Argumentação e prova: análise de argumentos geométricos de alunos da educação básica

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

In 2005, a research project with the purpose of investigating the presence, the teaching and the learning of proof in mathematics in Basic Education, began at PUC/SP. This project generated 1998 student protocols for geometry activities and the same number for algebra activities, the students come from the 8th and 9th grades of High Schools, in the state of São Paulo. As a participant in this project, I used the experience to structure my research and chose to direct to geometry activitys, seekns to a survey students conceptions about geometry arguments and proofs. In order to execute a more detailed analysis of the protocols, from the original sample of 1998, a smalles sample with 50 students was extracted; I also selected for, two questions in which the students were requested to present a solution and a justification for the given solution. From the students productions that compose the sample of 50: a quantitative analysis determining the frequency of the answers and the justifications, was carried out, along with on a qualitative analysis, focusing the presented arguments, the specific knowledge and the mobilized cognitive processes. In order to confirm or to refute the conjectures raised in these analyses, seven students were interviewed, completins the data set for the smalles sample. In sequence, I analyzed the data of the complete sample of 1998 protocols. The analysis was carried through two moments: in the first, from an organization in tables, it was based on the frequencies of solutions and justifications; second, the analysis was supported by three data treatments, carried out through statistical multidimensional software CHIC. The results suggested the following conclusions: On whole the students solutions left much to desive; the protocols evidenced two extremes: a large group of students (26,5%), typically from the 9th grade, provided no solutions or justifications at au, while a much smalles group (1,9%) of students, generally from the 8th grade, were able to construct valid arguments. Overall perfomance of 8th grade students was better than students of the 9th grade. Finally, the study presents, on the basic of a synthesis of the findings some indications for possible developments in the teaching and learning of proof

ASSUNTO(S)

geometria geometria educação básica geometry matematica educacao matematica argument and proof basic education argumentação e prova matematica -- estudo e ensino

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