The children difficulties with division: an intervention study / As dificuldades das crianÃas com a divisÃo: um estudo de intervenÃÃo

AUTOR(ES)
DATA DE PUBLICAÇÃO

2005

RESUMO

Children encounter difficulties in dealing with the division concepts. Researches on cognitive psychology and on mathematical education approaches pointed to, between others, two types of difficulties on this area: (a) the difficulty to understand the inverse relations between the division terms while the dividend is held constant, and (b) the difficulty to deal the remainder. In this present research we have investigated the effect of a specific intervention intending to reduce children difficulties with the division concepts. 206 low-income Brazilian children; ranging from 8 to 15 years old; studying on the third year of fundamental course (public schools of the city of Recife), were submitted to a general pre-test. The pre-test consisted of solving 12 division problems allowing to the selection of children presenting difficulties with the division concept. 100 children were selected and equally divided into two groups: control and experimental. Afterwards, they were submitted to other specific pre-test which consisted of three tasks. The children in the experimental group individually received specific intervention involving the solution of division problems in which the researcher presented situations requiring the children to: (i) understand the inverse relations between the number of the parts and the size of the parts when the dividend is held constant; (ii) understand the effect of enhance the remainder value above the others terms, and (iii) analyze the procedures of correct and incorrect solutions presented on pictographic form. The examiner role, during the whole process of resolution adopted by the child, consisted of providing feedback and explanations, emphasizing the division invariant principles presented in the solution. A general and a specific post-test were applied to the children of both groups. Data on pre and post tests were analyzed in function of both the performance and the explanations children give for the solution they have adopted. The explanations ranged from vague and inadequate explanations to those expressing a comprehension of the division invariants. The findings have showed that both groups (control and experimental) do not differentiated one of each other in the pre-tests (general and specific), presenting the same degree of difficulty. After the intervention process has been done the children in the experimental group demonstrated to be more successful in the post-test than they were in the pre-test (general and specific). Those children either presented an improved performance as they were capable of given explanations more elaborated expressing a better understanding of the division invariants. The same improvement was not presented by the control group. We then conclude that the intervention process helped the children to overcome their division difficulties. They became capable to identify and analyze the invariant principles necessaries to understand the division as a mathematical operation. Also the children have developed metacognitive abilities that are crucial for learning specific academics contents like the mathematics concepts

ASSUNTO(S)

learning difficulties dificuldades de aprendizagem intervenÃÃo psicologia cognitiva division invariants intervention invariantes da divisÃo

ACESSO AO ARTIGO

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