Central Executive Load And Fractional Knowledge Effect Sixth Graders' Symbolic And Non-symbolic Fraction Arithmetic

Fraction cognition is increasingly becoming one of the hot issues in mathematics cognitive science.At present,most of the researches on fraction cognition are focused on the individual understanding of fraction.Fraction calculation is still less.Fraction calculation is crucial to individual later mathematics achievement and the ability to succeed in many industries.However,learning fraction have brought great difficulties to individuals.The research on fraction arithmetic is helpful to know why learning fraction is so difficult.The study found that the individual's performance will be affected by strategy use.The research on the arithmetic strategy use of whole number shows that the individuals' strategy is restricted by the central executive load.Individuals' arithmetic knowledge also has a great influence on the arithmetic strategy use.And Procedural and conceptual knowledge of fractions will affect the individual's ability to fraction arithmetic.It plays an important role in deepening the understanding of the mechanism of fractional strategy use to study the effect of the central executive load and fractional knowledge on symbolic and non-symbolic fraction arithmetic strategy.The novelty of this study lies in the choice of non-symbolic fraction.Children's performance on fractions was directly compared with their performance on non-symbolic fractions.This contrast allowed us to test whether symbolic notation had a positive or negative impact on the processing of the fraction arithmetic.The results of the study can provide some scientific basis for fractional teaching,and further enrich and improve the theory of arithmetic cognitive strategy.In Experiment 1,we used a self-designed symbolic and non-symbolic fraction addition materials to systematically investigate 80 grade six elementary school children's ability of fraction estimation and their strategies used during the estimation process.In Experiment 2,we used dual-task paradigm(fractional estimation task and letter task).With 2(fraction knowledge:high,low)X 2(load situation:load,no-load)X 2(fraction type:symbol,non-symbol)mixed experimental design(fraction knowledge is between-subject variable,load situation and fraction type are within-subject variable),we investigate whether the central execution and the fraction knowledge will affect the strategy use of symbolic and non-symbolic fraction arithmetic.The result suggests that:(1)Children use similar seven strategies to estimate the symbolic and non-symbolic fraction,including changing fraction to another fraction easier to work with,the numerator and denominator added respectively,trying to find a common denominator,changing fraction to decimal fraction,reduction of fractions to a common denominator,the numerator added and denominator multiplied,the numerator and denominator multiplied respectively.(2)The differences in frequency of use of symbolic and non-symbolic fraction estimation strategies were very great.As a whole,some strategies were used more frequently in symbolic and non symbolic fraction estimation,such as changing fraction to another fraction easier to work with,the numerator and denominator added respectively,trying to find a common denominator.(3)Symbolic and non-symbolic fraction estimation strategies showed great differences in efficacy.In symbolic and non-symbolic fraction estimation,numerator and denominator added respectively is the fastest and changing fraction to decimal fraction is the most accurate,but the strategy of changing fraction to another fraction easier to work with is the best strategy for both speed and accuracy.(4)The fraction type had a greater impact on children's performances of fraction estimations and the strategy execution.Compared with the non-symbolic fraction,the individuals' strategy execution is faster and the accuracy is higher.(5)The fraction knowledge influences the performance of individual fraction estimation strategy execution.Individuals with high-level fraction knowledge are faster and more accurate than those with low-level fraction knowledge.However,the effect of fraction knowledge on the strategy execution of the non-symbolic fraction is larger than that of the symbolic fraction.(6)It showed that strategy execution was also impacted by central executive load.Children's strategy execution efficiency in central executive load condition were worse than those in no load condition.However,rich fraction knowledge can reduce the degree of constraint of central executive load in the fraction estimation strategy execution.