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Anxiety is a state of mind of intense worry that can affect students' performance both positively and negatively. Internationally, recent studies show high percentages of students diagnosed with anxiety and depression. This paper seeks to quantitatively analyze how anxiety is related to academic performance in Ecuadorian students. An Ordinary Least Squares (OLS) model with school fixed effects estimates an educational production function. The results confirm that, up to certain levels of anxiety, students' scores improve. However, once anxiety levels are elevated -a threshold that is higher for male students-scores are negatively affected. These findings are relevant for two reasons. First, during adolescence, experiences and interpersonal relationships impact personality construction and influence the development of cognitive, non-cognitive and emotional skills. Second, given the current post-pandemic situation, in which anxiety is a frequent scenario. This research concludes that it is necessary to reflect on the importance of rethinking pedagogical processes in schools and to analyze strategies to introduce mental health in the school curriculum. [ABSTRACT FROM AUTHOR]

In this paper, we describe the elements that characterize the teaching of Mathematics in the Ave María Schools, founded and run by Andrés Manjón in Granada between 1889 and 1923. He stood up for a peculiar model of integrated education, based on Christian values, and he also developed his own methodological principles, similar in many ways to those of the emerging École Nouvelle. The selection and analysis of several sources has allowed us to set his teaching of Mathematics within this pedagogical framework and has suggested us the idea that the strategies used by Manjón in order to teach Arithmetic and Geometry could be innovative at that time and, perhaps, valuable from the point of view of contemporary Didactics. [ABSTRACT FROM AUTHOR]

This paper presents the results of the management of a didactic device formulated by a Mathematics male and Biology female teacher from a secondary school in which they sought a codisciplinary study. Based on the Anthropological Theory of the Didactic, the results of an exploratory study that sought to characterize the management of a didactic device for the study of plant growth in secondary school are reported; In particular, we analyze the relevance of mathematical knowledge in its development. The main results indicate that the study enabled the protagonists to be the students: they formulated and answered questions, achieving autonomy and responsibility for the search for information in various media; however, mathematical knowledge did not occupy a prominent place during the study. [ABSTRACT FROM AUTHOR]

This paper explores the relationship between students' perceptions of the type of teaching they experience in mathematics [more or less student centred] and their reported emotions, self-concept and disposition. It also addresses the question of whether there are differences in this relationship for girls and boys. It uses survey data from almost 300 year 7 Chilean students, clustered in 8 different classrooms. A correlational analysis suggests that there is a positive significant association between how student centred the teaching is perceived to be and students' more positive attitudes. Nevertheless, this effect was independent of sex, suggesting that more student-centred teching do not necessarily offer an advantage for girls, but are positive for both, boys and girls. [ABSTRACT FROM AUTHOR]

The definite integral is a central concept in the applications of calculus to experimental sciences and engineering, and consequently, a relevant didactic research topic. This paper analyses the different meanings of the definite integral by applying theoretical tools of the ontosemiotic approach to mathematical knowledge and instruction, particularly, the interpretation of meaning in terms of systems of operational and discursive practices related to the resolution of types of problems and the algebraization levels model of mathematical activity. Types of problem-situations and configurations of practices, objects, and processes are identified that allow us to characterize and articulate the various partial meanings of the definite integral (geometric-intuitive, as a limit of Riemann sums and cumulative function) as well as its extensions to the case of the double integral (as a particular case of the multiple) and the line, from the most intuitive to the most formal. The analysis allows us to identify the generality degrees of the objects of integral calculus and the role of algebra in the characterization of the meanings of the definite integral, which must be considered in the planning and management of the processes of teaching and learning of integral calculus in engineering degrees. [ABSTRACT FROM AUTHOR]

