A Research On The Proportional Reasoning Ability Development Of Children Aged 5-6

The concept of proportionality has been closely related to human daily life since ancient times.Studies have shown that the concept of proportionality is an important cornerstone for children to learn mathematics problems such as rational numbers and functions.Proportional reasoning is an important turning point in the development of children's thinking.This study examines the developmental characteristics of proportional reasoning abilities of children aged 5-6 through four proportional reasoning tasks,and explores the performance of children in proportional reasoning tasks of different natures,different types,and different variables,and children's proportional reasoning tasks.The relationship between scoring in various proportional reasoning tasks.In addition,through the life situation task,the differences and characteristics of children with different proportions of reasoning ability in problem solving were examined.The subjects studied were from five kindergartens in Changning District,Shanghai,of which three were Class I kindergarten and two were Class?kindergarten.According to research needs,237 children were randomly selected as subjects in these 5 kindergartens.The research tools are collectively referred to as the children's proportional reasoning ability test.The test is divided into four items,which are adapted from the classic proportional reasoning tasks of Noelting(1980),Miao Danmin(1991),Boyer,Levine(2001),Spinillo(1991),and Yang Rong(2003).The descriptive statistics method was used to examine the development characteristics of proportional reasoning ability of children aged 5-6 years;the multivariate analysis of variance was used to examine the differences in the reasoning ability of 5-6-year-old children's proportion reasoning between gender and institution;and the correlation analysis was used.The method examines the performance of children aged 5-6 years in proportional reasoning problems of different natures,types,and variables,and the relationship between children's proportional reasoning ability and the solution ofproportions in life;finally,it explains the 5 to 6-year-old children's performance in solving the problem of proportional reasoning in the context of life.The results show that: 1.5-6 years old children already have a certain proportion of reasoning ability,and presents the following characteristics: children's proportional reasoning ability differs among children of different genders;children perform differently on proportional ratio reasoning of different ratios,of which the proportional reasoning problem with a 1/2 contrast ratio has the highest degree of completion.2.The proportion reasoning ability of children aged 5-6 has significant gender differences,and there is no significant difference at the level of the kindergarten.3.Children aged 5-6 years have different performances in tasks with different characteristics,different types,and different variables.4.Children's performance in solving qualitative proportional reasoning tasks is superior to performance in quantitative proportional reasoning tasks;children perform better in partial-to-whole type proportional reasoning tasks than in expanding or contracting types and related collective types;children performed better in continuous variables proportional reasoning task performed better.Children aged 5-6 years are more likely to adopt a partial-partial comparison strategy in solving part-whole types and expanding or shrinking types of proportional reasoning.5.The children of 5-6 years old showed a significant positive correlation in the proportion of reasoning tasks,and the proportion reasoning ability of children was positively correlated with the performance of solving proportional reasoning problems in life.6.Children with different proportions of reasoning ability have the following characteristics in solving the problem of proportional reasoning in life situations:(1)In the state of question representation,children with strong ability often show direct answers to solve simple problems.On complex issues,questions and self-talk are usually given;children with weak abilities will directly answer or keep silent when solving simple problems,and they often show silence and abandon when solving complex problems.In terms ofrepresentation,Children with strong abilities often use non-visual representations,while children with weak abilities often use visual representations;in terms of content representation,children with strong abilities often refer to numbers and content in questions,but children with weak abilities talk about pictures and their own life experience.(2)in the aspect of strategy selection Children show different strategies for different difficulty levels.Children with strong abilities will use additive strategies and divide-and-half accumulating strategies on simple issues.Individual children will adopt unit price ratio strategies on complex issues;children with weak abilities use intuition strategies and addition strategies.(3)in the aspect of computing skills: Some children will show preference for computing skills,that is,children who use the multiplication method for the first question will also choose multiplication on other issues.The children who use the counting strategy for the first question will also use the same strategy.Children with strong abilities often use additive methods for calculations,and individual children use multiplicative calculations.Children with weak abilities often use counting methods to perform calculations.