managed to gain attention in the pharmaceutical industry. These innovative developments involve detailed processes in materials science, as it is required to encapsulate different types of cells, as an active component within a material that releases the drug or conjugate directly on the tumor or in the affected area. Against this backdrop, the main objective of this work is to explore the state of participation of polymeric materials in medical and pharmaceutical sciences, in a context where recent cancer statistics are provided in some countries. From the review of the literature, it is evident the importance of the synthesis of new materials or polymeric conjugates, because these materials at the beginning have been used only as storage and delivery systems of drugs, but today they are used as direct treatment against diseases such as cancer, that is, as bioactive agents. Finally, it is possible to conclude that the conjugated polymer-proteins or polymer-drugs, currently on the market and others in the clinical research phase, these materials present physical properties such as biocompatibility and biodegradability, that is, compatibility with the living organism.

Material physics has traditionally been used in the area of mechatronics and aeronautical engineering. However, in recent years, bioclimatic architecture has used physical principles and conservation of matter to evaluate the performance of buildings where the comfort and safety of its inhabitants are sought, with the mortar being an adequate alternative in minimizing heat transfer. However, this material is fragile and has a high risk of fragmentation. This problem has been addressed through the incorporation of inorganic aggregates to maximize their mechanical properties but the cost of production is high compared to the traditional process. This work proposes the analysis of cement-sand modules with coconut endocarp and mesocarp (coconut fiber) aggregates, by evaluating their mechanical resistance, under a compressing force, and permeability and comparing to current regulations. The results showed that coconut fiber has a large impact on the mechanical resistance of the prototypes: a proportion of fiber greater than 3% compromises the mechanical resistance of the prototypes due to the water adsorption capacity of coconut fiber. Whereas, the prototypes identified under the endocarp to fiber ratio of 10% to 1% showed the highest performance in the deformation tests under compression with respect to the modules without the presence of this waste material. The resulting mixture meets the Mexican standard for mortar and could be an alternative for avoiding the burning of plant residues in regions with an active coconut industry.

The generation of new building materials responds to the reduction of energy consumption and regulation of building interior temperatures as strategy to improve energy efficiency in materials engineering and architecture. This research focuses on the study of the rice husk incidence on the physical, mechanical and thermal properties of H10 block manufactured in the metropolitan area of San José de Cúcuta, Colombia. The methodology consists in 4 stages: In first instance, raw material characterization to identify chemical, structural and morphological components of clay and rice husk. Then, H10 blocks manufacturing in 2 clay mixtures, fired at 900 °C, 1000 °C and 1100 °C. Likewise, tests of manufactured samples to analyze its physical and mechanical properties. Parallel to the manufacturing process, transfer and heat fluxes simulations to evaluate surface temperatures and energy concentration of H10 block. In conclusion, rice husk acts as a technological nutrient added to clay mixture and strengthens thermal and insulating capacity of blocks. Nevertheless, the presence of rice husk in clay mixtures increases water absorption capacity of the products, as the percentage of husk increases. And therefore, the compressive strength decreases, which is a factor to consider for the constructive application of H10 block.

In this research work, a description was made of thermoset polymer materials and their relationship with the environment. The traditional thermoset manufacturing processes make their recycling and reuse complicated. Consequently, most products made with this type of material end up accumulating in landfills and their disposal generates a high environmental impact. This is why a description of thermoset and biodegradable polymers is made to identify the differences between them and the advantages of biodegradable materials. This being so, it is found that the scientific community presents as a proposal or alternative solution to this environmental problem the development of new methodologies and technologies to synthesize families of thermoset biodegradable materials, as for example the case of "glycix", "titan" and "hydro", and that from capital investment in science and technology processes in the area of materials engineering, by the productive sector and Universities of countries such as for example; Mexico and Argentina, managed to develop on an industrial scale biodegradable resins that can be processed by all conventional plastic molding methods and significantly reduce the carbon footprint.

This research reveals the perspectives in the teaching of numerical thinking through a documentary review. The representation of physical elements such as functions, vectors and operators, and their subsequent interpretation through numerical thinking gives meaning to the physical quantities that such elements represent. A documentary sample integrated for 40 sources on numerical thinking such as articles published in indexed journals, postgraduate dissertations, and books is considered. A qualitative content analysis method is used. First, an encoding procedure is applied for tagging the extracted information from the source documents. Then, a split and merge procedure is considered in order to establish from the tags the dimensions and categories that allow determining the conceptual relationships that support the developmental perspectives of numerical thinking. The method reveals that the numerical thinking can be developed in the global context from four perspectives, namely, historical, theoretical, curricular, and social perspectives. From these results, an incorporation of the such perspectives can be institutionalized for promoting curricular, didactic and evaluative new proposals for numerical thinking teaching.

