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.

Adaptação do paradigma orientado a notificações para desenvolvimento de sistemas fuzzy

This work proposes to adjust the Notification Oriented Paradigm (NOP) so that it provides support to fuzzy concepts. NOP is inspired by elements of imperative and declarative paradigms, seeking to solve some of the drawbacks of both. By decomposing an application into a network of smaller computational entities that are executed only when necessary, NOP eliminates the need to perform unnecessary computations and helps to achieve better logical-causal uncoupling, facilitating code reuse and application distribution over multiple processors or machines. In addition, NOP allows to express the logical-causal knowledge at a high level of abstraction, through rules in IF-THEN format. Fuzzy systems, in turn, perform logical inferences on causal knowledge bases (IF-THEN rules) that can deal with problems involving uncertainty. Since PON uses IF-THEN rules in an alternative way, reducing redundant evaluations and providing better decoupling, this research has been carried out to identify, propose and evaluate the necessary changes to be made on NOP allowing to be used in the development of fuzzy systems. After that, two fully usable materializations were created: a C++ framework, and a complete programming language (LingPONFuzzy) that provide support to fuzzy inference systems. From there study cases have been created and several tests cases were conducted, in order to validate the proposed solution. The test results have shown a significant reduction in the number of rules evaluated in comparison to a fuzzy system developed using conventional tools (frameworks), which could represent an improvement in performance of the applications.