Proposta de ensino de geometria euclidiana plana para o sexto ano do ensino fundamental sob a ótica do raciocínio lógico-dedutivo

This study will introduce a brief history of the Geometry development, focused in the appearing of the organization in the logical deductive structure achieved by Euclid. Following will be discussed the situation of the learning and teaching of geometry topics since antiquity until the present day, where we will notice that it does not happen with the logical-deductive perspective. After this contextualization, we will propose the realization of a geometry workshop for students of the sixth grade of elementary school, focusing to the development of logical-deductive reasoning. Applied to workshop, changes were observed in the organization of thought of the participating students in the research, furthering the understanding of the concepts and properties of flat euclidean geometry.

Representações sociais sobre educação ambiental e objetivações em práticas pedagógicas no ensino fundamental

This work presents results, reflections, conclusions and considerations about the research entitled "Social representations of environmental education and objectivations in teaching practices in elementary school ". She intended to make known research whose objectives were to know the current environmental education framework (EA) developed by the teachers of the early years of elementary school of that city; identify their social representations about EA and the ways in which these representations are objectified in their teaching practices. Thus, the methodology is characterized by the qualitative approach; whose data collection instruments were the Free Evocation Questionnaire (QEV), the semi-structured interviews and documentary research. The QEV consists of free recall questions and essay questions, whose data is quantitative and qualitative. Data from this instrument were analyzed according to the procedures of the Structural Approach to Theory of Social Representations. In turn, the analysis of data obtained through the interview and reading the documents followed the guidelines of the Content Analysis method. The theoretical and methodological basis of this research was the Theory of Social Representations and critical approach to environmental education. Thus, the results obtained in the investigation allowed us to identify the social representations of EA of participants; confirm that such representations are being targeted in their pedagogical practices that are characterized as conservative. Also confirm that the teaching documents of the surveyed network are in line with the official documents on EA; the AE actions developed in the network are referenced in the teaching documents of the network and in the official documents of EA and the EA practices of survey participants teachers relate directly with their social representations on Environmental Education.

Características tecnológicas de espécies de pescado com potencial de criação na região sudoeste do Paraná

The fish meat has a particular chemical composition which gives its high nutritional value. However, this food is identified for being highly perishable and this aspect is often named as a barrier to fish consumption. The southwestern Paraná region, parallel to the country's reality, it is characterized by low fish consumption; and one of the strategies aimed at increasing the consumption of this important protein source is encouraging the production of other species besides tilapia. Within this context, it is necessary to know about the meat characteristics. In this sense, the objective of this study was to evaluate the technological potential of pacu, grass carp and catfish species. To do so, at first, it was discussed the chemical and biometric assessment under two distinct descriptive statistical methods, of the three species; and it was also evaluated the discriminating capacity of the study. In a second moment, an evaluation of effects done by two different processes of washing (acid and alkaline) regarding the removal of nitrogen compounds, pigments and the emulsifying ability of the proteins contained in the protein base obtained. Finally, in the third phase, it was aimed to realize the methodology optimization in GC-MS for the analysis geosmin and MIB (2-metilisoborneol) compounds that are responsible for taste/smell of soil and mold in freshwater fish. The results showed a high protein and low lipid content for the three species. The comparison between means and medians revealed symmetry only for protein values and biometric measurements. Lipids, when evaluated only by the means, overestimate the levels for all species. Correlations between body measurements and fillet yield had low correlation, regardless of the species analyzed, and the best prediction equation relates the total weight and fillet weight. The biometric variables were the best discriminating among the species. The evaluation of the washings, it was found that the acidic and basic processes were equally (p ≥ 0.05) efficient (p ≤ 0.05) for the removal of nitrogen compounds on the fish pulps. Regarding the extraction of pigments, a removal efficiency was recorded only for the pacu species, the data were assessed by the parameters L *, a *, b *. When evaluated by the total color difference (ΔE) before and after washing for both processes (acid/alkaline) the ΔE proved feasible perceived by naked eye for all species. The catfish was characterized as the fish that presents the clearest meat with the basic washing considered the most effective in removing pigments for this species. Protein bases obtained by alkaline washes have higher emulsifying capacity (p ≤ 0.05) when compared to unwashed and washed in acid process pulps. The methodology applied for the quantification of MIB and geosmin, allowed to establish that the method of extraction and purification of analytes had low recovery and future studies should be developed for identification and quantification of MIB and geosmin on fish samples.

Demonstração de fórmulas matemáticas no ensino médio

The objective of this study is to analyze the validity of working with proofs in the classroom and to present a partial list of proofs of mathematical formulae of the Brazilian secondary/high school curriculum. The adaptation of the proofs into the knowledge and abilities of a secondary school student should also be considered. How the teaching of proofs is treated in official publications in Brazil and other countries is also described. Working with proofs provides a number of benefits to the students, including: the development of logical reasoning, argumentative capacity, analytical skills on a daily basis, as well as motivation and a better understanding of mathematics as a science. The convenience of including the teaching of proofs in Brazilian secondary school curriculum and the need of a balance between the abstraction of proofs and contextualization of the school programmes is discussed. The approach of the proof teaching in the classroom can become a motivating factor or, conversely, a discouraging one. The conclusion is that it would be very useful to create a reference list covering the mathematical expressions of school programmes with their respective proofs that can be understood by secondary school students.