Uma nova proposta para o ensino de Análise Combinatória

Abstract

The objective of this study is to show the importance of developing the study of Combinatorial Analysis starting from the central idea of each topic and develop a study based on more general application of multiplicative and additive principles . For this, we assume that basically there are two types of cluster formations : the ordered clusters "sequences training method"and those which have not ordered "subsets of training method". Through this principle we developed the concepts that today are treated as arrangements, permutations and combinations. We analyze and solve problems of Combinatorial Analysis through these two methods (additive and multiplicative), making an association methods applied in textbooks, showing the importance that understanding these two methods has to develop a better understanding of what is being studied. Furthermore, we have developed a technique for calculating the number of subsets that can form from the elements of a given set, always based on the subset definition. We deliver questionnaires to high school students and other mathematics teachers of high school and also found was in the understanding of the topics covered by students and teachers, and also dificulties of teachers to make their students understand the diferences between arrangements, combinations and permutations. But we have not sought formmular "paths"to try to make their students understand the concepts covered in the matter, apparently the idea that maybe it is easier to teach Combinatorial Analysis through easily understood issues. So teachers and students are stashed. The student believes he is able to solve combinatorial problems and the teacher believes that managed to make their students understand the subjects taught. We found that both students and future teachers have great dificulty in understanding the ideas presented in each issue and the definitions in textbooks, especially if these ideas are a bit more complex, but more easily understand the concepts of sequences and subsets. Since then, the following question arose: Would knowing the arrangements formulas, permutations and combinations makes the student is able to solve Combinatorial Analysis problems. And we could see that the answer to the previous question is no. Because as previously we say the biggest dificulty is not only calculating but mostly the understanding of the statement.