Describing the practices of Didactics of Mathematics in Latin America.

Latin American Journal of Didactics of Mathematics and Mathematics Education.

Mathematics is a fundamental tool for the scientific, technological and social development of countries.

However, the results of international tests show that students in Latin America have a low level of mathematical competence. This is due to several factors, such as lack of resources, poor teacher training, traditional teaching methods and student demotivation.

Cuba Cuba stands out as a unique case in the Latin American and Caribbean (LAC) region when it comes to its educational approach, especially in the field of mathematics. In Cuba, teachers receive their training at the university level.

The basic training provided to educators is considered satisfactory in mathematics and includes specific practices for effectively teaching this subject.

A fundamental component of the Cuban educational system is the Network of Cuban Higher Pedagogical Institutes. These institutes play a vital role in the country's educational system, especially in the field of mathematics.

They offer robust curricula for mathematics and computer science teachers. The government's public policies in Cuba aimed at science and technology not only provide strong support for mathematics but also for science in general.

According to Cuba's strategic plan, the exact sciences, including mathematics, are considered essential not only for technological progress but also for strengthening education at all levels and nurturing the capacity of the new generations of Cuban scientists.Cuban’s recognize the importance of involving the entire scientific community in improving education, particularly in the field of mathematics, they use various strategies, including non-formal approaches, to achieve this goal.

Despite the achievements in education and support for mathematics in Cuba, the education system faces challenges such as limited resources due to economic restrictions, centralization that can reduce the diversity of pedagogical approaches, the possible overrepresentation of the sciences at the expense of other disciplines, and limitations in accessing external resources due to its political situation, which could restrict opportunities for international collaboration and educational enrichment.

According to Lilliam Álvarez Díaz in her article "The Science of Daily Language" (2014), we can corroborate Epicurus's idea that letters and atoms come together in various orders and positions to create, as well as Galileo's notion that "mathematics is the alphabet with which God has written the universe."

Furthermore, Álvarez Díaz reflects on Edgar Allan Poe's idea that the universe is "the most sublime of poems." She emphasizes the importance of studying, experimenting, and investigating the properties of matter and energy, considering only measurable attributes, and describes it as a labor worthy of artists seeking to multiply their beauty, as she does herself.

In addition to her academic achievements, such as a Bachelor's degree in Physics from the University of Havana, a Master's in Nuclear Physics, and a Ph.D. in Mathematical Physics from the Academy of Sciences of the former USSR, Lilliam Álvarez Díaz tirelessly strives to raise the visibility of the work of Cuban female scientists and to add more women to a field that has historically been denied to them (Álvarez Díaz, 2014)

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In Argentina, mathematics teaching is focused on developing mathematical skills and competencies in students from initial levels to secondary level. Mathematics teaching is based on a constructivist approach, which seeks for students to be active in their own learning and build their mathematical knowledge through problem solving and concept exploration.

In the first educational levels, learning through play and the manipulation of specific objects is prioritized, which helps students understand mathematical concepts in a visual and practical way. As students advance through educational levels, greater emphasis is placed on understanding mathematical concepts, problem solving, and mathematical communication. It is intended that students not only perform calculations, but also be able to argue and justify their answers in a logical and coherent manner.

Argentina

Technology plays an important role in the teaching of mathematics in Argentina. Digital tools, such as educational software and graphing calculators, are used to help students visualize and explore mathematical concepts in dynamic ways. Furthermore, in Argentina the development of critical thinking and the resolution of real-life problems through mathematics is promoted. The aim is for students to be able to apply mathematical knowledge in everyday situations and develop decision-making skills based on numerical evidence.

The way mathematics is taught in Argentina varies according to the educational level. At the initial and primary level, teaching is based on playful and manipulative activities, which allow children to build mathematical knowledge through exploration and problem solving. At the secondary level, logical reasoning and the application of mathematical concepts in real situations are emphasized.

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Mathematics education studies the learning and teaching of mathematics in societies with particular characteristics, under social conditions that are part of the objects of study of the discipline. From this perspective, a social science is also interested in raising and trying to solve social problems that, in the case of mathematics education, impact the educational system of a country.

For Gidem, we must move from the didactic triangle to a complex didactic model that develops learning and teaching (Mora, 2005).

Some of the principles of critical mathematics education in Venezuelan society are the following (Mora, 2005; Serrano, 2009): . 1. The contents to be developed are mathematical and interdisciplinary, since school mathematics is linked to reality and to other disciplines of knowledge.

2. Learning communities are school and extracurricular. The mathematics classroom is a research environment, where multidisciplinary discussion groups are created.

3. Communication is a source for the discussion of ideas, for participation, criticism and group activity.

Active student participation is necessary to address cultural and social complexity.

4. Mathematics is conceived from a sociocultural vision and addresses topics that address the real needs of a community, as well as the regional, national and global environment, where mathematics plays an important role in its understanding

Venezuela

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The socio-mathematical activity of a young Venezuelan must produce learning to understand the consumerist society that we want to overcome, to have environmental awareness and save the human species, to achieve the political and economic sovereignty that guides the Plan of the Homeland (Ministry of Popular Power of Planning, 2012). On the other hand, teacher training universities must also rethink their curriculum so that their students link mathematics with reality and serve as an instrument in decision-making; In this way, you will stop hearing the frequent phrase, mathematics is in everything, but when it comes to planning learning activities, they have no meaning and have little or nothing to do with reality of students, teachers and the community where mathematics education is developed.