This paper sets out different contexts where mathematics helps create a thinking and reasoning habit, with special emphasis on problem solving. Intelligence is thought to be connected to problem solving ability and so we are interested in the relationship between intelligence and mathematical problem solving. These problems will be posed in a broad sense, not just considering classical written problems but also problems that appear in situations such as chess, magic tricks, and board games. These settings motivate students better, solving them requires different approaches, and they relate to other fields of knowledge. This paper reports on our experience of posing problems and reasoning with gifted students through magic tricks based on mathematical ideas and we give some examples of the activities we have done with them. We also present recreational mathematics as a discipline that promotes student motivation and increases curiosity and inquiry. We show some ideas from Miguel De Guzmán, Martín Gardner, and Raymond Smullyan that have been used in different frameworks. We describe some games that have been shown to be useful tools for creating reasoning schemas, presenting the particular case of chess as an educational tool. Finally, we set out some conclusions about the introduction of new materials, methods, and ideas for solving problems and we formulate a proposal for continuing this work and applying it in the classroom. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical model for the study of mathematical talent, grounded in the Anthropological Theory of Didactics (ATD) and the notion of creativity. This model proposes two components of creative mathematical activity: the mathematical component, which supports mathematical techniques; and the creative component, defined by four functions: producing new techniques, optimizing techniques, considering tasks from different angles, and adapting a technique. Based on the theoretical model and a reference epistemological model on infinite sequences, a learning design comprising six problem situations was developed and then implemented in an institution established to foster mathematical talent. The analysis of two tasks performed by a pair of children offers a case study that illustrates how tackling challenging tasks of the same kind, in a favorable institutional setting, makes it possible to develop mathematical talent. [ABSTRACT FROM AUTHOR]

This paper presents the theoretical and methodological conceptions of designing teaching tasks to promote the contextualization of lessons in Mathematical Analysis in educational Mathematics. It is aimed at conceiving teaching tasks, by adopting a pedagogical professional approach, to promote this contextualization. Theoretical (historical-logical, analytic-synthetic, and inductive-deductive) methods of research were used. Students, graduates, and experienced professors were interviewed in order to collect data on professors' performance in promoting the contextualization of lessons in Mathematical Analysis in educational Mathematics. Additionally, such documents as syllabuses, regulations, scientific papers, doctoral and master's theses were analyzed. This paper contributes to the contextualization of lessons in Mathematical Analysis in educational Mathematics through the pedagogical professional approach. [ABSTRACT FROM AUTHOR]

This paper aims to explain Leibniz's opinion according to which creation and demonstration in mathematics are founded upon a certain general logic that is conversant not only with syllogisms and prosyllogisms, but also with the rules of particular progressions or functions. If this is the case, there would be a universal mathematics or good characteristics, bringing several consequences on what is thought to be the foundation and range of human knowledge. We intend to do such an inquiry mainly using the fictional clash between Theophilus, that stands for Leibniz himself, and Philalethes, that stands for the English philosopher John Locke, regarding the alleged impossibility of squaring the circle claimed by the latter, that is portrayed in the New Essays. [ABSTRACT FROM AUTHOR]

This article examines how effective education institutions improve educational achievement, regardless of students' socioeconomic backgrounds. The paper utilizes a multilevel model using data from the Third Regional Comparative and Explanatory Study (TERCE) for Ecuadorian students in reading and mathematics. Findings show that between 31 and 52% of the variation in test results is due to differences between schools, thus underlining the importance of the compensatory effect of schools in promoting equality of opportunity. [ABSTRACT FROM AUTHOR]

This paper, a product of the research entitled "Mathematics teachers' Narratives and Subjectivities about their professional experience", presents matters related to mathematics teachers' training. Unveiling the mathematics teachers' subjectivities in narrative wefts which are made about their professional experiences and their formation trajectories is the main purpose of this inquiry. It assumes the narrative perspective in its epistemological and methodological dimension, in a way which claims the narrative thinking as a way of the knowing of the world and self-knowing. The analysis of the considered investigation antecedents and the voices of teachers who narrate themselves allowed to assume the training mathematics teachers' curricula as a criticism object, so it became a first inquiry result. Thus, the curricula were interrogated in connection with: a) The logic-scientific thinking hegemony and ignoring the narrative thinking contributions in the training processes; b) the absence of intentional actions for understanding the subjectivation modes which underlie the formative processes; c) the identity configurations and subjectivities that underlie in the formation trajectories. It concludes that the hegemony of a logic-scientific thinking way and ignoring the narrative knowing way in the mathematics teachers' training processes show the formation as decontextualized, apolitical, and ahistorical. Besides, the logic-scientific thinking configures a knowing way which prevails the truth search and shows faith in rational knowledge as the most powerful force for the world understanding and the self-understanding. [ABSTRACT FROM AUTHOR]

This paper presents, from an introductory point of view and oriented to non-experts in network theory, the fundamentals of graphs and networks that allow projecting information about cultural networks in a formal context. It also describes some of the most common measures and tools to design quantitative mechanisms for the subsequent analysis of these networks. This article does not pretend to be a complete course or tutorial on network theory, for that the reader can refer to any of the references listed at the end, but rather it is an introduction oriented to go through, in a single document, some of the details that are considered more important and that are usually leTh out of the initial explanations on the subject. [ABSTRACT FROM AUTHOR]

