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This paper addresses three aspects of the conceptual framework for a doctoral dissertation research in process in the field of Mathematics Education, in particular, in the subfield of teaching and learning basic concepts of Probability Theory at the College level. It intends to contrast, sustain and elucidate the central statement that the meanings of some of these basic terms used in Probability Theory were not formally defined by any specific theory but relate to primordial ideas developed in Western culture from Ancient Greek myths. The first aspect deals with the notion of uncertainty, with that Greek thinkers described several archaic gods and goddesses of Destiny, like Parcas and Moiras, often personified in the goddess Tyche—Fortuna for the Romans—, as regarded in Werner Jaeger’s “Paideia”. The second aspect treats the idea of hazard from two different approaches: the first approach deals with hazard, denoted by Plato with the already demythologized term ‘tyche’ from the viewpoint of innate knowledge, as Jaeger points out. The second approach deals with hazard from a perspective that could be called “phenomenological”, from which Aristotle attempted to articulate uncertainty with a discourse based on the hypothesis of causality. The term ‘causal’ was opposed both to ‘casual’ and to ‘spontaneous’ (as used in the expression “spontaneous generation”), attributing uncertainty to ignorance of the future, thus respecting causal flow. The third aspect treated in the paper refers to some definitions and etymologies of some other modern words that have become technical terms in current Probability Theory, confirming the above-mentioned main proposition of this paper.

Nowadays, it is recognized that education plays a fundamental role in training citizens aware of biodiversity and its conservation issues. Biodiversity, as an integrating and polysemic concept, raises challenges for its approach in the classroom by teachers and researchers. This paper aimed to characterize and reflect on the trends and challenges of biodiversity teaching in the Brazilian context, identifying approaches given to the concept, methodological approach, didactic resources and difficulties pointed out both in research and reports of pedagogical experiences where teaching this concept was explicitly addressed to school’s audience. Twenty research papers about experiences developed at different educational levels were analyzed. It was found that the scope of biological-ecological explanation is privileged on sociocultural elements of the concept. Active methodologies related to the approach of problems of local biodiversity, project construction and school research are the pedagogical approaches that guide these practices. The main resources used correspond to the natural resources and the context, contemporary and dynamic. Teaching the concept still raises challenges about its place in the curriculum, the textbook, and teacher’s training processes. This paper aimed to characterize and reflect on the trends and challenges of biodiversity teaching in the Brazilian context, identifying approaches given to the concept, methodological approach, didactic resources and difficulties pointed out both in research and reports of pedagogical experiences where teaching this concept was explicitly addressed to school’s audience. Twenty research papers about experiences developed at different educational levels were analyzed. It was found that the scope of biological-ecological explanation is privileged on sociocultural elements of the concept. Active methodologies related to the approach of problems of local biodiversity, project construction and school research are the pedagogical approaches that guide these practices. The main resources used correspond to the natural resources and the context, contemporary and dynamic. Teaching the concept still raises challenges about its place in the curriculum, the textbook, and teacher’s training processes.

This initial study presents the results of the classroom implementation of a learning sequence derived from Fibonacci’s error in solving ‘The lion in the pit’ problem. The study was carried out with 35 physics students in a general first-semester course ‘Development of complex-thinking skills’. The learning sequence was implemented as a paper-and-pencil activity in personal and group modes. The most important results are the following: (a) Students were able to provide an acceptable procedure about how Fibonacci might get the wrong answer, (b) students can argue why that answer is wrong, (c) some students’ solutions presented good conceptual and procedural clarity, frequently missed in historic literature, and (d) students grasped the importance of knowing about errors made by famous mathematicians in two connected aspects: mathematics is a human activity prone to errors and, consequently, fear of errors shouldn’t be an obstacle in learning of school mathematics.

In this paper we did an analysis of theoretical foundations in order to study essential characteristics of developing evaluation in Mathematics teachers education. From our perspective it is essential to analyse evaluation as a process integrating aspects from a variety of disciplines like psychology, philosophy, didactics and mathematics. Thus, is very important to clarify this didactic category designed specially to develop evaluation processes in Angola's environment. In the proposal development was used predominantly a qualitative paradigm, based on data obtained through several empirical methods. We present the strategy to achieve this evaluation process on the socio- historical context, promptly related with professional's training. Finally, we present results of testing this strategy.

