Resolvendo adiÃÃo de fraÃÃes atravÃs de estimativas: um estudo exploratÃrio

AUTOR(ES)
DATA DE PUBLICAÇÃO

2003

RESUMO

According to the National Curriculum Parameters, the teaching of fractions and operations with fractions should be formally introduced, respectively, in the 3rd and 4th grades of Elementary School Education. These grades correspond to the period in which children have the necessary knowledge for the comprehension of such subjects. However, a number of researchers have demonstrated that younger children can solve problems that involve logical-mathematical concepts (such as proportion and probability) through estimations when they are offered reference points that serve as anchors in the thinking process. Thus, the aim of the present study was to investigate whether children who have not been formally instructed on fractions could solve the addition of fractions through estimations, having two reference points as their base: half and whole. 42 middleclass children from private schools in the city of Recife participated in the study, with equal divisions of 2nd and 3rd grade elementary school students. Each child was asked individually to solve the addition of fractions in four separate tasks. Task 1 was made up of 6 fraction addition units formed by two equal parcels and two unequal parcels. The reference given in this task as an anchor for solving the operations was half. Task 2 consisted of solving nine fraction addition units, formed by three equal parcels, or by two equal parcels and one different, or by three unequal parcels. The referential given in this task as the anchor for solving the problems was whole. Task 3 was a task of equivalence between fraction operations. 12 fraction addition units were presented. In six of these the  fraction was offered (reference of half) as the anchor for composing the equivalence. In the remaining six additions other fraction units were offered as references (1/4 or 1/6 or 1/3). Task 4 was made up of six fraction additions displayed on a sheet of paper using the formal mathematical symbolism. The results were analyzed in relation to the grades, the number of correct answers for each item and in relation to the type of justification or strategy the children exhibited. In general, no significant differences were found between the grades regarding the number of correct answers. In Tasks 1 and 2, it was observed that the addition of fractions with equal parcels was more difficult than when the parcels were different. In Task 3, the childrenâs performance was significantly higher for the items in which the  fraction was offered as the referential than when other fraction units were given as anchors in the solving of the operations. In Task 4, the children were unsuccessful in arriving at correct answers when trying to solve the operations by using the formal mathematical representation. In regards to the justifications and strategies, it was verified that correct answers were often associated to the operations in which the children explicitly utilized half and whole as references. From the data it can be concluded that: (1) even before any formal instruction on fractions, children are able to solve operations with fractions through estimations and the use of references such as half and whole; (2) the reference of half, as occurs in regards to other relational concepts, is an important tool in the solving of fraction additions; (3) children in both grades display the same level of intuitive knowledge on fractions. The data represent relevant contributions to psychology and to mathematic education in elementary school teaching.

ASSUNTO(S)

teaching of fractions mathematics ensino fundamental - 3Â e 4Â sÃries matemÃtica ensino de fraÃÃes psicologia cognitiva elementary school education

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