The Relationship Between Symbolic Numerical Representation And Arithmetic Ability:The Mediating Role Of Numeral-order Processing And Serial Order Working Memory

Symbolic numerical representation includes two meanings: understanding the size and the relative position relationship of the number,namely,the magnitude and ordinal.Arithmetic ability includes arithmetic fluency and numerical calculation ability,which respectively reflect the speed and accuracy of calculation.Generally speaking,if the symbolic numerical representation ability is strong,the arithmetic ability is also better.However,the internal mechanism of the relationship between the symbolic numerical representation and arithmetic ability is still unclear,mainly in:First,there is controversy over the organization of the symbolic numerical representation system stored in the brain.Approximate number mapping theory emphasizes the understanding of “magnitude” in the symbolic numerical representation.However,the semantic association theory emphasizes the understanding of the “ordinal”of numbers.Second,most of the previous researches believed that the understanding of the“magnitude” of the number is the key cognitive mechanism that explains the relationship between the symbolic numerical representation and arithmetic ability,which ignores the role of the number “ordinal”.Third,whether the mediating role of number cognitive ability(e.g.number order processing)and working memory(e.g.serial order working memory)is valid in the symbolic numerical representation and different arithmetic abilities is not clear.Based on the above questions,this research is divided into three parts:Experiment 1 is to start the comparison task and the number sequence task to verify whether the symbolic numerical representation system is based on the ANS number system or semantic association theory.The result shows that:(1)Priming distance effect appears in the priming comparison task,but the size effect does not appear,which supports the semantic association theory.(2)In the task of judging numerical order,the response to serial order conditions and addition equation conditions is better than equilibrium conditions and random conditions,which also supports the semantic connection theory.On the basis of the conclusion of experiment 1 that the ordinal is more emphasized,the second experiment explores the mediating effect of the quantity comparison ability of the magnitude and the number ordering ability reflecting the ordinal between the symbolic numerical representation and arithmetic ability.The result shows that:(1)Magnitude processing does not play an intermediary role between the symbolic numerical representation and the fluency of calculation and the ability of numerical calculation;(2)Numeral-order processing plays a part of the intermediary role between symbolic numerical representation and the fluency of calculation;(3)After controlling the arithmetic fluency,numeral-order processing does not play an intermediary role between the symbolic numerical representation and the ability of numerical calculation.The research results combined experiment 2 and experiment 3,with serial order working memory to explore more comprehensively how the symbolic numerical representation affects arithmetic ability.The result shows that:(1)Numeral-order processing and serial order working memory jointly play a completely mediating role between the symbolic numerical representation and arithmetic fluency;(2)After controlling the arithmetic fluency,only serial order working memory plays a complete mediating role between the symbolic numerical representation and the numerical calculation.To sum up,first of all,this research supports the view of the semantic association theory,so the symbolic numerical representation emphasizes the understanding of the“ordinal” of the number.Then,it is verified that the symbolic numerical representation mainly acts on the arithmetic ability through the numeral-order processing,and is mainly reflected in the fluency of calculation.Finally,numerical-order processing and serial order working memory jointly explain the relationship between the symbolic numerical representation and the fluency of calculation;after controlling the fluency of calculations,serial order working memory is the only cognitive mechanism that explains the relationship between the symbolic numerical representation and the ability to perform numerical operations.