O ensino da estatística nos anos finais do ensino fundamental

Result of a professional master course of research work in Teaching Science and Technology of the Federal Technological University of Paraná (UTFPR), this work aims to provide the mathematics teacher of the final years of elementary school a teaching sequence (SE) which includes basic content of Statistics provided in the curriculum. In this book a text about the importance of the teaching of statistics is presented, as well as issues related to literacy skills, reasoning and statistical thinking. The development of the SE was designed considering the presuppositions of contextualization, being structured in six steps. We chose to develop a work with the basic contents of Statistics through real data collected with the participation of students, within a context for them significant. This option was due to be possible to develop with the students situations such as: raising hypotheses , communication situations experienced by different graphs and tables , results of discussion and understanding of the significance of the results obtained by means of statistical calculations. Thus, it is believed to be possible to contribute to the development of statistical skills by the students.

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.

A contribution to semantic description of images and videos: an application of soft biometrics

Humans have a high ability to extract visual data information acquired by sight. Trought a learning process, which starts at birth and continues throughout life, image interpretation becomes almost instinctively. At a glance, one can easily describe a scene with reasonable precision, naming its main components. Usually, this is done by extracting low-level features such as edges, shapes and textures, and associanting them to high level meanings. In this way, a semantic description of the scene is done. An example of this, is the human capacity to recognize and describe other people physical and behavioral characteristics, or biometrics. Soft-biometrics also represents inherent characteristics of human body and behaviour, but do not allow unique person identification. Computer vision area aims to develop methods capable of performing visual interpretation with performance similar to humans. This thesis aims to propose computer vison methods which allows high level information extraction from images in the form of soft biometrics. This problem is approached in two ways, unsupervised and supervised learning methods. The first seeks to group images via an automatic feature extraction learning , using both convolution techniques, evolutionary computing and clustering. In this approach employed images contains faces and people. Second approach employs convolutional neural networks, which have the ability to operate on raw images, learning both feature extraction and classification processes. Here, images are classified according to gender and clothes, divided into upper and lower parts of human body. First approach, when tested with different image datasets obtained an accuracy of approximately 80% for faces and non-faces and 70% for people and non-person. The second tested using images and videos, obtained an accuracy of about 70% for gender, 80% to the upper clothes and 90% to lower clothes. The results of these case studies, show that proposed methods are promising, allowing the realization of automatic high level information image annotation. This opens possibilities for development of applications in diverse areas such as content-based image and video search and automatica video survaillance, reducing human effort in the task of manual annotation and monitoring.