Working Memory And Magnitude Representation As The Mechanisms On Arithmetic Learning Difficulty In Primary School Children

The acquisition of basic arithmetic skills is important for not only the individual's future academic achievement and career success,but also many aspects of daily life,such as paying bills or budgeting for expenses.However,prevalence studies existing literature has shown that 3-6.5% of school-age children have arithmetic learning difficulties,which is a developmental learning difficulty affecting the ability to acquire school-level arithmetic skills.The research on underlying mechanisms of arithmetic learning difficulties was initially focused on working memory ability,from the perspective of domain-general cognitive ability ility,whereas many studies have begun to study magnitude representation ability as a potential factor on learning arithmetic difficulties,from the perspective of domain-specific cognitive ability,in the recent years.However,the empirical findings in this field are yet controversial now.The main purpose of this study was to explore the cognitive processing mechanism of working memory and magnitude representation abilities on arithmetic learning difficulties of primary school children.This study adopted a cross-sectional design.Among the 1224 children in grade 1,3 and 5 of primary school,74 children were screened out and selected as the experimental group.The control group consisted of 74 children with normal arithmetic development who had comparable levels of non-verbal intelligence,reading comprehension and learning motivation.This study investigated the origin of arithmetic learning difficulties vie testing different hypotheses,such as working memory deficit,number sense deficit,access deficit and symbol magnitude representation deficit.The study also investigated the effects of working memory and magnitude representation cognitive ability to cause arithmetic learning difficulties,and explored a more integrative and efficient identification model for arithmetic learning difficulties.Four empirical studies were included:The first study investigated the cognitive deficits in working memory of children with arithmetical learning difficulties.The central executive system was measured by N-back task,the phonological loop system was measured by word recall task,and the visuospatial sketchpad loop was measured by visual pattern span task.The results showed that:(1)Children with arithmetic learning difficulties performed worse than the control group on all the working memory tasks.(2)There were age differences concerning the damage pattern of children with arithmetic learning difficulties in central execution and visuospatial sketchpad,and the extent to which children in the difficult group fell far behind children with normal development increased over time.The second study investigated the cognitive deficits in magnitude representation of children with arithmetic learning difficulties.The non-symbolic magnitude representation was measured by dots comparison task,the numerical magnitude mapping was measured by digits-dots matching task,and the symbolic magnitude representation was measured by digits comparison task.The results showed that:(1)Children with arithmetic learning difficulties performed significantly worse in magnitude representation tasks than the normal group and showed a larger numerical size effect.(2)There were age differences concerning the damage pattern of children with arithmetic learning difficulties in symbolic magnitude representation ability.The children in the experimental group fell behind the control group to the greatest extent in the first grade,the difference then narrowed in the third grade,but widened again in the fifth grade.The third study investigated the mechanism of arithmetic learning difficulties caused by working memory and magnitude representation abilities.First,the predictive effect of six cognitive abilities(i.e.central executive,phonological loop,visuospatial sketchpad,non-symbolic magnitude representation,numerical magnitude mapping and symbolic magnitude representation)on arithmetic performance were analyzed with the group as the moderator.The results showed that: the moderation effect of the group was not significant in the prediction of most cognitive abilities on arithmetic scores.The different prediction models between two groups only appeared in the prediction of symbolic magnitude representation on arithmetic performance.Compared to the difficulty group,the symbolic magnitude representation ability in the normal group had a greater influence on the arithmetic performance.Second,this study analyzed of mediating and moderating effects in the relationship path of arithmetic learning difficulties caused by different stages of quantitative development.The results showed that:(1)Non-symbolic magnitude representation ability predicted arithmetic performance through numerical magnitude mapping ability.The mediating effect of symbolic magnitude representation between non-symbolic magnitude representation ability and arithmetic performance was moderated by group.(2)Phonological loop and visuospatial sketchpad abilities,not central executive,predicted arithmetic performance through numerical magnitude mapping ability.(3)The mediating effect of symbolic magnitude representation between working memory and arithmetic performance was moderated by group.The fourth study attempted to construct a more integrative and efficient pattern of identifying arithmetic learning difficulty.First,this study investigated the relationship between low working memory or magnitude representation skills and arithmetic learning difficulty.Each cognitive ability was identified according to the criteria of relative defects.The results showed that: there were more working memory deficits in the first grade children with arithmetic learning difficulties,and more magnitude representation deficits in the third and fifth grade children with arithmetic learning difficulties.Second,using logistic regression analysis,this study examined the predictive effect of six cognitive factors on arithmetic learning difficulty.The results showed that: visuospatial sketchpad and symbolic magnitude representation had significant explanatory power on whether arithmetic learning difficulty or not in the first grade;symbolic magnitude representation had significant explanatory power on whether arithmetic learning difficulty or not in the third and fifth grade.The major findings of this study were:(1)Children with arithmetical learning difficulties had common impairments in working memory and magnitude representation cognitive abilities,the origin of the latter damage is the number sense deficit.(2)Working memory and magnitude representation cognitive factors had different predictive patterns for arithmetic performance in children with or without arithmetical learning difficulties,specifically,in their prediction of symbolic magnitude representation on arithmetic performance.(3)The effect of non-symbol magnitude representation ability on arithmetic performance was mediated by the ability of numerical magnitude mapping or symbol magnitude representation.The effect of working memory ability on arithmetic performance was mediated by the ability of numerical magnitude mapping or symbol magnitude representation.(4)A combination of visuospatial sketchpad and symbolic magnitude representation abilities could effectively predict arithmetical learning difficulties of lower grade primary school students.A single symbolic magnitude representation ability could identify middle-grade and high-grade primary school students who have arithmetical learning difficulties sensitively.