Requirements Engineering is considered the most important phase of the life cycle of software products because it specifies the needs of the customers, and it is also the basis for the execution of the other phases of software engineering. The models currently used to perform the requirements elicitation have been proposed and widely documented, but they are focused only on the techniques to collect information, disregarding the activity of properly documenting this information. Moreover, to structure the requirements specification, natural language continues to be used as a means of communication and understanding with the customer. Due to the ambiguities caused by this language, its interpretation becomes difficult, and this leads to reprocesses in the later stages of the software life cycle. According to the above, it is necessary for software development organizations to consider formalizing the process of requirements elicitation if they wish to make their development process more efficient. A literature review is carried out in this paper to determine the process and evolution of the formal methods from the requirements engineering perspective. [ABSTRACT FROM AUTHOR]

The current period is, at the same time, highly uncertainty and intensive in data production. In the analysis of scenarios produced by the COVID-19 pandemic, we make forecast based on mathematical models where exact assumptions are never true. This leads to a reconsideration of the usual form of data analysis, both in journalism and academic research, bolding on the need for exhaustive testing of the available information, since researchers are often not clear enough in their parameters or assumptions. These omissions usually become in different levels of importance in the media, because journalists tend to assume the same attitudes towards complex data just in the way they do with the news in "normal periods". However, it is necessary to obtain an adequate understanding of the data on positive COVID-19 cases, defunctions or politics aimed to containing the virus, designing some basic rules that both specialists and journalists may take into account when they have to write papers or publish news at a time as critical as nowadays. [ABSTRACT FROM AUTHOR]

This research explored the relationship between a set of variables, such as reading comprehension and logical-mathematical intelligence, along with two sets of cognitive and learning variables, in respect to overall school performance and school performance in the subject of Spanish Language in a population of socially vulnerable secondary school students (N=688). The main objective of this study was to examine the differences and quantify the effect of the addition of the above-mentioned variables to an explanatory model for academic performance. For this purpose, comparative analysis, bivariate correlation and stepwise multiple regression models were used. The results showed that 34.9% of the variance of students' grade point average in the subject of Spanish Language could be explained by the variables that were added to the model. The positive effect of reading comprehension, achievement attributed to effort, and the self-regulation strategy of revision stood out in this model. At the same time, a negative effect was found for older age and attributing achievement to external causes. In addition, the explanatory model introduced in this article showed greater predictive power for the female group; notably the variable critical comprehension also had a positive effect for the female group. Finally, the main educational implications for these findings are analyzed and discussed in this paper. [ABSTRACT FROM AUTHOR]

This paper describes a study of mathematical argumentation in primary school. The principal aim is to explore the nature of complex argumentation at a structural level. The context of the study was a teaching experiment involving nine tasks that promoted argumentation among fifth graders. We use the framework and method of reconstructing complex argumentation in the classroom proposed by Knipping (2008). The findings show that complex argumentation at a structural level in the context of refuting conclusions is characterized by a source-like structure with the addition of a new refutation argument element. [ABSTRACT FROM AUTHOR]

This paper presents the results of a research study aimed to explore the main beliefs and conceptions that have teachers who teach mathematics at the secondary level in Honduras (students 13 to 18 years), in relation to the teaching /learning and assessment of mathematics. The results show, among other elements, that for Honduran teachers the learning of mathematics is achieved by the active participation of the students. This belief is highlighted by teachers with a bachelor in Mathematics; and that the evaluation is a process that improves teaching and learning, providing useful results but, they must be taken with special scrutiny due to mistakes and inaccuracies that always exist. As conclusions highlight the need to improve initial training and continuous training of teachers so that use resources that promotes active student participation and improve the evaluation processes. [ABSTRACT FROM AUTHOR]

In the course of General Physics it is possible to find the problem related to the study of the motion of bodies in a liquid when their densities are greater than that of the liquid. A problem not found in the bibliography consulted is: What depth will be obtained for an sphere when it falls freely from a height H above the free surface, if its density is less than that of the liquid? To carry out the study of this problem, a theoretical model was applied and an analytical solution was found to this depth. In addition, an experiment was designed based in the video analysis technique, using Tracker for Windows to know the real depth obtained. The main goal of this paper is to estimate the energy interchanged in the impact of the sphere on the surface linking both results. [ABSTRACT FROM AUTHOR]