The most outstanding characteristics of school mathematics in Venezuela during much of the 20th century are: 1) presence of concentric or cyclical teaching. 2) Insistence on solving abundant exercises and problems. 3) Presentation of some topics discriminated by cases. 4) Attempts to link some themes with reality, although most of the time they fall into the use of elements that simulate it, which in the case of problems leads to what Beyer considers "dressed problems." 5) Presence of didactic proposals that insisted on mental calculation. 6) Little presence of geometry. 7) Structuring of teaching, going from the particular to the general and from the concrete to the abstract.

8) Mathematics focused on arithmetic (Ramírez, 2011).

Venezuela participated in CANP 2012, the international seminar school Building Capacity in Mathematics and Mathematics Education, organized by the International Commission on Mathematical Instruction (ICMI) and held in Costa Rica, where a team of teachers from three national universities developed a report on the initial and continuous training of mathematics teachers in the country. The most important result of CANP Costa Rica 2012 was the founding of the Mathematics Education Network of Central America and the Caribbean, which seeks to enhance capabilities in mathematics and mathematics education in the region (http://redumatematicacyc.net).

The network begins its work with the support of several international organizations and already has the support of various societies of mathematics educators in the region, including the InterAmerican Committee on Mathematics Education (Ciaem).

It is concluded that the main challenges for the community of mathematics educators in Venezuela include: a) collecting reliable statistics to make a more accurate diagnosis about the teacher deficit and other parameters; b) precisely determine the deficiencies in the current training of Venezuelan teachers; c) stimulate the incorporation of more high school graduates into the study of teaching careers, particularly that of secondary school teachers; d) promote a profound renewal of teacher training curricula, so that they contain an adequate component of mathematics teaching and are consistent with the tasks to be performed by graduates, in addition to ensuring that this curriculum is harmoniously integrated among its various components; e) promote efficient mechanisms for the continuous training of teachers; f) contribute to reducing the gap between educational reforms and the necessary changes in teacher training, and g) produce appropriate materials that contribute to the improvement of teacher training and incorporate teachers into research, innovation and development of teaching materials projects.

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Chile Chile has made significant strides in enhancing the quality of mathematics education. A crucial step involves the active involvement of researchers and prominent mathematicians in improving the knowledge and training of school teachers. This engagement has shifted from focusing solely on research and university-level teaching to direct involvement in school-level education. It has taken steps to address heterogeneity in mathematics teaching programs and the lack of connection between discipline knowledge and teaching techniques. Researchers and mathematicians are contributing by creating online courses to enhance skill-building in mathematics teaching, especially at the high-school and elementary school levels.

Compared with Colombia, regarding implementation of technology. Chile has been creating online courses for skill-building in mathematics teaching, but Colombia works on collaborative training with students from other parts of the region.

One of the main challenges is the training of teachers in mathematics pedagogy, since this is not considered as an essential area of learning, also the availability and access to adequate educational resources, such as textbooks, didactic materials, and technological tools, and the effective integration of technology into mathematics education

Claudia Vargas-Díaz, a Ph.D. in Mathematics Education, reflects on the significance of mathematics education in Chile and its societal relevance. She emphasizes the need to contextualize math instruction to instill genuine interest in students and underscores the importance of research in this field. Teacher training for math educators in Chile is addressed, with a focus on the need for effective teacher preparation to answer the key question from students: "What is math used for?" The challenges in teacher training and the significance of research in this domain has been also discussed. In Chile, the existence of gaps and challenges in math learning is explored, highlighting the importance of addressing errors and learning obstacles and emphasizing the relevance of considering socioemotional aspects in the educational process.

Chile has moved towards more equitable educational policies and continually seeks highquality education while emphasizing the importance of generating advanced research in mathematics education for the country's growth.

Considering the reading of "good pedagogical practices," the most prevalent teaching strategy during classes in Chile is the explicitation of reasoning processes, which is consistently highlighted. Additionally, strategies like relating content to everyday life and connecting it to prior knowledge are also significant. In Chile, the predominant teaching approach centers on oneway communication from the teacher and is related to a view of teaching as mere knowledge transmission.

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1. That various strategies be established that minimize the dropout of students from school institutions. It is crucial to monitor the enrollment, attendance and progress of students; understand why some children have not returned to school, and support them to return and stay there.

2. Implement a system of periodic selfassessment of learning levels. Selfassessment practices and other related policy measures to achieve learning recovery and better outcomes. New forms of assessment must not only capture students' knowledge and skills, but also focus on helping them become more aware of how and what they learn.

3. Focus the teaching of key competencies.

The essential contents are lost and prioritize basic literacy and numeracy skills and knowledge, which students need to acquire progress in all subjects and to acquire more advanced skills in the future.

4. To increase the effectiveness of teaching, school systems must implement strategies that make education more effective, relevant and relational, and that ensure that teachers can support the recovery process in the classroom.

Proposal of solutions to reduce the problem and enhance the educational process in Colombia

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