This paper investigates the relationship between the epistemological profile of the student, their mental images and drivers built after the use of virtual experiments. For this, was chosen as the dual behavior knowledge content of matter and electromagnetic radiation, fundamental topic of Quantum Mechanics in the curriculum of physics undergraduate students. The theoretical framework adopted for reading the data was the Cognitive Mediation Networks Theory, seeking to explain how computer mediation modifies the cognitive structure of students. Also used the idea of Epistemological Profile Bachelardian to relate it to the reasoning presented by the students. Observed changes of psychophysical and cultural drivers already in the cognitive structure of students. Despite this positive result, there was a conceptual inconsistency of students for the dual behavior of the explanation of quantum objects.

This paper describes the developing and validating steps of a Likert’s evaluative scale. The aim is to systematize the answers of Biological Sciences students about to: 1) Understanding or notunderstanding thescientific knowledge; and 2).If there is a relationship amongscientific concepts in order to contemplate a systemic thinking about natural phenomena. The described scale was validated by Cronbach's Alpha tests (α = 0.741), KMO (0.779) and Bartlett (0.000) and a Multivariate Analysis was fulfilled, typePrincipal Component Analysis (PCA). We understood that this kind of instrument allows a large amount of data to be collected and it groups can be compared efficiently, which justified the development of evaluative scale presented here.

This paper aims to analyze which are statistical research contributions for teaching and learning of statics in the final years of elementary school, characterized for contextualized activities. To achieve the proposed objective, we adopted the methodology of teaching by research, covering the statistics’ basic contents in a class of students from the 9th grade of elementary school, in a private school of a northern city of Parana, Brazil. Results regarding students’ performance were analyzed under a qualitative approach, which allowed highlighting the intervention contribution: those students had a meaningful learning regarding statistic basic contents and the development of statistical skills.

The Language is the mechanism that allows us to share all the knowledge acquired in the learning and teaching process. Through it the scientific knowledge is arranged. The language’s communicative property is the most meaningful ability which allows man to report, to reason or to refute an idea. The teaching strategies which aim to develop scientific enculturation, bring science closer to the school routine, introducing distinguished conceptions that favour problematic teaching. The investigative methodologies lead the student to develop communication abilities, specially reasoning, in scientific speech perspective. Knowing about this difficulty that the students, specifically the ones of the seventh grade of the primary school of brazil’s state school, have in understanding certain parts of the contents in the subject of Science, most of the times lacking in a concrete referential idea, the theme of microorganisms was chosen to substantiate the investigative activities proposed. Therefore, the goal of this paper is to identify and to analyse the communicative abilities of language, regarding argumentation and its development, as the improvement of semantic and pragmatic aspects of language. To organize this activity of investigation, the approach of the National Research Council was used, as well as the assumption idealized by S. Toulmin, regarding the argument structure. The pragmatic and semantic abilities were referred through the theory of the Speech Acts. Analyzing the obtained data, it was possible to ascertain that some students were benefited with this methodology and were able to absorb concepts that substantiated and contributed to the structural quality of the argument. Besides that, it was realized that the improvement of the semantic and pragmatic aspects framed an efficient communication.

This paper presents an analysis centered on the following questions: I) the human being has the need to relationship, but how this is reflected in the school environment? II) What are the possibilities of promoting the need of relationship in the classroom, specifically in high school physics classes, through Didactic Activities (AD) based on learning per inquiry? For the analysis planned we seek theoretical support in Self-Determination Theory, which provides for a set of three basic psychological needs (competence, autonomy and relationship) to assess and explain the involvement and motivation of people in their activities. The need to relationship (focus of this study) encompasses safe and satisfying connections of people in a social context. So we cannot ignore this need in the school context, precisely because its influence in the teaching-learning process. That led us to assess how were offered supports for promotion and satisfaction the relationship need in didactic activities of teaching per inquiry. It was observed that the activities provided a school environment conducive to effective discussion and exchange of ideas, with reciprocity and trust towards the construction of knowledge with greater protagonism of the students. That way, we see in this educational perspective a possibility to satisfy the need of relationship.