This paper aims to show the situation of the mathematical lexicon in the nineteenth century. Undoubtedly, one of the possible approach for the diachronic analysis of the language is to use the historical dictionaries. Another path is access the sources which served as a vehicle for the scientific expression, for example, the lexicological and lexicographic works of Felipe Picatoste. With both, this mathematician noticed that mathematical terms were being subjected to an abandonment. Ultimately, the study is progressing in the historical study of Spanish language from its scientific perspective. [ABSTRACT FROM AUTHOR]

The deep movement of transformation and renewal of the social, economic and cultural orders befallen in the late Middle Ages, as well as the economic dynamism of the fifteenth and sixteenth centuries and the eagerness of wealth from of the bourgeois class contributes, along with a rapid urban expansion and an increase of continental commercial relationships, the urgent need to learn arithmetic in order to carry out successfully the new accounting. Consequently, in order to satisfy those social needs and for the sake of arrive to the greater number of readers, during the Renaissance were published, first in Spanish, many works devoted to the calculations. The publication of these arithmetic-algebraic treatises --whose purpose was essentially practical-- in the five-hundred century brought with it, not only the democratization of the calculation, but also, from a linguistic viewpoint, dignified the use of the vernacular languages as transmitters of knowledge expressed traditionally in Latin to a minority elite and favored the construction of a type of speech whose rhetoric we analyze in this paper. In short, our aim is bring to light, through extracted fragments of the most significant sixteenth century treatises that containing arithmetic and algebra, the stylistic and informative characteristics of this specialised vocabulary. Motivated by humanist pedagogical theory and to instruct (docere), highlighted in the corpus studied the use of many examples, citations and allusions to authorities, instructions and warnings, among other rhetorical resources which we consider key to the establishment and dissemination of these disciplines in the Iberian Peninsula just like the configuration of the mathematical technolect in Spanish. [ABSTRACT FROM AUTHOR]

Using the classification methods for mathematical problems in textbooks (Fan & Zhu, 2000) and strategies used to solve problems (Fan & Zhu, 2007), this paper reports the results of an analysis and classification of the type of mathematical problems and problem-solving strategies in a sample made up of the five most widely-used mathematics textbooks for the first year of junior high school in the 2013- 2014 school year in Mexico. It is concluded that the textbooks focus on providing a comprehensive range of problems that, for the most part, do not allow multiple problem-solving strategies, whereas others can be solved using an algorithm or direct procedure. [ABSTRACT FROM AUTHOR]

During the 20th century, one of the most debated issues regarding Aquinas's theory of knowledge was the process of abstraction. Attention was mainly focused on the role of abstraction in the definition of objects of speculative sciences. Leaving aside the particular features (and disparities) of this debate, this paper aims to focus on the analysis of a very peculiar text in which abstraction -still considered as the cause of the distinction of mathematical objects-does not seem to designate some sort of intellectual operation. On the contrary, abstraction there appears as a property of the very mathematical essences or forms. The consequences of this could lead to the revision of some established ideas in Thomistic Epistemology. [ABSTRACT FROM AUTHOR]

This paper will analyze the importance of playfulness as an instrument for learning mathematics, taking into account that the body allows to develop not only motor skills but also intellectual faculties involving high levels of abstraction, such as mathematical operations like addition, subtraction, multiplication and division. The methodology used was action research, through interviews to students, parents and teachers, as well as the systematization of experiences in the classroom by means of a field diary. It was found that traditional -tedious- teaching does not allow students to realize the importance of learning mathematics. It is concluded that it is necessary for the teachers to implement strategies that link playfulness and the body, in order to improve teaching-learning processes, which allows that mathematics do not be considered as something far from reality, but that be granted the status of a knowledge that improves the processes of understanding and reflection, facilitating the solution of practical problems. [ABSTRACT FROM AUTHOR]

This paper offers the results of an analysis of the level of mathematical anxiety, understood to mean a feeling of discomfort experienced when someone is required to take mathematics classes, as displayed in students of secondary education in Costa Rica. The study was performed with a sample of 3,725 students in public secondary education in Costa Rica in 2013. The results show statistically significant differences between the sexes in the level of mathematical anxiety, with female students experiencing moderately higher anxiety levels. Differences in anxiety levels are also determined by the student's educational level, with significant differences found between third-cycle students (7th, 8th and 9th grades) and diversified education students (10th and 11th grades); the latter displayed moderately higher anxiety levels. Nonetheless, the study concludes that despite the differences observed, only 22.4% of students show high or very high levels of mathematical anxiety. [ABSTRACT FROM AUTHOR]

