This study aims to understand the impact of the COVID-19 pandemic on the educational landscape, with a focus on the effectiveness of the Google Meet and Google Classroom platforms in the context of hybrid and remote teaching. To achieve this, an explanatory qualitative methodology was adopted, with data collection carried out exclusively through online questionnaires directed at high school teachers from both public and private schools in the Western Pará region. The theoretical framework is based on the National Common Curricular Base (BNCC) and the Theory of Cognitive Flexibility, encompassing contemporary studies on Information and Communication Technologies (ICTs), Virtual Learning Environments (VLEs), and Virtual Learning Objects (VLOs). The results indicate that both teachers and students have adapted to a culture of remote and hybrid teaching, in which Google Meet plays a crucial role in addressing the educational challenges posed by the pandemic. In the specific context of mathematics education, the study suggests that a deeper mastery of virtual learning environments can enhance pedagogical benefits.

Large-scale external evaluations make it possible to construct national education performance indices. This study, by general objective, intends to verify if the State Department of Education (SEDUC), within the scope of the 5th Regional Teaching Unit to which schools in the city of Santarém-PA, make use of the results of large-scale evaluations, for example, as a guideline for the elaboration of measures that reflect on the pedagogical practices of the school and aim to improve teaching and learning and consequently the indexes of schools in these evaluations. Bibliographic and field research was used as a methodology, through the application of questionnaires to eight managers and twelve teachers from eight State High Schools and to the reference technician of the 5th URE, in Santarém, using Google Forms as a tool for collect. It was found that Santarena schools have a good index in IDEB, being the first school in the ranking of the State of Pará, Escola São Francisco with IDEB of 5.6. For managers and teachers, large-scale external evaluations are fundamental for school planning, and therefore, they seek information about the results, considering that their dissemination should be expanded by the 5th URE. They consider that the results of these evaluations are not enough to promote education, thus, they hold regular discussions with the school team for the efficient use of the data, as these demonstrate whether or not there has been learning. In this way, they consider that the dissemination of the results of external evaluations should be improved, as they demonstrate what should be changed in national education, being used as a reference for the school curriculum. Teachers reported having knowledge about the exam's referential matrix, about the distractors and the proficiency scales of the external assessments. For the 5th URE's reference technician, the results of external evaluations are made available quickly, as they are very relevant to face the low indicators of approval, failure and school dropout. Thus, the institution uses strategies for diagnostic assessment, as well as access to digital platforms for student learning, in addition to continuing education for teachers on external assessments. It was concluded that the results of large-scale external evaluations in Santarém are being used by the 5th URE to promote actions that strengthen the teachinglearning process of state schools, so that the student can have access to quality education, reaching the goals proposed by the MEC for national education.

The corona virus pandemic started in 2020, still makes many victims in the world, has already claimed thousands of lives, and has become a great challenge to doctors and science, and to the entire world population that had to adapt to various situations. of survival and coping with this deadly virus that has spread fear in all countries. All types of work activities had to adapt to the new reality, among the security measures, social isolation was imposed on everyone, with rare exceptions (essential activities). And the educational sector was completely affected, with face-to-face classes paralyzed, and only months after the beginning of the pandemic, a teaching proposal in the Ead modality, Distance Education. It is about this reality that still prevails in several schools in the world and in Brazil, which is intended to address in this work aimed at five schools, public and private, in the municipality of Santarém-PA.
The objective of this work is to investigate which methodological strategies, in the teaching of mathematics, were used by teachers to promote learning, even during the period of the corona virus pandemic.
The methodology used was bibliographic research with qualitative analysis.
It was found that the insertion of existing technologies becomes a proposal to assist in these changes that are necessary in the teaching process, mainly due to the period in which we live in the corona virus pandemic and that the use of technology as a facilitating instrument of the teaching process -learning, while the corona virus pandemic is still worryingly present in the world, is a way to provide continuity without major damage to elementary and high school students.

