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In this paper we study the levels of anxiety towards mathematics teaching in a group of Spanish students for primary education teaching through the MATAS survey. The data collected in the survey is analyzed to determine if there are significant differences between the levels of anxiety when the sample is differentiated according to three criteria: if they have taken any previous mathematics subject, if they have any previous degree in education and if they have teaching experience in mathematics. As a result, it is obtained that most of the group of students present medium or high levels of anxiety towards the teaching of mathematics and that those who have no teaching experience or no previous degree present significantly higher mean levels of anxiety. [ABSTRACT FROM AUTHOR]

This paper describes the design, implementation and results of a formative action with 61 students for primary education teachers, oriented to the development of the competence of analysis of the didactic suitability of educational videos about percentages. The a priori analysis of the video made by the researchers revealed important deficiencies in the different facets of didactic suitability, being especially relevant those detected in the epistemic dimension. Most of the students for teacher made quite relevant global assessments of the didactic suitability (70.49% considered it between low and medium) basing their judgment on the precision or degree of fulfillment of the suitability indicators in the different components. However, although the suggestions for improvement indicated are quite timely, not all students who identify weaknesses in the videos are able to explicitly make changes to the resource. [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 presents the results of a research based on the process of reflection on school mathematics of middle school teacher. For this purpose, a three-component theoretical model was configured, articulated with the Socioepistemological Theory. Specifically, it shows how the process takes place: what and how awareness is acquired, what knowledge is constructed and what is transformed. For the analysis we considered a category of meanings and another on the forms of argumentation related to direct proportionality; both categories allowed us to understand the state of the teacher's knowledge at the beginning and at the end of the ref lective process. Among the results we have that the ref lection of school proportionality gives evidence that the change of relationship to this mathematical knowledge promotes the awareness of responsibility for mathematical education and the development of autonomy over mathematical knowledge (both related to proportionality), two aspects that characterize the professionalization of mathematics teachers. [ABSTRACT FROM AUTHOR]

This paper reflects on the importance that the dialectic of hypothesis - conjectures can have, not only for the development of demonstrative thinking in students, but also for the development of stochastic thinking. It argues for curricular reasons, for an approach to teaching based on problem solving, for a way of solving problems that considers simulation as a method of resolution with heuristic content and, finally, for new proposals on mathematics that the citizen of the XXI century will require and that includes the analysis of data in contexts of uncertainty. Consequently, a proposal is presented for the training of pre-service teachers to enable them to deal with such challenges. [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]

Analogies, often used to make an idea understandable using previous knowledge or experience, have been considered as a component of pedagogical content knowledge since earliest conceptualizations of teacher's knowledge. This paper addressed the mathematics teacher's specialized knowledge in the use of the analogy of function as a machine, based on lessons observation of two Chilean high school teachers and a subsequent interview. Study's findings regarding the teacher's knowledge about the function in the use of analogy allow establishing relations between different knowledge manifested by teachers in the functions' teaching - learning process, advancing in the understanding of their knowledge. [ABSTRACT FROM AUTHOR]

On this paper, an analysis of the strategies used by children in first and second grade of elementary education (7-8 years old) from two academic institutions in Bogota, Colombia, for solving multiplicative situations before receiving instruction on multiplication and division, is introduced. The analysis focuses on identifying whether children recognize different units, simple or compound, and the use they made of them, particularly if children build units to address the given situations, and whether the children re-interpretate the said situations with these units. This research was conducted by using the method of task-based interviews, from which it was possible to find evidence of the strategies used by the children, in particular two emerging strategies that have not been reported in the international literature: equivalence between different types of unit and coordinated use of composite units. [ABSTRACT FROM AUTHOR]

