Equivalência de estímulos e aquisição do conceito de proporção: efeito de instruções programadas, manipulação de material concreto e treino de composição

Abstract

Literature points that children in sixth grade of Middle School show difficulty to solve fractional problems that demand the concept of proportion. Behavior analysis affords efficient techniques and procedures to form stimulus classes that originate concepts. Nevertheless, few production about concepts formation based on this perspective were achieved on Math field. The present study s goal is to investigate the effect of conditional relationship training between: fractional pictorial stimulus (group A) and numerical (group B) and, numerical (group B) and numerical (group C), both performed by means of the stimulus equivalence paradigm, concerning formation of equivalence classes with fractional stimulus, generalization of responses to new situations and the expansion of the formed classes after the training among members of group A and a new group of numerical stimulus (D). Three experiments were conducted with an amount of 90 children enrolled in State educational system in Goiania and Trindade cities, falling into both genres whose ages range from 11 to 14 years old. The participants, divided in experimental and control groups, were initially submitted to a pencil and paper evaluation about fractional problems (IE) expressed in absolute and relative way. In the first experiment, one group was exposed only to the training with programmed instructions about fractional problem resolutions (PIG), another one only to conditional relationship training (EQG) and a third one to both trainings (EQPIG). In experiment 2, one group handled concrete material presented in form of fraction (CMG), another one went through the training of the two conditions (CMGEQ). In experiment 3, one group trained conditional relationships with fractional stimulus (EQG), another one went through the training of compounding (copying) fractions from models visually presented and conditional relationship tests (EQCTG) and to a third group was asked the exposition of the strategies adopted to solve problems during the trainings and conditional relationship tests (GEQR). At the end of the procedures all of them went through a final evaluation (FE) identical to the initial evaluation (IE). The control participants took only the initial and final evaluations. The results show that participants presented difficulty to solve problems expressed in relative way. Generally, all the participants of the experimental groups of the three experiments formed three fractional stimulus classes (ABC), however there was no expansion of these classes after the training between one of its members and a new stimulus. The highest generalization indexes occurred in the first programmed test and decreased in the second evaluation. Only participants of experimental groups presented systematic gains from IE to FE, considering that the highest performances to problems with fractions occurred to participants in EQPIG group.