This paper presents the results of a research carried out with students of 4th year of Primary Education in which we analyze the effects of the use of a methodology based on the invention and reconstruction of problematic situations in Mathematics class, on the development of metacognition. Results indicate that the implementation of the program improves the following areas in the students: Metacognitive Declarative Knowledge, Procedural Metacognitive Knowledge, Conditional Metacognitive Knowledge and Metacognitive Ability of Prediction. The invention of problematic situations allows students to discover the error and to recognize it in order to avoid it in the construction of new knowledge. These situations promote the awareness of the mental processes involved in the development of the task and in the decision making for the implementation of solving strategies. [ABSTRACT FROM AUTHOR]

In this paper we present some operational indicators to assess the theses presented by graduates of the MA in Mathematics Education. The paper presents data from the theses by orientation, by thematic field, and by theoretical framework and methodological tools; and lists the authors most often cited. Using this information, we infer graduates? vision concerning mathematics education; their role as teachers; and the knowledge that various courses have left with them for their professional development. The question this research seeks to answer is: what theoretical framework and methodological tools did students working on their Masters Degree in Mathematics Education use to carry out their proposals for pedagogical intervention in their theses? [ABSTRACT FROM AUTHOR]

This article tries to follow the changes involved in the development of the concept «public opinion» since its first use in the middle of the 18th century until statistical surveying became predominant in social research in western democracies from the 1930s. It is argued that theoretical and methodological perspectives are not only related but supplementary, and that the concept of «public opinion» is influenced and mediatized by the methodology which is being used to «register», to «measure». The paper outlines not only the beginnings of the notion of public opinion, but also the mathematical origins of polls through the representations of entities which are not easily appraisable or evidently part of the «physical world» --such as opinions- by early authors of social statistics, obviously influenced by the political and social context of their time. The paper concludes with a brief consideration of the rise of opinion polls in the U.S. in the 1930s, acquiring the «necessary legitimation» to become the predominant methodology in public opinion investigation. [ABSTRACT FROM AUTHOR]

This paper presents the results of a research carried out with students of 4th year of Primary Education in which we analyze the effects of the use of a methodology based on the invention and reconstruction of problematic situations in Mathematics class, on the development of metacognition. Results indicate that the implementation of the program improves the following areas in the students: Metacognitive Declarative Knowledge, Procedural Metacognitive Knowledge, Conditional Metacognitive Knowledge and Metacognitive Ability of Prediction. The invention of problematic situations allows students to discover the error and to recognize it in order to avoid it in the construction of new knowledge. These situations promote the awareness of the mental processes involved in the development of the task and in the decision making for the implementation of solving strategies. [ABSTRACT FROM AUTHOR]

The lack of updating and training of teachers in the use of information technology and communications (ICT) as a teaching and learning of mathematics, have limited its methodological work, causing poor performance in the integral learning students and ability to solve practical problems they face in society. That is why this paper aims to consider the more specific contradictions that occur in the teaching and learning of mathematics based on the use of ICT. In this context, it is concluded that recognizes the mathematical task computerized (TMI) as a means to contribute to the improvement of student learning, taking into account the contradiction occurs between the comprehensive nature of the student's education to society and the diverse nature of the ownership of the contents taught in the course. [ABSTRACT FROM AUTHOR]

At present, the teaching - learning process in higher education increasingly heads to the fact that the student could turn into a much more active individual in his/her training, which demands the student a more independent training where the individual acquisition of knowledge made by the student must be the center of the process with a systematic, independent and creative dedication to the study and with a high development of the ability of managing its own knowledge, and where the information technology and communications play an important role in the achievement of these transformations. With this aim, courses and subjects are planned and improved, and new methods and teaching means are developed. By means of this paper, emphasis is made on the importance of the independent work to improve the student's cognitive autonomy and his/her creative thinking in higher education, particularly in the process of assimilating mathematics -- a science in constant development and existent in almost every curricula of university courses because of its importance in the accomplishment of certain skills in the organization of ideas or thoughts of future professionals, and as key element in scientific and technological advances of mankind. To carry out this analysis a study was made of how from the perspective of students and teachers the Guiding, Enforcement and Control of the Independent Work is performed, results that show the need of carrying on with its improvement to attain the fulfilment of its true role in the learning process. [ABSTRACT FROM AUTHOR]

In this paper, the authors make an analysis of the efficiency and promotion results in the teaching - learning process of the Mathematics Discipline, during the period 2003-2010, for the first and second year of Agricultural Mechanization and Agricultural Engineering careers, in which the discipline is almost taught entirely, as it is also analyzed the results of the optional subject Experimental Design, in third year, Agricultural Engineering. It is also discussed the strengths and weaknesses that the Discipline has had throughout the period under review, and some of the mistakes made by the students in first and second years are illustrated. [ABSTRACT FROM AUTHOR]