We describe in a very concise way the multidisciplinary program of artificial mathematical intelligence and the need of a new and improved paradigm of formal computation based on conceptual generation, called conceptual computation, with the potential of being a global paradigm-shifting technique in theoretical physics and computational mathematics. Furthermore, we describe some of the most outstanding results regarding fundamental cognitive abilities needed for the materialization of conceptual computation such as analogical reasoning, metaphorical thinking and conceptual blending. Finally, we present a concrete example of the conceptual computation of the notion of binary continuous operation as a formal blend (i.e. many-sorted first order categorical colimit (pushout)) of the notions of continuous function between topological spaces and perfect square topological space.

The stigmatization of natural sciences and mathematics as difficult, boring and non-practical subjects, starting at the secondary levels, has caused an increased disarticulation between the significant learning of physics and the student, this can be reflected in a less development of basic competences, an almost instinctive revulsion of a large number of students towards these subjects and poor results in the tests that are carried out. Reflecting on this situation, we apply the inquiry-based science education. The intervention was carried out in a private calendar B school in the town of Chía, Colombia; Latitude: 4.85, Longitude: -74.05 4° 51' 0''. The participants were 80 students, the instruments used to collect the information were: class observations, surveys, interviews, an entrance, an exit test and another after the exit test. Two specific inquiry based-science type activities were designed: laboratory practices and the manufacture of a device by the student. These two activities in turn had matrices with defined evaluation criteria to evaluate the impact of the intervention. The students found in the investigation, a much more conducive environment for their learning and in the end the proposal allowed to identify positive impacts of the inquiry based-science as well as not so desired results.

The wave movements can be studied from autonomous work done by the student since they are processes in which he can appreciate and understand how the transmission of energy from one part to another without transfer of matter is. Problem-based learning constitutes a good alternative to study the concept of waves since it sequentially leads the student to structure the knowledge to use it in the context, to develop effective processes of reasoning, to develop self-directed learning skills and to motivate him/her to learn, together with the development of the capacity to work in a team and it favors the development of the mathematical physical thought. The research is developed from the multi-method methodological approach developing in-depth interviews to teachers and knowledge tests to students with the purpose of establishing both pre-knowledge and initial situations for structuring the pedagogical intervention and the evaluation of its results. The pedagogical intervention is structured on a quasi-experimental design in which the strategy of problem-based learning is applied to the teaching and learning of physics and is compared with the traditional methodology. The research allows us to conclude that applying the problem-based learning methodology to physics teaching, we obtain better educational yields than with traditional teaching, while it generates a greater motivation and a greater interest in learning. It also allows the student to integrate the knowledge into his or her context, visualize the usefulness of learning and apply knowledge to the solution of problems in his or her environment, in other words, it allows the student to achieve significant learning and therefore a development of mathematical physical thinking.

The research identifies storytelling concepts in Physics from university professors. The research follows a qualitative approach applied to 250 participants from universities in the department Norte de Santander, Colombia. The design implements as an interview technique the Socratic dialogue and as a quantitative support used elements of the correlational design. Interview and virtual survey instruments had a kappa index equal to 0.8 and α = 0.78. The results identify three categories associated with the application of science, the function of the history of Physics and scientific production. It is concluded that participant's concept storytelling is the art of telling a story in motion and a didactic resource associated with approaches, the development of skills, useful to analyse the development of discoveries in Physics, its actors, its application in scientific advances and its contribution to innovation and community development. Classical mechanics, electricity and magnetism with storytelling, identifies in physical science axiological aspects associated with tradition; epistemological aspects associated with experimental physics; and critical aspects.

The work presents a didactic proposal on the use of concept maps, for the understanding of mechanical physics. A didactic intervention based on Ausubel's theory was applied with the following activities: design, implementation and application of workshops based on real physical situations, where the elaboration of concept maps is the central axis, under the quantitative paradigm of interpretative level and action research method. The informants were 43 tenth grade students from a public educational institution located in the Department of Norte de Santander, Colombia. The results obtained showed that the use of concept maps as a didactic intervention favoured the significant learning of classical mechanics concepts. It was evident that the participating students achieved reflective analysis about the resolution of problems about the concepts of mechanics.

This research is part of a line of research in education that aims to determine the degree of influence that affects have on the study of basic sciences that usually generate high rates of academic loss or repetition in school environments. The aim of this research was to analyze the system of beliefs that a group of students had about themselves as physics students, about physics as a discipline, about the physics teacher and his or her teaching practices, and about the importance of this area of knowledge in their social environment. To achieve this objective, a private educational institution is intentionally selected, with a home in San José de Cúcuta, Colombia, characterized by good results in the Saber 11 state tests. The informants were all students enrolled in 2019 in grades nine and eleven. A questionnaire was designed consisting of 36 items evaluated by means of a Likert scale with five levels of response. The results attested to the internal consistency and validity of the questionnaire. Subsequently, a complete characterization of the informants was carried out, allowing us to discover that the women in the sample have a better attitude and abilities in the study of physics. Finally, a factorial analysis was carried out in order to verify whether the opinions of the respondents fit into the four categories of beliefs considered by the researchers. Six factors were identified that explain 80% of the common variance, highlighting within them the beliefs that the student has about himself and his relationship with the teacher as the main factor explaining 41% of the variance.