The purpose of this article is to present a bibliographic survey of the current trends in Colombia regarding teacher training and professional development located for the teaching of Language andMathematics at primary and secondary academic education levels. The aim is to focus on three categories of analysis: learning communities, situated professional development and pedagogical practice, demonstrating in a concrete way how the quality of education in the country has been impacted, from the official sector, by analyzing the results obtained in the research carried out in this educational field. These categories develop some dimensions that allow to solve the question of what are the changes that occur in the pedagogical practice of the teachers after applying a training in the methodology of the study of classes. The analysis of this system of categories and dimensions has been carried out under the process of teaching Language andMathematics, and how it contributes significantly in improving the processes of reading comprehension and solving mathematical problems. The studies
Este artículo tiene como propósito presentar un rastreo bibliográfico de las tendencias actuales en Colombia acerca de la formación docente y desarrollo profesional situado para la enseñanza del Lenguaje y Matemáticas en los niveles de educación básica primaria y media académica. Se pretende focalizar en tres categorías de análisis: comunidades de aprendizaje, desarrollo profesional situado y práctica pedagógica, demostrando de manera concreta cómo se ha impactado en la calidad de la educación del país, desde el sector oficial, mediante el análisis de los resultados obte- nidos en las investigaciones realizadas en este campo educativo. Estas categorías desarrollan algunas dimensiones que permiten resolver el interrogante de cuáles son los cambios que se dan en la práctica pedagógica de los docentes luego de aplicar un entrenamiento en la meto- dología del estudio de clases. El análisis de este sistema de categorías y dimensiones se ha realizado bajo el proceso de la enseñanza del Lenguaje y Matemáticas, y de cómo este contribuye significativamente en el mejora- miento de los procesos de comprensión de lectura y resolución de problemas matemá- ticos. Los estudios abordados demuestran un efecto positivo sobre la enseñanza e instruc- ción orientada por los docentes, especialmente en sus metodologías, estrategias didácticas, desarrollo profesional situado y las prácticas evaluativas, así como en el aprendizaje de los estudiantes. Esto se materializa en la conso- lidación de comunidades de aprendizaje conformadas por los docentes de lenguaje y matemáticas del país –teniendo en cuenta áreas de conocimiento y perfil de cada uno de ellos-, donde se realizan constantemente procesos de planeación, ejecución, observación y retroalimentación de las clases, por medio de equipos de estudio
For this empirical exercise, RMCAB data for 2011 was gathered so it could be merged as our air quality variable for estimations of the Hedonic Pricing Model. Using PM10 concentration as a measure of air quality data offer two advantages: first, it allowed us to work with the city’s most relevant pollutant, and second, it is one of the most visible, helping to mitigate possible biases due to households´ subjective perception of pollution. For obtaining a measure of air quality for each of the households in our sample of the EMB we use Inverse Distance Weighted interpolation from the monitoring readings, a standard interpolation technique. Figure 4 shows the results of the interpolation showing the spatial variability suggested in Figure 1. Even though, our study area encompasses a single urban area, we identified some spatial variation of pollution levels: important PM10 concentrations are observed in the south and southwest areas of the city, while the north and center areas presented relatively low measures. Additional measures of air quality were gathered so that we could test for robust results. Particularly, the Voronoi Neighborhood Averaging methodology is used for replicating the interpolation of monitoring data method used by EPA’s Environmental Benefits Mapping and Analysis Program (RTI International, 2015). For both interpolation methods we used the mean annual stock of concentrations as
In the design of our teaching proposal, we consider the three worlds of mathematical thinking: embodied, symbolic and formal, given by Tall (2004, 2008). The embodied world is where we make use of visual and physical attributes of concepts, combined with enactive sensual experiences to build mental conceptions. The symbolic world is where the symbolic representations of concepts are manipulated and where it is possible to “switch effortlessly from processes to do mathematics, to concepts to think about” (Tall, 2004, p. 30). The formal world is where properties of objects are formalized as axioms, and logical deduction is used to build and prove theorems. This theory suggests the existence of different ways of thinking in mathematics which are not isolated but interact offering advantages.