Jorge Luis Borges often consulted Mathematics and Imagination, by E. Kasner and J. Newman, where set theory is addressed (the branch of mathematics that studies the relationship between sets). This theory was proposed by Georg Cantor (1845-1918) and by it transfinite arithmetic is established (beyond finite arithmetic) and an epistemic system is created to represent different levels of the infinite. This way Cantor labels the different levels of the infinite by assigning to each the first letter of the Hebrew alphabet, the Aleph, followed by a number, depending on level of the infinite he is referring to (Aleph-zero, Aleph-one, etc.). Following these ideas, Borges weaves several narratives in which the infinite and the absolute are discussed. An example of such narratives is the collection of stories compiled under the title The Aleph, which opens with "The Immortal" and closes with the story that gives the collection its title. The objective of this paper is to study "The Immortal" under the Cantorian lens to discuss one particular absolute, the self, and to suggest that it is impossible to establish a final vocabulary, or a definite definition, about this topic. This impossibility, Borges proposes, is in part due to the apparent finitude of language while at the same time the fallible attributes of human memory also is crucial when it comes to defining anything. However, as the ironist Borges is, he is capable of providing through "The Immortal" a re-description of these issues by means of a transfinite language that resolves some paradoxes while at the same time reveals others. By this way of writing, I propose, Borges fosters the continuation of the dialogue among the different disciplines. Though I will center my analysis on "The Immortal", to develop these ideas I also revisit other stories contained in The Aleph departing from a theoretical approach rooted in the philosophy of language. [ABSTRACT FROM AUTHOR]

A review of the most relevant results, according to the author, is, hereby, presented. These results have been motivated by the work done by the famous mathematician H. Poincaré in 1885. Works after 1997 are presented. This paper was done in such a way that it can be understood by readers who have only basic notions of calculus. The preliminaries provide elements to the reader to understand the results without great difficulties. [ABSTRACT FROM AUTHOR]

This article investigates the association between normative use of alcohol and popularity among adolescents attending private schools in Montevideo, Uruguay. The study replicates the methodology of an investigation conducted in the United States and finds similar results to those encountered for American adolescents (Balsa, French, Homer and Norton, 2010). Concretely, the paper analyzes how a students' divergence from the normative alcohol consumption of their reference group affects their levels of popularity. Popularity is measured by the number of friend nominations received by students from their classmates. Our approach minimizes selection bias and omitted variables bias by using school and grade fixed effects and by adjusting for a rich set of individual and classroom level controls. Results show that adolescents socially reward their peers for consuming alcohol at the normative levels of the classroom, regardless of the actual level of this norm. Boys accept and reward consumption that approaches the classroom mean, but penalize consumption that exceeds the classroom average. Coefficients on women, on the other hand, suggest a marginal penalty for increasing consumption, even at levels below the classroom average, but this penalty is not statistically significant. [ABSTRACT FROM AUTHOR]

Many achievements, that take place worldwide in the field of sciences and engineering, are supported in high level mathematical theories; moreover, the rapid development of technologies of information and communication facilitates the application of mathematical concepts to the problems that arise. That is why the teaching of mathematics should not be limited to a mere transmission of knowledge: it is important that students learn how to think and learn, which presupposes a major challenge for teachers. This paper is the result of the author's professional experience and analysis, in which a reflection is made on what issues are integrated into the process of teaching - learning of mathematics at a superior level, in order to achieve a better educational use and increase motivation for the study of this science. [ABSTRACT FROM AUTHOR]

In measuring quantities such as longitudes, areas, weighs, etc, it is not enough to count -which would be solved with natural numbers-because in general the measurement of the given quantity cannot be expressed using multiples of the selected unit. In effective measures it is necessary to resort other numerical domains, such as the rational numbers. In this paper we will analyze the explicit relation between numerical domains and measurements, in some current curricular documents, through the focal points which refer to the study of numbers and operations, and geometry and measurement. [ABSTRACT FROM AUTHOR]

Leon city has a growing concern about the problem of water, which is polluted mainly by the tannery industries, shoe manufacturers and agroindustries. By law, environmental authorities have asked each polluter to abate pollution, but the task has gone to no avail. The purpose of this paper is to prove that the problem has a solution. To find it, it was built a non-linear-dynamic program starting from the traditionally used treatment processes to clean the waste currents as a solution for a new strategy for a lower cost which shares among the emitters using analytical ranking. [ABSTRACT FROM AUTHOR]