Arguing and representing are abilities promoted in the school curricula of many countries. This paper presents the arguments used by six students from grades one to four regarding external representations they created. The structure of the arguments is analyzed with respect to some of the components presented in these representations using Toulmin's simple model, interpreting the arguments, and integrating the representation created with the argumentation. Verbal and gestural argumentative elements appear to be influenced by the students' oral expression abilities and numerical and geometrical knowledge. The arguments about the logical component, the variable, and about the numerical component, the frequency, were verbalized by the students, while the linear components, the linear basis and the graphical linearity, were argued for using spoken language, gestures, and metaphors. [ABSTRACT FROM AUTHOR]

This paper intends to describe a phenomenon observed when children aged 6 and 7 years old, who had not yet received formal instruction about division, tried to solve a problem of distribution by means of drawings. The phenomenon called "frames of meaning" attempts to explain why some children were successful in solving problems and others were not. We illustrate this hypothesis empirically through a case study. This hypothesis is a powerful theoretical and methodological tool for understanding the underlying mathematical thinking and arithmetic problem-solving abilities of children this age. However, it is necessary to continue to expand our analysis and the application of this framework. This would lead to reconsider conventional educational and evaluative practices. In this article we try to point the way by which these changes could be made. [ABSTRACT FROM AUTHOR]

The limit of a function is one of the most controversial concepts in mathematics education, to such an extent that its teaching and learning are a real challenge for researchers. Many papers have been prepared in relation to this mathematical object, which focus on areas such as APOS, the theory of epistemological obstacles and the TAD, and mathematical studies have even been developed based on their study. In this paper, based on the onto-semiotic approach to mathematical cognition and instruction, we go more in-depth into the intended, assessed and personal meanings of a study process regarding the limit of a function. The results indicate that, despite some intuitive classes being analyzed in relation to the limit (i.e. without using the metric definition of ε and λ), students encounter numerous semiotic conflicts when interrelating with said concept. [ABSTRACT FROM AUTHOR]

The concept of infinity is essential for understanding mathematical notions as a limit, continuity, derivative, integral, succession and series, among others. This paper studies the evolution of the concept of infinity from the last year of primary education (students aged between 11 and 12) to the first year of university education (students aged between 18 and 19 years old). A questionnaire designed in part on the basis of the existing bibliography in this field was taken by more than 2,000 students in order to identify the tacit models of infinity in their performance or in their expressions. During the analysis of answers, a new indicator was used, the pattern of level evolution (PEN) as a quantifying element which allows our results to be compared with those of other investigations. Together with models already identified in other studies, our paper found three new tacit intuitive models. [ABSTRACT FROM AUTHOR]

In this paper we analyze the graphs produced by 207 preservice primary school teachers when solving an open-ended task in which they should compare three pairs of distributions. The graphs produced are classified according whether they are correct or not, and according to the kind of error in case of an incorrect graph. The analysis allows us to explain some of these errors in terms of semiotic conflicts. Results suggest the semiotic conflicts are related to knowledge of conventions in building the graphs, selecting the graphs, number sense and conceptual misunderstanding. The influence of using computers on the errors produced is also analyzed. [ABSTRACT FROM AUTHOR]

This paper presents the mathematical design of a small part of a reference epistemological model which, once concluded, should support the educational organization of a study process comprising: the development of the functional modelling with parameters, elementary differential calculus raison d'être in high school, and the first developments of calculus in several variables at university. Hereto we focus in the moment in which we already hold the derivative as a work tool to show the progressive development, and the relative completion of mathematical praxeologies that are built as progress gains ground in the different levels of functional modelling. This proposal is submitted from an Anthropological Theory of the Didactic scope and represents a small contribution to the didactic purpose of placing the mathematical modelling as an instrument that allows to articulate and give meaning to school mathematics. [ABSTRACT FROM AUTHOR]

The goal of this study is to characterize the processes involved in mathematical proof, in the context of geometry, from a cognitive perspective. In particular, the focus of this study is the characterization of the interaction between reasoning processes and verification procedures that secondary students use when solving geometry problems in a pencil-and-paper environment. The results show that the different ways of using alternative verification procedures to validate a proposition are related to the different outcomes of the reasoning in problems that require a proof. [ABSTRACT FROM AUTHOR]

