A resolu??o de problemas como ferramenta para a aprendizagem de progress?es aritm?ticas e geom?tricas no ensino m?dio.

As progress?es aritm?ticas e geom?tricas s?o conte?dos de fundamental import?ncia no Ensino M?dio. Contudo, percebe-se, ao longo da experi?ncia profissional e no contato com os colegas, que ? tradicional o ensino das Progress?es exclusivamente por meio de manipula??o de f?rmulas entregues aos alunos, muitas vezes sem as devidas demonstra??es destas e tamb?m sua aplicabilidade, sendo assim empregados em exerc?cios tradicionais de sala de aula. Na aprendizagem da matem?tica, os problemas permitem ao aluno colocar-se diante de questionamentos e pensar por si pr?prio, possibilitando o exerc?cio do racioc?nio l?gico e n?o apenas o uso padronizado de regras. Esta pesquisa apresenta os estudos acerca da Resolu??o de Problemas segundo Pozo, Schoenfeld, Lester, Onuchic, entre outros, para construir uma proposta de ensino de progress?es aritm?ticas e geom?tricas. O prop?sito da pesquisa era responder ? seguinte quest?o: Que contribui??es, uma proposta de ensino baseada na resolu??o de problemas, pode trazer para a aprendizagem de progress?es aritm?ticas e geom?tricas? Para isso, foi desenvolvida e implementada uma proposta de ensino de Progress?es fundamentada na resolu??o de situa??es problemas e investiga??o em pequenos e grandes grupos em uma turma de 46 alunos do primeiro ano do Ensino M?dio de uma escola particular de Ponte Nova/MG. Procurou-se apresentar aos alunos os conte?dos considerados pr?-requisitos para posteriormente aplicar a metodologia de Ensino-Aprendizagem-Avalia??o de Matem?tica atrav?s da Resolu??o de Problemas. Durante as atividades procurou-se seguir o roteiro sugerido por Onuchic (2008). A coleta de dados se deu por meio de di?rio de campo do pesquisador e registros produzidos pelos alunos ao longo das aulas. A an?lise de dados evidencia que al?m de envolver o pesquisado no processo de busca de seu conhecimento e oferecer-lhe oportunidade de pensar, possibilitou-lhe o desenvolvimento de habilidades como identifica??o do problema, sele??o de estrat?gias de resolu??o, utiliza??o de racioc?nios indutivos e dedutivos; elaborar e validar conjecturas e finalmente a capacidade de argumenta??o.The geometric and arithmetic progressions are contents of great importance within High School curriculum. However, it is possible to realize throughout the years of experience and contact with colleagues that the former topics are exclusively taught through the manipulation of formulas handed to the students. Most of the times the appropriate demonstrations and applicability are not exposed to students, therefore arithmetic and geometric progressions are used only in traditional classroom exercises. When it comes to Math, problem solving allows students to question the situations and think for themselves, replacing the simple use of standard rules for logical thinking. This piece of research presents the studies involving Problem Solving by Pozo, Schoenfeld, Lester, Onuchic, among others. Considering these studies the aim is to build a proposition for the teaching of arithmetic and geometric progressions. This piece of research aimed to answer the following question: What contributions could a proposal of teaching arithmetic and geometric progressions through problem solving bring to the learning process? In order to find answers a teaching strategy was developed and implemented. This strategy was based on problem solving and investigations carried out in small and large groups of a Freshman class of 46 students (first year of High School) of a private High School located in Ponte Nova/MG. The Ensino-Aprendizagem-Avalia??o de Matem?tica atrav?s da Resolu??o de Problemas (Math Teaching-Learning Evaluation through Problem Solving) methodology was carried out after students were presented with the required topics. The model suggested by Onuchic (2008) was followed during the activities. The data were collected through journals produced by the researcher and the students. The analysis of the data shows that through problem solving students had the opportunity to think and get involved in the search for their own knowledge. Improvements could also be observed in the ability to identify the problem, select strategies to solve it, use inductive and deductive thinking, as well as elaborating and validating conjectures and finally in the ability to discuss the process and results. The performances of students and their abilities to work with problem solving showed clear upturn according to the analysis of the data