This research is based on the notion of didactic suitability criteria proposed by the Ontosemiótic Approach (OSA) of Mathematical Knowledge and Instruction (Godino, Batanero, and Font, 2007). It is aimed at describing the components and indicators for each of these criteria. Theoretical framework systematization and case study were used as fundamental methods; the latter was used to compare the proposed descriptors to the indicators of successful performance used by an in-service teacher to describe his teaching practice in his master degree dissertation. The components and indicators corresponding to each of the suitability criteria and its correspondence to teachers’ qualification description referred to in the case study are offered as a scientific result.

ABSTRACT The current information society demands that civil engineers have an adequate command of the contents of Differential and Integral Calculus as a basis for their successful professional performance. However, there are many national and international reports of learning difficulties of these contents during the undergraduate training period. The objective of this article is to explain the interdisciplinary dynamic that underlies the teaching-learning process of Differential and Integral Calculus by Civil Engineering students. The research methods used were the content analysis of relevant theoretical sources and holistic-configurational modeling. The main result reveals the interdisciplinary logic established between the systematization and engineering functionality of the content of Differential and Integral Calculus and its projective-structural generalization, which constitutes an essential necessary condition for the development of competence for the application of the referred content to the resolution of projective-structural problems.

This paper shows the results of a historical-epistemological analysis that points out the practices performed by Poincaré (1890), Lorenz (1963) and May (1974) in their encounter with chaotic dynamics, we are interested in their argumentations against the erratic (coming from unexpected events), in the transit between the predictable and unpredictable; we assume that the way to act in this kind of situations indicates a way to build specialized mathematical knowledge. Socioepistemological approach methods were applied to search the practices associated with mathematical concepts processing: temporal recurrence, sensitivity to initial conditions and parameter graphics. The findings show that searching the circular, comparing solutions over time and classifying behaviors are practices that give meaning to this kind of situations and are part of an a priori analysis that provides elements for the characterization of a form of variational thinking to face the unexpected. This study provides elements for the construction of a situation that presents unexpected cases, facilitates to study cases of actions in pre-university students and will serve as a guide for the creation of specific examples that allow their integration at school.

Mathematics, as a body of scientific knowledge, includes not only a set of concepts and theories described in books and scientific journals but a procedural knowledge used for solving problems and proving the resulting solution. There is a tool for proving solutions, the so-called mathematical proof, which is worth to be included in the educational process. To complete the study herein described a random stratified sample was selected and given a test demanding to explain the answers given. However, high school students (15-18 years old) do not rely on the use of the known proof scheme. For that reason, a diagnostic study was carried out at the Autonomous University of Querétaro (UAQ) in order to identify the strategies the students are currently following and finding ways to teach such mathematical proof scheme. The findings are a description of individual students’ argumentative practices and the identification and grouping of the most frequently used proof scheme.

The teaching-learning process of Mathematics is currently undergoing constant changes resulting from the achievements of Information and Communication Technologies, that UNESCO has recognized a priority of the agenda for the Education 2030. However, majors at the University of Camagüey "Ignacio Agramonte Loynaz” still fails to satisfy such demands and expectations. This fact, among other causes, is due to insufficient Mathematics teachers’ training on the didactic-technological contents, and in the absence of a didactics of mathematics theoretical framework Mathematics Didactics. The authors assessed teachers’ the didactic-technological training by given interviews and surveys, as well making use of analysis-synthesis and studying current theoretical frameworks from Godino’s Onto-semiotic Approach of knowledge and mathematical instruction, the Theoretical Model of Technological Pedagogical Contents Knowledge of Mishra and Koehler and the Theoretical Model of Technological Pedagogical Disciplinary Knowledge-Practical Disciplinary of Yeh. The study of this framework leads the authors to construct the theoretical frame of reference for the didactic-technological analysis of Mathematics teaching-learning process in the 21st century.