Abstract: The modern world faces the paradigms of traditional teaching-learning in contrast to new technologies, which, in addition to the attention of young people and adults, covers almost all branches of science and academia. In this paper we propose the analysis of computer tools for the development of didactic strategies for the teaching of mathematics, an area of study that has historically generated great difficulties in the student sector, From a constructivist perspective and applying the qualitative-quantitative method, the information collected is managed through interviews, surveys and observation forms; those applied to 52 first-level PUCESE students, two teachers in the area and one manager; lead to the analysis and generation of results that show that in the educational environment in question, a traditional teaching-learning style is maintained, which is not necessarily mediated with educational technological tools, but also reflects the interest of students to integrate educational software and simulations, such as support resources, for math classes. Based on the results, free educational software Exe-Learning is proposed and it is demonstrated, through statistical analysis, that this resource strengthens the teaching-learning process of mathematics.
In recent years, through different types of teaching innovation experiments and participation in the above European projects we have built a stable, open teaching team to adapt the different math subjects in our University Schools of Engineering to the new teaching scenario. We encapsulate the evolution of our thinking in a few references. References  y  address the possibilities of the use of CAS in math subjects, specifically Calculus in Several Variables and Differential Equations. Also, the use of CAS may involve an innovation in teaching, as seen from references  and . We also encourage the students for the construction of toolboxes . The next step is the adaptation of the Bologna Accord specifications in teaching with CAS ,  and . For a globalized process of teaching it is crucial to choose a suitable CAS. One important argument in this is the ease of access and in general, it is preferable to use open-code, freely distributed software. Experience with different types of CAS and the comparative study described in  support this priority. Now may be the time to consider the new devices than can be called hand-held technology. Drijvers and Trouche  suggest that we should be aware that hand-held technology is no longer an isolated artifact but integrated in and articulated within a network of resources, particularly on-line resources.
Journal for Educators, Teachers and Trainers JETT, Vol. 10 (1); ISSN: 1989-9572 25 In the study, first a problem-based education program for teaching middle school mathematics in a training course was designed and implemented for middle school mathematics teachers based on the theoretical frameworks of Polya (1978) and Schoenfeld (1985). After the problem- based trainings in four levels, as it was outlined in the procedure section of the study, a test and a questionnaire were used, where the standard questionnaire based on the four levels of Kirkpatrick were distributed among the teachers. After examining the pre-tests and post-tests of the problem-solving performance, a significant difference was found between the problem- solving performance in two groups of control and experimental after the training, with regard to the teachers' scores before the training, then we designed a new mode to compare the relationship between Kirkpatrick's levels with the post-test of mathematics teacher's problem- solving performance. Therefore, by structural equations in R software, we showed that each level of Kirkpatrick model has a positive effect on the mathematics teachers’ post-test scores. Moreover, with regard to the standard load factor values, since the third level of the Kirkpatrick model has a larger standardized coefficient, it can be said that the third level of the Kirkpatrick's model has the greatest impact on the post-test score of the mathematics teachers. Also, the second most important level is the fourth level, the third most important level is the second level, and finally, it can be said that the first level of Kirkpatrick model has the least effect on the post- test scores of the mathematics teachers. When the assessment is done in a coherent way and in a pre-determined manner, such as in Kirkpatrick's model, educational approaches and
The purpose of this article is to identify if the pedagogical work of teachers in the General direction of army schools, is part of the pedagogical model that characterizes to the Lyceum. The methodology, studied the literature referred to the concepts of pedagogical practice, pedagogical model, educational management. Through documentary analysis, we studied the institutional education project (PEI) and the pedagogical model. They were five (5) focus groups involving teachers in the institution, to investigate concepts taken as references of this study were conducted. The results identified that the pedagogical model is not consistent with the pedagogical practices of teachers; the educational management of the institution should promote open and reflective professionalism of the actors of the educational community; in addition, it is necessary to define clear objectives that will facilitate and enhance the pedagogical practices of teachers.
Polyhedra are very interesting objects for architecture and construction, mainly because of their possibilities to be understood as a set of planes and lines. Given that simplicity, from the geometrical point of view, such objects have a lower formal complexity and therefore are less interesting than curves and surfaces, which become main characters of the experience. The great contribution of mathematical knowledge applied to this matter, is that it allows the student to determine the variables that define the forms, it is what characterizes them radically since their inception. The mathematical formulation let us identify the precise parameters of a curve or surface, and then we aproach through the numerical abstraction. Mathematical geometry and programming eases rigorous approach to the study of the object (Coloma, Mesa 2012).
