Improving Math Ability via Primitive Number Sense Training

数学能力对于人类生存的几乎每个方面都至关重要，但 成年人的数学能力存在很大差异，并且成年人的数学能力极差 与长期健康问题和较高的犯罪率有关（Parsons 和 Bynner， 2005）。入学时的数学技能可以预测以后的数学成绩，并且是更好的 与读写能力相比，它更能预测以后的整体学业成就（Jordan 等人，2009 年； 邓肯等人，2007）。因此，提高幼儿的早期数学技能可以 对学业成功甚至生活成果产生全球影响。此举的目标 该提案是建立在我们研究小组最近的一项发现的基础上的，该发现表明 使用点数组进行近似非符号算术 (ApprA) 训练会导致 精确符号算术 (SymA) 性能中的正迁移（Park 和 Brannon，In 按）。在目标 1 中，我们询问为什么 ApprA 训练可以改善 SymA。我们分解 ApprA 培训的认知成分，用于评估哪些方面对于改进至关重要 符号算术。在目标 2 中，我们测试有关大脑重叠程度的具体预测 支持近似非符号算术和精确符号算术的区域 产生这种转移效应。例如，我们询问 ApprA 训练是否发生变化 顶内沟的神经调谐曲线，已知体现了 数量的心理表征。这样的发现将提供强有力的证据表明 ApprA 通过改变原始数感来改进 SymA。最后目标 3 提出 在不同公立学区进行的一项 iPad 干预研究，以测试 ApprA 的功效 旨在改善幼儿 SymA 的培训。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 理解人类数学的根源。虽然 ApprA 培训不太可能 作为提高成人或老年人数学能力的有效途径 对于掌握了符号数字系统的孩子来说，这可能至关重要 提高尚未掌握符号的幼儿的数学能力 号码系统。

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.