This paper is part of a qualitative research study that took place in five public schools of Lima between 2005 and 2007. The goal was to identify teachers' conceptions about teaching and learning in order to understand their pedagogic practice. The sample included 9 sixth grade teachers of primary schools. Results show that traditional pedagogic conceptions are strongly rooted and this is reflected in the pedagogic practice of all teachers. Mathematics teaching is characterized by the following of rules and procedures, the routine practice of exercises, the use of key words and the lack of a significant context for learning. [ABSTRACT FROM AUTHOR]

This paper reconstructs some findings of the project "Common arithmetic knowledge and productive and social practices"; the questions which direct it are: What sort of number and calculus problems its productive and social insertion poses to these organizations? IA/hat are the social worries that support the strategies in the solving of arithmetic problems? The empirical referent is constructed through the perspective of two women who lead two productive organizations (in Mexico and Argentina) of self-management linked to craft production. Some analytical advances referred to Mexico (Purepecha indigenous community) are reported. In particular, the uses of numeracy and their links to the community social criteria of extra mathematical order that underlie and cross different situations which are framed not in an individual action, but in a collective one. These criteria rule two kinds of relations: the inner ones and the outer ones, crossed by the concerns around power (the nice power) and the defence (to face the outside) of the organization. The reconstructing of these senses implies a positioning that redefines the polarity literacy! illiteracy, by asking how one can learn to read or write numbers under such circumstances, when the knowledge of the number writings is limited. [ABSTRACT FROM AUTHOR]

One of the components of the methodological and theoretical framework that Filloy named "Local Theoretical Models" is the description of the competence in the domain of which teaching and learning are going to be researched. In this paper we show in which sense the term competence is used in this framework and provide examples of the construction of competence models in some investigations. This leads us to examine the relationship between the competence in a mathematical domain and the phenomenological analysis of this domain. Incidentally, we study the use of the term competence in several PISA documents. [ABSTRACT FROM AUTHOR]

The aim of this paper is to scrutinize Hintikkas's affirmation which claims that true elemental logic is not classical logic, but IF logic. Thus, the framework in which the relation between logics and mathematics is ordinarily thought is completely inadequate. In order to achieve this goal, we expose the functions or characteristics that a logic must have, and secondly, we present the constitutive ideas of the IF logic. Further ahead we demonstrate some of the mathematical properties of the IF logic and analyze the complexities which result from the negation in this system. At the end, we offer some reasons to contextualize and to question the conclusions which Hintikka obtains from his proposal for a philosophy of mathematics. [ABSTRACT FROM AUTHOR]

"Mathematics, synthetic unity and constitutive a priori". Starting from the emphasis about the kantian idea of the originary synthetic unity of apperception like the basic function on which rest the production of all synthetic judgment, in this paper I defend the idea of constitutive a priori of experience under the form of a similar synthetic principle but essentially formal, namely, the concept of transformation and group of transformations. To the same time, I try to show that Kant himself inspired, for articulate his own position, on mathematics, especially on synthetic geometry. [ABSTRACT FROM AUTHOR]

This paper deals with the development and application of a series of relations that allow evaluating the contact ratio in gear transmissions where the pinion and the wheel have undercut. The procedure is applied in the solution of four problems. [ABSTRACT FROM AUTHOR]

In this paper, we used the data of Mathematics achievements from the sample of 13- year-old Spanish boys and girl who took part in the Second National Assessment of Educational Progress, carried out by the Educational Testing Service. With the aim of identifying variables related to high achievement, our goals are: 1) to analyse whether there are significant differences in 13-year-old Spanish boys and girls in their attitudes towards mathematics, their study strategies, and their performance; 2) to analyse the influence of their attitudes and study strategies on their performance, and to examine whether these relations are the same in boys and girls; 3) to propose a theoretical model that explains the relationship among the variables defined by means of structural equation modelling. The results show that: a) there are significant differences between boys and girls in the variables studied; b) it is not possible to reject the proposed model that relates study strategies and attitudes towards performance in mathematics; and c) the model tends to be stable both among boys and girls. [ABSTRACT FROM AUTHOR]

In this paper we characterize the term reflexive mathematics teacher in order to elucidate teacher training programs and analyze teachers' development and its relation to their professional knowledge. We describe some of the research variables that are used to characterize and train reflective mathematics teachers. With this purpose, we introduce some theoretical considerations and present some of the research projects we are currently working on concerning the reflection processes of preservice teachers in a methods course of the mathematics degree. [ABSTRACT FROM AUTHOR]