In this paper we assess pre-service primary school teachers' knowledge in relation to fair games. Common knowledge of content is assessed through the responses given by 167 pre- service primary school teachers to two open-problems. In addition, two components of didactic knowledge are inferred trough the participants analyses, when working in small groups: (a) Specialized knowledge of content is assessed from their analyses of the tasks' mathematical content; and (b) knowledge of content and students is assessed from their assessment of responses provided by primary school students. Results suggest the need to reinforce the training of pre-service teachers both in the mathematical and the didactic knowledge. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to show how a didactic analysis carried out using the model proposed by the onto-semiotic focus of knowledge and mathematical instruction allows us to provide a detailed description of the structure and functioning of a non-significant behavioral type mathematics class, as well as its implications on the understanding of the student. Said model is designed to describe (what has occurred here?), to explain (why has it occurred?) and to assess (what could be improved?) mathematics instruction processes in the classroom. The main result expected from the application of the model is the obtaining of an assessment based on the didactic suitability of said processes. [ABSTRACT FROM AUTHOR]

This paper presents a vision of mathematical arguments and demonstrations from a socio-epistemological point of view. It allows us to understand that the arguments used in different settings are different to those of deductive arguments. The presence in classrooms of different types of arguments cannot always be explained using Aristotelian logic. Likewise, the non-appearance of forms based on Aristotelian logic in non-mathematical settings, provides us with the possibility of understanding that, with regards socio-cultural aspects, arguments are constructed in non-academic settings which are transferred by students to school settings, due to the fact that they simultaneously experience both settings. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the process that we followed in order to prepare a genetic decomposition of the concept of linear transformation, showing the steps we took in its construction and the difficulties that we encountered. The design is based on a theoretical analysis determined by the research cycle related to APOS theory. We propose two genetic decompositions that describe two possible ways to construct this concept, one that uses the mechanism of interiorization and another that uses coordination. [ABSTRACT FROM AUTHOR]

This study is part of a research project that analyzes the processes of conceptualization of the notion of infinitesimals in college students majoring in Mathematics. The research project originates from an interest in understanding the processes of teaching and learning key concepts of Mathematical Analysis such as limit, real numbers, and continuity among others. From mathematical and cognition points of view, these notions are recognized as complex. In order to conceptualize them, students rely on an intuitive understanding of infinitesimals. In this paper, we describe, analyze, and characterize the epistemological conceptual frameworks associated with the historical evolution of the notion of infinitesimals. We identify seven epistemological concept frameworks: The infinitesimal as a ratio, as an indeterminate, as a difference, as an increment, as an arithmetic ratio, as a symbol, and as a function. Furthermore, ideas, methods, representations, and problems that mathematicians use in specific contexts are presented. [ABSTRACT FROM AUTHOR]

This paper reports a cognitive study of a qualitative character in relation to the learning of the two variable functions and partial derivative concepts in the engineering context. It defends the fact that didactic settings in context can be conducive to a logical meaningful learning for the student with sense in the future professional area. This motivated us to research what happened at cognitive levels for students in this type of didactic environment. The theoretical framework is described by the study of cognitive functioning in a mental act of learning (the process of resolving problem). The analysis reports the experience which results in the implementation of didactic setting designs with one group of engineering students. [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]

In this paper, we apply some theoretical notions of the onto-semiotic approach to mathematical cognition and instruction to analyse a lesson on addition and subtraction taken from a Spanish textbook directed to the fifth grade in primary education. Our aims are: (1) to illustrate a technique for analysing mathematics textbooks based on the ontosemiotic approach, and (2) to identify suitability criteria for developing didactical units to study the additive structures in primary education. The results obtained might be useful in the training of prospective mathematics teachers. [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]

