Experimental Studies On The Characteristics And Influencing Factors To Solve Proportional Reasoning Problems For 4-6 Years Old Children

The origin and the development of Children's rate concepts and their capability in proportional reasoning was one of focuses in psychological researches, as well as one of the keys in subject instruction, since Piaget's original work. This article, in which a numerical comparison task paradigm was used, designed two experiments to study the characteristics and Influencing factors to solve proportional reasoning problems with different comparison difficulties for 4 to 6 younger children. The first study principally explored the half boundary effect \n children's proportional reasoning problem solving. A game context was provided to children in which three rectangles, which indicated a box full of black and white toy bricks, was presented on the test paper. At the same time one another rectangle, which indicated picture of a box full of black and white toy bricks, was presented on a large wall map. The black area in all of these rectangles was given a corresponding rate and the children were required to choose one rectangle in three options to match the rate with target rectangle. To be further, the second study, which has more complicated conditions with different presenting modes and stimuli size, used similar materials to explore the achievement differences in children's proportional reasoning problem solving with three kinds of comparison difficulties.The two studies totally sampled 141 4 to 6-year-old boys and girls from 4 kindergartens in Chengdu and Chonqqing as subjects and the results showed that:(1) The half boundaryplays a significant role in children's numerical comparisonproportional reasoning problem solving. Children at 5 years old can make use of this condition to aid their problem solving and their performance under the cross-half condition are better than their half condition and within-half counterparts. The main trouble in problem solving with complicated conditions for 4 to 6-year-old children consists in their insufficient understanding on the first-order relations.(2) 4-year-old children cannot understand great than relation'yet. Though 5 and 6- year-old children can understand this kind of relation, they cannot differentiate three kinds of comparison difficulties good enough under the complicated conditions. Children's proportional reasoning ability arises at age stage 5 and enhances with the increase of age. The older, the better the children's capability of making differences among three kinds of comparison difficulties and the more significant the performance superiority under the cross-half condition.(3) The orientation of target stimuli has no effect on children's proportional reasoning, and the gender factor has no effect too. Instead, stimuli size and presenting mode factors influence the children's performances in proportional reasoning problem solving significantly. The task condition with different size and switch of vision focus in proportional reasoning problem solving requires too much efficacy for 4 to 6-year-old children and they can hardly achieve acceptable scores.