In this paper we present a qualitative research, in which we explore what readings or interpretations are done by the students of elementary school on the graphs that are shared socially; it is to say, those used by the means of information and that are directed wide social sectors. The graphs put in the scene of the reading are referred to population, financial subject matters and one to the mathematical context. This work, which involved to students of elementary school, allowed us to detect interpretations in which the most of the students identify what changes (the variables), they do reading of data by data or point by point (according to it corresponds), favoring to the maximums and minimums, they make qualitative descriptions of how it changes something, adducing that rises or low. Nevertheless, they do not establish covariationals relations; they do not calculate how much they change to the variables nor note that use the change reasons. The evidences indicate, in addition, a little knowledge on the meaning of the social concepts represented in the graphs. [ABSTRACT FROM AUTHOR]

There are three different stages that generally take place while learning mathematics: the first concrete stage is when children learn to add, usually incorporating fingers as the most common object of support; a second pictorial stage or of icons, in which children assimilate a pictorial representation of the concrete object and, finally, an abstract or symbolic stage, in which children handle symbols that represent mathematical quantities. The main goal of this paper is to discuss the construction of a mathematics test for university students administered to a sample of 564 participants. The aim of this study is to evaluate achievements in mathematic abilities of young people that have finished high school and are ready to start university studies. The sample's mean age was 24 years old with a standard deviation of 8.7 years and was 40% male and 60% female. The test has 50 items that measure simple algorithms for arithmetic problems: some items require the use of decimal numbers, some stress the use of proportions or percentages, and a few others are algebraic and geometric questions. All of the items are multiple choice tasks with four options and only one correct answer. There is no time limit to take the test, but its duration is usually not longer than one hour. The mean of the total scores is 25.36 with a standard deviation of 8.06. The exploratory item analysis shows the percentages of correct answers for each item, as well as the values of item-total correlations. Cronbach's alpha reliability index is .936. To study the construct validity we factor analyzed the results and came up with one factor that saturates many items of arithmetic calculation type and three other factors which are not very significant. The test measures, fundamentally, arithmetic calculation, but a lengthy analysis indicates that the items imply other inferential processes. The application of this test indicates that it is very difficult to differentiate mathematical abilities from the aptitude to solve new problems, and that, we are actually evaluating an individual's problem-solving abilities. Such an aptitude improves only with a mathematical instruction centered on the understanding processes, so that if the students are taught to understand the structure and the logic of mathematics, they will have more flexibility and will be more capable of remembering, adapting and organizing data. One of the difficulties observed in the test was that some participants thought that, when multiplying, the values always increase and, when dividing, they always diminish. That is the reason why they struggled so much with decimal exercises. The 50% of the examined participants had difficulties in solving problems with decimals, many had difficulties in finding percentage or interpreting a simple graph of columns. Currently, manual computers are used, but students have difficulties in the interpretation of its results, e.g. when it is presented in mathematical notation. It is very difficult, in this type of test, to differentiate mathematical abilities from mathematical knowledge because it is also important to consider a very strong inferential cognitive aspect. [ABSTRACT FROM AUTHOR]

This paper examines the impact of the school reinforcement program that "Un Techo Para Chile" offers to the poorest communities in the Metropolitan Region, in Chile. The data were taken from a survey specially designed by the authors. The effects of the program on low-income students attending elementary education show an increase in mathematics and language grades during the academic period 2004-2003. The impact of the program is estimated using parametric methods. The robustness of the results is analyzed with non-parametric estimations and using different control groups. The main results indicate that the program has a positive impact on student's grades. In addition, the grades obtained in 2003 did not determine student's participation in the program during 2004. [ABSTRACT FROM AUTHOR]

The scientific productivity of the Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (Mexico) researchers is analysed, showing a panorama of the countries and journals where their papers were published, as well as the different disciplines in which this Institute is involved, according to the ISI classification. [ABSTRACT FROM AUTHOR]

In this paper, I want to illustrate a phenomenon related to the treatment and conversion of semiotic representations whose sense derives from a shared practice. On the one hand, the passage from one representation of a mathematical object to another, through transformations, maintains the meaning of the object itself, but on the other hand, sometimes can change its sense. This is shown in detail through an example, inserted within a wide theoretical framework that takes into account mathematical objects, their meanings and their representations. [ABSTRACT FROM AUTHOR]