In any long journey, there is likely to be some terrain that is very difficult to cross, such as getting over a mountain range moving up through narrow mountain passes. In learning mathematics there are many such ‘mountain ranges’, where students have to work hard to build new concepts and develop new skills, and might lose track of the direction in which they are heading. Teaching through problem solving can be very effective here if there is a very carefully designed sequence of tasks. This approach has been developed to a high degree in Japan, and forms the basis of some Japanese school textbooks. The example below is from a presentation by Akihiko Takahashi of DePaul University Chicago drawing on material from the Lesson Study Alliance (http://www.LSAlliance.org) following the Japanese curriculum (Takahashi, 2018). The overarching goals are that students should learn the ideas deeply and have experience of using them flexibly.
However, rationality in planning and organizing the society was definitely a characteristic of Sweden. The narrative about the centralization of school governance, mentioned above, concerns this. And the new mathematics syllabus of 1969, which was based on New Math, was prepared in this spirit. The preparations began in 1960, when the Nordic Committee for the Modernization of MathematicsTeaching (Nordiska kommittén för matematikundervisningens modernisering) was formed. Sweden, Norway, Denmark and Finland had decided to cooperate in the reformation of school mathematics. Apart from producing a new syllabus, a key element in the project was textbook development. About 30 authors were contracted to produce new textbooks that fitted a radically new syllabus. The textbooks were also tried in teaching, in some cases for up to three years. In total, the trials involved 1,310 school classes. By the end, the project received an even more scientific character as comparisons between experimental classes and control classes were made, but with much fewer classes (Prytz & Karlberg, 2016, p. 73). It is important to note that the results from the trials indicated that new types of textbooks were possible to use in teaching. For further details about the trials and their results, see Prytz & Karlberg (2016).
In this article we present one of the proposed games in the laboratory: The Mate-Trivial, a board game to play individually, although competitions can also be established through a ranking. In it, students have the same capacity to move across and about the board with the object of reaching its centre, at which point the game is considered to be over. In order to achieve this end they will have to face up to a series of mathematical questions, as a test, which will allow them to achieve their ultimate objective. Why have these games been chosen? The game has the nature of a pastime and entertainment which, although at first sight is opposed to the idea of study, can also be used in its benefit. In fact, the idea of entertainment and the possibility of going into action quickly which underlies all games, can be used to initiate students into mathematics. The game can be an attractive and motivating element which turns the task into a much more pleasant and stimulating one.
recognizing the work of teachers, for example the Global Teacher Prize, also referred to as the Nobel Prize for teaching recognises the work of teachers all over the world. Their objective which is to support the teaching profession and quality of education by awarding teachers who have impact on the children, schools and community. Their website reveals that a best teacher is one that 1) employs effective instructional strategies that influence and improve the quality of education. 2) uses innovative strategies to address challenges of a school, community and country 3) achieves the learning outcomes of his class and improve the teaching process by raising its bar 4) impacts his community beyond the classroom and 5) help students become global citizens of the world who are informed socially and economically and equip them for the world where they would live, work and socialise with people from different cultures and religions. Maarit Rossi and Colin Hegarty are mathematics teachers who were recognized as among the 10 best teachers of the world, Colin Hegarty from the United Kingdom teaches students ages 11-18 and he believes that no child is bad at mathematics as they just need the right support. While Maarit Rossi from Finland who also teaches mathematics by incorporating fun activities and enabling students see the relevance of it in their lives, these teachers are innovative who employ effective instructional strategies that influence and improve the quality of education globally. There is a substantial amount of research regarding the calibre of a good teacher. Students are the most significant people who are close to the teachers because they spent most of the times with them. Therefore, it is important that views and opinions of students representing different backgrounds and culturally diverse are considered. Although the context of this research study is mathematics teachers andteaching, it also contributes to a broader discussion of teachers in different subjects and disciplines. Defining a good mathematics teacher can sometimes be difficult. At hand, many researchers have made attempts to describe good mathematics teachers andteaching. According to Ball et al (2008) a
This study investigates K-1 teachers´ perceptions, practices, and equity issues in the integration of contextualized problem solving into the curriculum as a way to adapt instruction to meet the needs of Latino students who were English language learners. We draw from three bodies of literature: Cognitively Guided Instruction, language and culture as pedagogical resources, and equity issues in mathematics. This qualitative study takes place in the context of a situated professional development between bilingual teachers and researchers in a southwestern elementary school in the United States. Data sources included classroom observations, videotaped lessons, and interviews with the teachers. Through classroom episodes, this study illustrates how both teachers: (1) valued the integration of contextualized problem solving into their curriculum and used language and culture to scaffold understanding of complex mathematics concepts, (2) prioritized the use of the native language in their teachingand the development of different ways to communicate mathematically their ideas and strategies, and (3) prioritized equitable teaching by valuing and promoting a student centered approach to teaching as well as students´ identity as mathematics learners.