Este trabajo presenta una investigación de carácter exploratorio descriptivo, en torno a las creencias de jóvenes aspirantes a ingresar a una universidad pública de la República Argentina. El objetivo es realizar un aporte a la enseñanza de la disciplina en cursos de los primeros años de la universidad. Se indaga acerca de “qué es la matemática”, “qué es hacer matemática” y “su relación con la matemática”. Para ello realizamos entrevistas grupales a dos grupos de aspirantes a ingresar en carreras universitarias donde la matemática jugará un rol diferente. A partir del análisis de las mismas se identifica el sistema de creencias de los jóvenes entrevistados.AbstractThis paper presents a descriptive exploratory research about the beliefs of young aspirants to enter a public university in Argentina. The aim of this work is to contribute to the teaching of mathematics in the first years of the university. We inquire about “what mathematics is”, “what the making of mathematics is” and “which relation with mathematics they have”. We carry out group interviews with two groups of candidates to enter university. The role that mathematics will play in the career of each of these groups is different. From the analysis of these interviews, the system of beliefs of the interviewed candidates is identified.

This paper contains a proposal of teaching strategy based on a situation of study, which uses three pedagogical moments: initial problematization, knowledge organization, and knowledge systematization, as a planning way of the proposed activity. In addition, it proposes to contextualize the situation of study in an interdisciplinary strategy from the theme "Healthy Eating", mentioning some concepts of Natural Sciences that can be approached in the case of this situation of study. This experience occurs from a lunch in a school, enabling a knowledge problematization and providing strategies to the construction of situation of study.

O artigo é resultado de um projeto de modelagem matemática, aplicado a crianças com dificuldades de aprendizagem do quarto e quinto anos do Ensino Fundamental, de uma escola da periferia do Município de Palmas, Paraná, Brasil. O projeto foi desenvolvido com o auxílio de alunos da Licenciatura em Matemática, constituindo-se em uma atividade integrante de sua formação profissional e tendo por objetivo contribuir para a melhoria da aprendizagem de matemática das crianças envolvidas. Foram construídas, sob a orientação dos professores e licenciandos, maquetes de casas planejadas pelos próprios alunos. Foram trabalhados diversos conceitos matemáticos, relacionados a operações básicas, frações, geometria, porcentagens, planejamentos financeiros, entre outros. Além da motivação observada, o trabalho contribuiu com o processo de ensino e aprendizagem dos alunos e proporcionou aos futuros docentes uma experiência significativa em sua formação.Mathematical modeling in basic education: an experience inspired in constructionAbstractThe paper is the result of a project for mathematical modeling applied to children with learning difficulties in the fourth and fifth years of Fundamental Education at a school on the periphery in the city of Palmas, PR. The project was developed with the help of mathematics undergraduates students, thus becoming an their professional training a activity and taking aim at contributing to improving the math learning of the children involved. They built houses maquettes designed by the students under the teachers and student teachers supervision. We worked many mathematical concepts related to basic operations, fractions, geometry, percentages, financial planning, among others. Besides the motivation observed, the work contributed to the teaching and learning formation of students and provided to prospective teachers a meaningful experience in their training.Keywords: maquettes construction, mathematical modeling, teaching andlearning in mathematics, teaching preparation.

Se plantea el diseño y la puesta en práctica de una estrategia de aula con la implementación de una secuencia didáctica, que se aplica a estudiantes de grado undécimo de un colegio público de la ciudad de Bogotá D.C. Dicha estrategia utiliza una metodología cualitativa a través de categorías de análisis de argumentación y toma de decisiones. Los resultados de esta experiencia de aula buscan evaluar la articulación entre la argumentación y la toma de decisiones, mediante el abordaje de la cuestión sociocientífica: uso y comercialización del Policloruro de Vinilo (PVC). En un primer momento se analizan las ideas previas de los estudiantes frente a los polímeros, específicamente el PVC, con el objetivo de establecer algunos parámetros que permitan mejorar la secuencia a implementar. Posteriormente se presentan los resultados obtenidos en las actividades planteadas de la secuencia, analizando el nivel de argumentación en la toma de decisiones que presentan los estudiantes.Development of Argumentative Competence through Decisions Making of Socio-Scientific Questions: "Use and Marketing of PVC"AbstractThis paper presents the design and implementation of a strategy of classroom with the implementation of a teaching sequence that applies to high school student’s (junior) of a public school in Bogotá-Colombia. This strategy uses a qualitative methodology through categories of analysis of argumentation and decision making. The results of this classroom experience seeking to assess the relevance to articulate the argument in decision-making; by addressing the socio-scientific issue "use and marketing of Polyvinyl Chloride (PVC)". At first previous ideas of students compared to polymers, specifically PVC, in order to establish some parameters to improve the sequence to implement are discussed. Subsequently, the results of the proposed activities of the sequence, analyzing the level of argumentation in the decision making of students.Keywords: argument, Polyvinyl Chloride (PVC), socio-scientific controversy, Teaching sequence