Failed attempts to solve the trisection problem of trisection from any angle resulted in numerous mathematical discoveries and served as a source for the emergence of new ideas and unknow paths is in its universe of trial and error that this work is found. Through the problem of Neusis construction, thus defined by the Greeks, the challenge of trisecting any angle using only a ruler and compass will be studied applying the theorical bases of the postulates described on the first book (or chapter) of Euclid’s most famous work: “The elements “. Even though Wantzel proved to be a mathematically impossible task to perform, the aim is to trisect the angle, and thus instigate the search for the solution causing the reader to discover the already known or even new relationships between lines, circles and angles
present in geometry.

The present work aims to analyze descriptively, the responses of teachers/candidates submitted to the National Access Exam (ENA), Notice 2019 of Profmat, candidates at the Federal University of Western Pará, using the parameters of the Classical Theory of Tests, to conduct a reflection on the teacher education of the mathematics teacher and the evaluation process to which these teachers were submitted. The ENA 2019 contains items that address areas of Mathematics of Basic Education, justifying the importance of this work in revealing which important areas of Basic Education teachers perform below expected taking into account the evaluation process used. Methodologically, the work began with a literary selection in the perspective of solidifying the theoretical foundations. Among the works chosen are those of the authors Hoffman (2005), Luckesi (1990), Rabelo (2013) and Pasquali (2017). Sequentially, we proceeded to characterize the sample to be analyzed, tabulating the responses collected in the response cards to perform the data processing and thereby generate the analysis using the parameters of the Classical Theory of Tests. This study measured, at the regional level, the performance of the teachers/candidates who responded, expressed by the difficulty index, bisserial point correlation, graphic and pedagogical analysis of the items answered by this group, besides diagnosing whether the ENA has been able to satisfactorily assess the knowledge necessary to enter Profmat, through the discrimination index and the item's accuracy index. This treatment of the data allowed a reflection on some aspects to be taken into account in the initial and continued training of the mathematics teacher submitted to an evaluative process used by them in their teaching work. Revealing more strongly, the lack of collective ability of teachers in more laborious issues dealing with Equations of the 2nd degree and Probability, a worrying panorama, since even though this performance was a reflection of a deficient academic background, these teachers have daily contact with these contents, because they are responsible for teaching classes on these domains in basic education. This performance of teachers/candidates also demonstrated that the Exam as an evaluation process with a view to selecting and classifying them is not fulfilling its objective efficiently, a fact verified by the analyses in which more than half of the test items present some limitation by not properly discriminating the most proficient subjects in the domains of the others. The work is structured as follows: in the initial sections we approach the theoretical aspects on Evaluation, Teacher Training of Mathematics and Classical Theory of Tests. Then, the details of the methodology used, the subjects and locus of the research. In the following section, the main results obtained from the analysis and treatment given the teachers' answers are given. Finally, the final considerations.

Large-scale assessments have been present in Brazilian schools for 30 years, and through these, along with other indicators, each school receives an index that indicates its development, thus showing whether the works are achieving the desired effects or not. The results of these assessments are made available for schools in the country to use in order to adopt strategies that aim to improve their performance. Thus, this work addresses a study on the possibilities, with emphasis on SAEB, of using its results to improve the teaching and learning process in the 9th grade classes, at the State School of Elementary and High School Frei Othmar in the city of Santarém -Pan. The objective is to analyze the actions taken at the school as a strategy to obtain improvements in the educational indicators of the school. The results pointed out in this work refer to the use of internal diagnostic evaluations and pedagogical practices of the school. The aim is to emphasize to the school community that the results of these assessments can be used as work tools and, in addition, contribute to overcome knowledge learning deficiencies at all levels of education. With the analysis of the school's results, considering the external evaluation to which it has been submitted and analyzing through a historical series, there are signs of positive results resulting from the actions taken.