The didactic use of the GeoGebra in exercises of different areas of mathematics and geometry, in particular, is a current issue. This article aims at explaining the teaching of the tangency between bodies, specifically between a sphere and a cone, attending to diagnosed teaching and learning difficulties. It starts with the presentation of two suitable exercises and their corresponding variants to give arguments to prove the convenience of using didactic options suggested by the current versions of the GeoGebra. The examples and arguments shown have contributed to the improvement of the teaching of mathematics and the improvement of teachers of secondary and higher education.

This article describes a study of the exponential function on students of the first semester of a private University in Lima, Peru. The research was aimed at analyzing the Instrumental genesis process of this mathematical object assisted by the use of Geogebra software. Rabardels Instrumental Approach was used as a theoretical framework. Likewise, some notions of Artigues Didactic Engineering were used as a methodology, focusing on a priori and a posteriori analysis. The students answers allowed to identify the use of schemes built and activated, while interacting with the symbolic artifact for the exponential function. The use of Geogebra favored the instrumentalization and instrumentation of the addressed mathematical object since it allowed the students to validate their conjectures.

The paper describes the results of a case study aimed at developing the competence to promoting positive assessment of mathematics in primary school teachers under training. The objective was to evaluate the effectiveness a pedagogical strategy aimed at developing such competence during the teaching practice as organized at “Salomé Ureña” College of Education in San Juan de la Maguana province, Dominican Republic. For the case study the Yin typology was assumed, and the type of multiple cases, the embedded design was selected for evaluating the two variants of the strategy. To evaluate the effectiveness of the training, four dimensions were defined and different techniques were selected: participant observation, portfolio analysis, evaluation of teaching practice, reflective workshops, among others. The findings allowed to conclude that the performance relative to the first level of the competition was reached, as well as actions on the family and the context, corresponding to the third level for both variants

Several directives of the Cuban Ministry of Education give arguments favoring the need to enhance the quality of communication. In this respect, Mathematics plays a fundamental role for its recognized contribution to the development of logical thinking of students. However, the analysis of the related research findings proves there are still difficulties in achieving such formative task at all level of education, especially at the university. The objective of this article is to evaluate a didactic strategy to improve the quality of communication in mathematics of university students. Theoretical methods and some principles related to communication in mathematics were used to construct a framework. This allowed the design of a didactic strategy, applied to three university majors (Bachelor of Education in Mathematics, Civil Engineering and Architecture). The findings prove it to pertinent in improving the quality of communication in mathematics of university students.

After recovering of 4995 entries from Scopus indexed journals related to research in mathematics education, a data matrix is shaped to facilitate the analysis of world scientific production. The findings highlight an exponential diachronic growth, clustering of citations around a relatively restricted subset of documents and authors, the increase of international collaboration, as well as the presence of 17 invisible colleges with different degrees of relationship and activity.

After recovering of 4995 entries from Scopus indexed journals related to research in mathematics education, a data matrix is shaped to facilitate the analysis of world scientific production. The findings highlight an exponential diachronic growth, clustering of citations around a relatively restricted subset of documents and authors, the increase of international collaboration, as well as the presence of 17 invisible colleges with different degrees of relationship and activity.

This article presents the results of a doctoral research that explores pupils’ emotional response from an experiential approach. It acknowledges the occurrence of an emotion as produced either by emergency or by concurrence. The aim is to characterize pre-service mathematics teachers’ emotions. More precisely, the interest is on what configures emotions and what do emotions configure in teachers training experiences. This is done through a qualitative approach; particularly open coding, based on personal logs, and in-depth interviews. The sample is composed of pre-service mathematics teachers from a private university located in Santiago, Chile. The findings support the appearance of emergency and concurrence elements, for example, configurations related to fear of functions or the fear and insecurities towards summative assessment and certain features of the current school system. Strangeness and curiosity emerge as emotions while involving with different styles of learning, which enables the creation of mathematical learning.

The paper describes a proposal of professional pedagogical performance tests to assess teachers role in the process of developing the skill of working with algorithms in Linear Algebra. It aims at devising a testing tool to assess teachers performance in the skill-developing process. This tool is a finding of Cuba theory of Advanced Education, systematically used in recent years. The findings include the test design and the illustration of its use in a sample of 22 Linear Algebra teachers during the first term of the 2017-2018 academic year at Informatics Sciences Engineering major.