Obstáculos superados pelos matemáticos no passado e vivenciados pelos alunos na atualidade : a polêmica multiplicação de números inteiros

In Mathematics literature some records highlight the difficulties encountered in the teaching-learning process of integers. In the past, and for a long time, many mathematicians have experienced and overcome such difficulties, which become epistemological obstacles imposed on the students and teachers nowadays. The present work comprises the results of a research conducted in the city of Natal, Brazil, in the first half of 2010, at a state school and at a federal university. It involved a total of 45 students: 20 middle high, 9 high school and 16 university students. The central aim of this study was to identify, on the one hand, which approach used for the justification of the multiplication between integers is better understood by the students and, on the other hand, the elements present in the justifications which contribute to surmount the epistemological obstacles in the processes of teaching and learning of integers. To that end, we tried to detect to which extent the epistemological obstacles faced by the students in the learning of integers get closer to the difficulties experienced by mathematicians throughout human history. Given the nature of our object of study, we have based the theoretical foundation of our research on works related to the daily life of Mathematics teaching, as well as on theorists who analyze the process of knowledge building. We conceived two research tools with the purpose of apprehending the following information about our subjects: school life; the diagnosis on the knowledge of integers and their operations, particularly the multiplication of two negative integers; the understanding of four different justifications, as elaborated by mathematicians, for the rule of signs in multiplication. Regarding the types of approach used to explain the rule of signs arithmetic, geometric, algebraic and axiomatic , we have identified in the fieldwork that, when multiplying two negative numbers, the students could better understand the arithmetic approach. Our findings indicate that the approach of the rule of signs which is considered by the majority of students to be the easiest one can be used to help understand the notion of unification of the number line, an obstacle widely known nowadays in the process of teaching-learning

Apropriação de novas mídias por estudantes universitárias

It is an investigation that seeks to reveal, record and analyze the process of appropriation and use of digital media by university students, aged between 40 and 60 years. Interested in studying how changes are perceived in the educational sphere for students Whois have gone through liberal/traditional school, ie, effected the first contact with technological devices media as adults, in the university. This investigation sought to contribute to the knowledge on the use of new learning strategies imposed by digital media by recording and analyzing the reports surveyed sample. Allowed to know the cultural universe of these women, revealing the context in which receive mediated messages and uses that maré these learning strategies within their daily academic life. Gathered in this work, reflexions guided by studies of media reception and role played by digital media as builders images and facilitators in knowledging acquisitions, it was chosen to work two main theorical notions: communication media and digital inclusion. As the research methodology, it was used the exploratory descriptive technical together with other appropriate tecniques. In ordem to approach the problem can be observed two phases: a quantitative one, which was used an investigative procedure, a survey data with closed questions; and a qualitative phase, which was used to collect data through a diary from situations encountered in the classroom. The main objective of analyzing how digital media are received, appropriated and used by university women has been fulfilled and it is remarkable that they access with dificulty and can not be considered included digitally. The results show that the problem of these agents is not the access, there are was of appropriation of digital media offered at IES, and it was possible to note that they seek to integrate to the technological world, and they even have devices that can insert them on this world. Insertion in cyberculture sets up the ability to find a favorable way to be aware of reality and production of knowledge and liberating and dignifying practices, in this case refers to an appropriation of citizenship through the field of technological devices offered as a perspective that they can interact

Escrita colaborativa com google docs: flash fiction, noticing e aprendizagem de inglês como L2

Google Docs (GD) is an online word processor with which multiple authors can work on the same document, in a synchronous or asynchronous manner, which can help develop the ability of writing in English (WEISSHEIMER; SOARES, 2012). As they write collaboratively, learners find more opportunities to notice the gaps in their written production, since they are exposed to more input from the fellow co-authors (WEISSHEIMER; BERGSLEITHNER; LEANDRO, 2012) and prioritize the process of text (re)construction instead of the concern with the final product, i.e., the final version of the text (LEANDRO; WEISSHEIMER; COOPER, 2013). Moreover, when it comes to second language (L2) learning, producing language enables the consolidation of existing knowledge as well as the internalization of new knowledge (SWAIN, 1985; 1993). Taking this into consideration, this mixed-method (DÖRNYEI, 2007) quasi-experimental (NUNAN, 1999) study aims at investigating the impact of collaborative writing through GD on the development of the writing skill in English and on the noticing of syntactic structures (SCHMIDT, 1990). Thirtyfour university students of English integrated the cohort of the study: twenty-five were assigned to the experimental group and nine were assigned to the control group. All learners went through a pre-test and a post-test so that we could measure their noticing of syntactic structures. Learners in the experimental group were exposed to a blended learning experience, in which they took reading and writing classes at the university and collaboratively wrote three pieces of flash fiction (a complete story told in a hundred words), outside the classroom, online through GD, during eleven weeks. Learners in the control group took reading and writing classes at the university but did not practice collaborative writing. The first and last stories produced by the learners in the experimental group were analysed in terms of grammatical accuracy, operationalized as the number of grammar errors per hundred words (SOUSA, 2014), and lexical density, which refers to the relationship between the number of words produced with lexical properties and the number of words produced with grammatical properties (WEISSHEIMER, 2007; MEHNERT, 1998). Additionally, learners in the experimental group answered an online questionnaire on the blended learning experience they were exposed to. The quantitative results showed that the collaborative task led to the production of more lexically dense texts over the 11 weeks. The noticing and grammatical accuracy results were different from what we expected; however, they provide us with insights on measurement issues, in the case of noticing, and on the participants‟ positive attitude towards collaborative writing with flash fiction. The qualitative results also shed light on the usefulness of computer-mediated collaborative writing in L2 learning.