El trabajo de G. Cirade (2006) muestra la enorme problematicidad que encierran las matemáticas que se enseñan en Secundaria y cómo los recursos matemáticos que permiten abordarla están, todavía, muy alejados de la cultura matemática de la comunidad docente dado que, en muchos casos, requieren elaboraciones matemáticas originales que evolucionarán para convertirse en herramientas matemáticas de uso didáctico. Por otra parte, estas elaboraciones necesarias distan mucho de ser triviales desde el punto de vista de los recursos matemáticos que solicitan. Un trabajo como The mathematics of physical quantities, de Hassler Whitney (1968) 3 , puede ser un buen ejemplo de este tipo de recursos, elaborado para aportar una respuesta funcional a la necesidad de justificar matemáticamente expresiones del tipo:
Although the surface of the curricular ocean may sometimes appear to have been swept by a tsunami, therefore, down in the depths curricular life goes on unper- turbed. For example, one can argue that every wave of curriculum reform in U.S. school mathematics (“unified mathematics,” “new math,” and “standards”) has left the curriculum unreformed. Changed, perhaps, but not reformed. And the changes that these reform efforts did bring about were not the changes the re- formers intended. The strong rhetoric of reform has actually been a mask for dis- unity, contradiction, misinterpretation, and indifference. A reasonable estimate might be that for the reform efforts in the U.S., fewer than 10% of mathematics teachers have been professionally involved in curriculum change. Nonetheless, the public is very much aware of reactions to reform efforts even if they are not necessarily well informed about the substance of the reforms.
The reflective-hermeneutic model describes teaching as a complex activity located in an unstable ecosystem, over-determined by the content, temporary and sociopolitical space loaded with conflicts of value that require ethical and political options. In this model, the teacher must engage in a commitment that goes beyond presenting content or teaching processes. The teacher must, rely on his or her own experience in the classroom, reflect in order to be able to make changes to the class and create new spaces in which he or she can become a methodological and theoretical reference. Moreover, the teacher must be committed to solid values and skills.
The current phenomenon of globalization, understood as the liberalization of the markets, linked with the concept of economic development as a primary objective of the countries, entails the constant change of their internal normativity to increase competitiveness and achieve benefits and opportunities for the individuals. It is needed then, an interdisciplinary work, especially the interaction between economic development and law, to create or modify, both normative and administrative aspects, that leads to the effective economic performance of the countries in a globalized world. However, the existence of the differentiating gap between countries, makes the benefits, as an effect of globalization, not homogeneous, and instead, allows that some countries receive more benefits than the other ones, which in despite their efforts of adaptation of their systems to the global scenario, represent not only an economic delay, but also social. All of this occurs due to the diversity of characteristics and needs of the countries, which must be taken into account for the creation of policies and the adoption of economic models that leads them to economic development. Colombia as a case of study, is a clear example of the effort to adapt its system through the relationship between economic development and law in contexts of globalization, efforts that even though, in some cases has helped the country, in others, has represented negative effects for itself.
integrally consider the territory (sánchez, 2005) involves, besides exploring it as a “so- cial and cultural” continent of productions, understand it as a complex network, where multiple frames are constructed, based on the simultaneous existence of internal and external elements that overlap or merge, causing changes in the population life structure, as reflected in their physical, political, economic and social organization, by the way territory is configured, pos- sibilities for integration and sociocultural articulation or danger of breakdown of the social bond.
- how do the changing needs of the workplace (travel, meetings, changing workloads) fit with the inflexibility of formal education and language institutes? In addition, how will these two aspects fit in with other normal and frequently non-schedulable requirements of adult family life?