Improving Math Ability via Primitive Number Sense Training

数学能力对人类生活的几乎每一个方面都是必不可少的， 成年人的数学能力存在很大的差异， 与长期健康问题和较高的犯罪率有关（Parsons和Bynner， 2005年）的报告。入学时的数学技能可以预测以后的数学成绩， 比识字技能更晚的整体学术成就的预测因素（Jordan，et al.，二○ ○九年; 邓肯等人，2007年）。因此，提高幼儿的早期数学技能可以 对学业成功甚至人生有着全球性的影响。这个目标 我们的建议是建立在我们研究小组最近的一项发现的基础上， 使用点阵列的近似非符号算术（ApprA）训练导致 精确符号算术（SymA）性能的正迁移（Park和Brannon，In Press）。在目标1中，我们问为什么ApprA训练可以改善SymA。我们分解 ApprA培训的认知成分，以评估哪些方面对改善至关重要 符号算术在目标2中，我们测试了关于大脑中的重叠如何的具体预测， 支持近似非符号运算和精确符号运算的区域 产生这种转移效应。例如，我们问ApprA培训是否会改变 顶内沟的神经调谐曲线，这是已知的体现， 量的心理表征。这一发现将提供强有力的证据， ApprA通过改变原始数的意义来改进SymA。第三个目的是提出 在一个多元化的公立学区进行iPad干预研究，以测试ApprA的功效 训练以改善幼儿的SymA。为所有三个目标提供了试点数据。 了解ApprA和SymA之间的关系可能具有广泛的意义 来理解人类数学的根源。虽然ApprA培训不太可能 作为提高成年人或老年人数学能力的途径， 掌握了数字符号系统的孩子们， 用于提高尚未掌握符号的幼儿的数学能力， 数制

Mathematical ability is essential for almost every aspect of human existence and yet there is large variability in math competency in adults and extremely poor math ability is linked with long-term health problems and higher criminality (Parsons and Bynner, 2005). Math skills at school-entry predict later math achievement and are a better predictor of later overall academic achievement than literacy skills (Jordan, et al., 2009; Duncan et al., 2007). Therefore improving early math skills in very young children could have global effects on academic success and perhaps life outcomes. The goal of this proposal is to build upon a recent finding from our research group demonstrating that training with approximate nonsymbolic arithmetic (ApprA) using dot arrays leads to positive transfer in exact symbolic arithmetic (SymA) performance (Park and Brannon, In press). In Aim 1 we ask why ApprA training improves SymA. We decompose the cognitive ingredients of ApprA training to assess which aspects are critical for improving symbolic arithmetic. In Aim 2 we test specific predictions about how overlap in the brain regions that support approximate nonsymbolic arithmetic and exact symbolic arithmetic give rise to this transfer effect. For example, we ask whether ApprA training changes the neural tuning curves in the intraparietal sulcus, which are known to embody the mental representation of quantity. Such a finding would provide strong evidence that ApprA improves SymA by changing the primitive number sense. Finally Aim 3 proposes an iPad intervention study in a diverse public school district to test the efficacy of ApprA training to improve SymA in young children. Pilot data is presented for all three aims. Understanding the relationship between ApprA and SymA could have broad implications for understanding the roots of human mathematics. While ApprA training is unlikely to be practically useful as an avenue for improving math competency in adults or older children who have mastered the symbolic number system it could be critically important for improving math ability in very young children who have yet to master the symbolic number system.