Os níveis de desenvolvimento do pensamento geométrico: o aprendizado do conteúdo de polígonos numa perspectiva do modelo Van Hiele

This work studies the van Hiele model, the levels of development of geometric thinking and its learning phases. Using this knowledge, we prepared a Research Instrument to identify the Level of Development in Geometric Thinking (Levels of van Hiele) of Middle School students, related to contents of Polygons. We have applied this Research Instrument to 237 students from a public school (state) in Curitiba, and we made an analysis of the acquired data. We have improved the Instrument’s questions so that it can be used by teachers during the class. Helping to identify to which level content the student belongs, related to the proposed.

Qualidade física e matéria orgânica do solo em sistema de integração lavoura - pecuária submetido a doses de nitrogênio

The animal trampling favors the soil compaction process in sheep raising and crop production integrated systems. This compression has negative effects, hindering the development of roots, the availability of nutrients, water and aeration, causing production losses, making it essential for the assessment of soil physical attributes for monitoring soil quality. Soil organic matter can be used to assess the quality of the soil, due to its relationship with the chemical, physical and biological soil properties. Conservation management system with tillage, along with systems integration between crops and livestock are being used to maintain and even increase the levels of soil organic matter. For that, a field experiment was carried out over a Oxisol clayey Alic in Guarapuava, PR, from de 2006 one. experiment sheep raising and crop production integrated systems The climate classified as Cfb .. The study was to evaluate the soil physical properties and quantify the stock of soil organic carbon and its compartmentalization in system integration crop - livestock with sheep under four nitrogen rates (0, 75, 150 and 225 kg ha-1) in the winter pasture, formed by the consortium oat (Avena strigosa) and ryegrass (Lolium multiflorum) and the effect of grazing (with and without). The soil samples blades density evaluations, total porosity, macro and micro, aggregation and carbon stocks were held in two phases: Phase livestock (after removal of the animals of the area) and phase crop (after maize cultivation). The collection of soil samples were carried out in layers of 0-0.5, 0.05-0.10, 0.10-0.20 and m. Data were subjected to analysis of variance and the hypotheses tested by the F test (p <0.05). For the quantitative effect data regression and the qualitative effect used the test medium. In non-significant regressions used the average and standard deviation treatments. The animal trampling caused an increase in bulk density in the 0.10-0.20 m layer. The dose of 225 kg N ha-1 in winter pasture increased total soil porosity at 8% compared to dose 0 kg N ha-1 in the crop stage. The grazing had no effect on soil macroporosity. GMD of aggregates in the phase after grazing the surface layer was damaged by grazing. Nitrogen rates used in the winter pasture and grazing not influence the total organic carbon stocks. The TOC is not influenced by nitrogen fertilization on grassland. The grazing increases the stock of POC in the 0.10-0.20 m layer livestock phase and cause the stock of POC in the 0-0.5 m layer in the crop stage. The MAC is not influenced by N rates applied in the pasture or by grazing.

Construções geométricas como recurso pedagógico no ensino médio

This work aims to provide high school students an development in his mathematical and geometrical knowledge, through the use of Geometric Constructions as a teaching resource in Mathematics classes. First a literature search to understand how it emerged and evolved the field of geometry was carried out and the Geometric Constructions. The ways in which the teaching of geometry happened in our country, also were studied some theories related to learning and in particular the Van Hiele theory which deals with the geometric learning also through the literature search were diagnosed. Two forms of the Geometric Constructions approach are analyzed in class: through the design of hand tools - ruler and compass - and through the computational tool - geometric software - being that we chose to approach using the ruler and compass instruments. It is proposed a workshop with nine Geometric Construction activities which was applied with a group of 3rd year of high school, the Escola de Educac¸ ˜ao B´asica Professor Anacleto Damiani in the city of Abelardo Luz, Santa Catarina. Each workshop activity includes the following topics: Activity Goals, Activity Sheet, Steps of Construction Activity Background and activity of the solution. After application of the workshop, the data were analyzed through content analysis according to three categories: Drawing Instruments, angles and their implications and Parallel and its Implications. Was observed that most of the students managed to achieve the research objectives, and had an development in their mathematical and geometrical knowledge, which can be perceived through the analysis of questionnaires administered to students, audio recordings, observations made during the workshop and especially through the improvement of the students in the development of the proposed activities.