This paper reports the presence or absence of a systemic thinking in students, when they solve the linear extension problem, which consists of determining a linear transformation through the images of the vectors of a basis. The problem is formulated geometrically, making use of the tools of the Cabri-géomètre II software. The difficulties that students present when face this problem, probably are due to that they do not carry out the adequate connections among the concepts involved. This phenomenon can be studied from the point of view of the theoretical approximation the theoretical thinking versus the practical thinking (Sierpinska, 2000). One of the characteristics of the theoretical thinking is that tries to be focused in the establishment and study of the relations between the concepts and its characterization inside a system that also contains other concepts (Sierpinska, et al. 2002). [ABSTRACT FROM AUTHOR]

In this paper are described the beliefs, conceptions and the professional knowledge that has a university professors group on the teaching of differential calculus to students of economics sciences. It is a study of cases in which participated ten mathematics professors; the data were obtained by means of an open questionnaire, that was supplied to the participating professors, with this questionnaire was requested them information related to their academic formation and their years of service as educators. The analysis was developed in function of some categories established from some systemic networks, and the results show that almost all the professors continue a traditional line at the moment to undertake the teaching of the derivative concept and they give a strong weight to the mathematical content itself, neglecting the economic content linked with the differential calculus. [ABSTRACT FROM AUTHOR]

In this paper some theoretical tools are utilized that contributes the ontosemiotic approach of the mathematical cognition (Godino, 2002), in order to study how is put into play a network of objects and semiotic functions in the fragment of a textbook of the second course of High School --representative of the introduction to the defined integral-- in students of the Autonomous Comunity of Andalucia (Spain). The analysis has as purpose to characterize the ontosemiotic complexity of the text and the potential semiotic conflicts that can be produced in the students that use it. Previously, a synthesis of the theoretical framework is presented, that includes the theory of the institutional and personal meanings of the mathematical objects and the theory of the semiotic functions. [ABSTRACT FROM AUTHOR]

This paper presents a longitudinal study of four undergraduate mathematics courses. The analysis of problems and exercises given in the outlines of the courses, allows us to describe a particular mathematical organization of the notion of completeness of the set of real numbers. It allows us also to make a hypothesis about the acquisition of knowledge of this topic, which is considered as an example of the passing from Calculus to Mathematical Analysis. [ABSTRACT FROM AUTHOR]

In this paper the discursive forms of description, exposition, narration and argument are analyzed, besides the gesticulation, that employ university students when they reflect on the mathematical notion of punctual continuity of a real function of real variable. We consider the gestural dimension of the visualization actions from an experimental design based on the socioepistemological approach to the research in Mathematics Education, that estimates to the mathematical knowledge among the students as the cultural product of a series of social practices connected with mathematical notions. [ABSTRACT FROM AUTHOR]

This paper synthesizes the results of an investigation work (Montiel, 2002) about the didactic system's interaction, when these are carried out in an education scenario at distance. We report, within the socioepistemological framework and empirical evidence, how a derivative learn situation can be develop, taking this (the derivative) like variations successive organization. [ABSTRACT FROM AUTHOR]

In this paper is presented a theoretical articulation of the notion of "mathematical convention" as knowledge generation process in the framework of the socioepistemologic approximation in Mathematics Education. To achieve this, is done a brief description of the basic notions of the socioepistemologic approximation and are presented the basic evidences that allow to interpret the "mathematical convention" as a generator of knowledge in this framework. Later we are sketched some examples that give evidences of the operation of this notion as constituent process in the construction of the mathematical knowledge. [ABSTRACT FROM AUTHOR]

The paper reports findings that are included in the Program of the Variational Thought and Language. It presents ways to think that the students put in play at the moment of to undertake the study of the variation. These evidences are obtained as a part of the results of a research in process, which undertakes the question of the routine representations of variation and mathematical representations that favor or obstruct the learning tending toward the formation of a variational thought in the students. In the first part a way to collect texts of the students is presented -- the binnacles of reflection -- and another to analyze those speeches -- metaphors identification. Next a visual episteme of variation is described; representations of the time; and, a didactic metaphor for the inverse. [ABSTRACT FROM AUTHOR]