Error is not only the effect of ignorance, uncertainty, chance, but the effect of prior knowledge, which is now an obstacle (Brosseau apud (CURY, 2007)). With this understanding, the study of errors, of their causes, can help the students in their difficulties and the teachers in the understanding and reduction of repetitions and school drop-outs (FELTES, 2007). A curricular component of the academy that has a high rate of reprobation and abandonment is the Differential and Integral Calculus, a traditional discipline that has preserved its original structure and that although in some cases its teaching explored with the most varied didactic resources, also observes that some errors remain frequent among students when the solution of derivatives and integrals (MARIANI, 2005). The present study aimed to investigate the errors committed by academics of the Integrated Degree in Mathematics and Physics, of Integrated Degree in Biology and Chemistry, and of professors in continuous formation of Profmat 2018 of UFOPA, in the city of Santarem during the second semester of 2018 in the solution of a test of Calculation. The research was based on the analysis of errors, a research methodology that uses the three phases of the content analysis of (BARDIN, 2002): the pre-analysis, the exploitation of the material and the treatment of the results. Following these phases, we tried to classify and analyze the errors committed by this group of students, present the results obtained and discuss the possible difficulties of students in items that follow the standards of national drafting bodies. The answers presented in the test, the opinions given in the questionnaires of students and teachers involved in the research showed that the difficulties of assimilation of the Calculus remain and related to knowledge of basic mathematics, as in the simplification of algebraic fractions and in the difficulty of representing a problem algebraically, as well as in basic concepts of the discipline (limits, derivatives and integrals). In this way, the analysis of errors allowed to detect, by the answers given in the test and in the questionnaires, the main difficulties of the students in Calculus.

The present work aims to present to the elementary school teacher an analysis and reflections on the results obtained by the students in the municipality of Santarém regarding the Objects of Knowledge of Mathematics and its Technologies in the ENEM of 2017. Some schools with different characteristics were selected as private, public,
and public schools with the aim of identifying proficiency in order to propose better planning and effective preparation of students in these places. The research deals with a brief reference about the evaluation process in Brazil, from the evaluating state to the large scale evaluation. A methodological construction of results was performed using R programming codes and using the ENEM Microdata of 2017 as a basis for information collection. As a result of the procedures, the analyzes were presented through tables and graphs created in Rstudio and Excel, where it was possible to observe the students' performance in relation to correct answers and errors in ENEM 2017 questions.

This research aims at the elaboration, application and analysis of two didactic sequences, one for the approach of operations with fractions associated with figural representation, and the other for notable products related to the rectangle areas. Such research is classified as field research regarding data collection, and as descriptive when addressing its objectives. The hypothesis of the research is that the application of didactic sequences facilitates the learning of the contents addressed. The methodology used was Didactic Engineering, which allowed us to validate the activities internally, and for the elaboration and analysis of the didactic sequences the Theory of Didactic Situations was used. The subjects of the research were students of the sixth and eighth years of two classes of elementary school in a public school in Juruti-PA. The data were collected through the production of the students and the observations made during the course of the application of the didactic sequences, besides the application of a questionnaire in a complementary way. In the sixth grade class there was a better performance in addition, subtraction and multiplication of fractions. The greatest difficulty was in the items related to the division operation. In the eighth year the insertion of fractions in some items of the activities negatively influenced the percentage of correct answers. The students demonstrated difficulties in the items pertinent to the production of some text, without this necessarily being related to their understanding of the concept approached. The application of the didactic sequences provided the structuring of didactic situations that presented the potential to allow its reapplication.

The objective of this work is to investigate the cases of learning difficulties on fractions commonly detected in elementary school classes. To carry on this research it will be taught some contents of fractions to students of 6^th Grade, using tractable materials. Firstly, the content of fractions will be taught in a traditional way and then the answers will be collected in test. The same content will then be explained with the touchable materials, assuming that the student will participate of the construction and development of them. The student takes the main part of learning process, being altogether the author of his own learning, and the teacher will be only a supervisor. Then another questionnaire with the same level of difficulty will be applied and the results are compared. After developing the contents with explanations using touchable materials, it is expected the student to have better perform in the resolutions of the activities, with more appropriated answers. However, the experience of working the contents fraction with touchable materials can be said to bring positive results because students are willing to face this challenge and thus solve activities with these materials and participate in content development with high self-esteem.