In this paper, we show that the hidden curriculum approach is relevant for math teaching at different levels of the French education system, from senior high school to tertiary education to first year of math secondary teacher training. Considering that the existence of learning necessities non explicitly cared about by any institution is a phenomenon that is impossible to avoid, we propose several ways to manage with the difficulties that creates this curriculum ignored by the education system. [ABSTRACT FROM AUTHOR]

This paper discusses the theoretical basis of a didactic proposal. It begins from the consideration that the difficulties in the learning process of mathematics among university students of sciences and engineering areas, not only obey to causes of pedagogical or technical order, but fundamentally, in the way in which the mathematical knowledge is selected, articulated and organized with didactical aims. We considered then, that the determination of "what to teach" and not only "how to teach" positivist classic posture is a didactic problem. This search has allowed us to formulate a reasonable >conjecture: it is possible to reconstruct the didactic discourse of a part of the mathematical analysis taking as a central idea the prediction notion >and its links with the Taylor's serie. In another sense, this hypothesis indicates that it is possible to redesign the curriculum and its didactic discorse around of that, we considered, was indispensable for the genesis of the knowledge. We will consider to the Taylor's serie, its contextual antecedents, motivations, situations, temporary evolutions, presentations on classic texts and possibilities of use, some still unexplored in current texts. The article provided with the theoretical base that sustained a Doctoral research in the field of Physics Didactis in Spain. [ABSTRACT FROM AUTHOR]

Within the framework of a doctoral research in which the link between the construction of the arithmetic language of the fractions and the development of concepts related to such numbers was explored qualitatively, we applied a questionnaire in a naturally constituted group of fourth grade (integrated by 37 students of 8-11 years old). The mentioned questionnaire was centered in the diverse assignable semantic contents to the fractions. Specifically, the present paper constitutes a partial communication derived from this doctoral research; here, we exclusively talked about the exploration caused by that questionnaire around the quotient meaning, taking care of its character of derived notion from actions and familiar situations for the children and offering for that reason an accessible beginning point for the teaching of fractions. The intention of this research was to identify the semantic, syntactic and "translation" components involved in the answers of the students engaged on distribution situations. In the continuation of such intention, special attention was granted to those components that affected the suitable unfolding of the children and the consequent learning to develop. We considered that all these phenomena are of vital importance for the professors and the corresponding organization of the instructional proposals that they develop. [ABSTRACT FROM AUTHOR]

Causing a cognitive conflict can be one way to make students aware of the inadequacy of the concepts that they possess and the methods that they use in solving a problem. Apart from discussions in a cooperative group and the use of mathematical games, the mathematical situations themselves have to possess certain characteristics to be able to provoke a conflict and furthermore facilitate the confrontation between the previous knowledge and new knowledge to be acquired. Moreover teachers need to have direct experiences at their level with this kind of activities, before they can employ them in their classes. In this paper we report the results of a study in which a cryptography activity was applied with a group of university and high school teachers, where the concepts of sets and binary operations came into play. [ABSTRACT FROM AUTHOR]

In this paper, some aspects of the ideas of real function, continuous function, domain of a function and integral are investigated in the learning of mathematics, mainly referred to Italian High School (pupils aged 16-19 years); the status of these concepts in classroom practice is studied by some tests. The role of representations is important in the learning of mathematics; in particular, the influence of visualization is studied: the graphic representation (namely the Cartesian representation of a function) is often tacitly considered the main act of the study of a mathematical function; this procedure may be ineffective for the correct characterization of a concept and for the full development of the ability to use and to co-ordinate registers of representation. [ABSTRACT FROM AUTHOR]