{"title":"直观的数感有助于符号方程的错误检测能力。","authors":"Harris Wong, Darko Odic","doi":"10.1037/xlm0000803","DOIUrl":null,"url":null,"abstract":"<p><p>Research over the past 20 years has suggested that our intuitive sense of number-the Approximate Number System (ANS)-is associated with individual differences in symbolic math performance. The mechanism supporting this relationship, however, remains unknown. Here, we test whether the ANS contributes to how well adult observers judge the <i>direction</i> and <i>magnitude</i> of symbolic math equation errors. We developed a novel task in which participants view symbolic equations with incorrect answers (e.g., 47 + 21 = 102), and indicate whether the provided answer was too high or too low. By varying the ratio between the correct and the provided answers, we measured individual differences in how well participants detect the <i>magnitude</i> and <i>direction</i> of symbolic equation errors. We find that individual differences in equation error detection were uniquely predicted by ANS acuity-that is, the precision of each participant's intuitive number representations-even when controlling for differences in surface area perception, working memory span, and operational span. This suggests that the ANS can act as a unique source of error detection variability for formal mathematics, providing a plausible mechanism for how our universally shared number sense might link with human-specific symbolic math abilities. (PsycInfo Database Record (c) 2021 APA, all rights reserved).</p>","PeriodicalId":504300,"journal":{"name":"Journal of Experimental Psychology: Learning, Memory, and Cognition","volume":" ","pages":"1-10"},"PeriodicalIF":0.0000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"The intuitive number sense contributes to symbolic equation error detection abilities.\",\"authors\":\"Harris Wong, Darko Odic\",\"doi\":\"10.1037/xlm0000803\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Research over the past 20 years has suggested that our intuitive sense of number-the Approximate Number System (ANS)-is associated with individual differences in symbolic math performance. The mechanism supporting this relationship, however, remains unknown. Here, we test whether the ANS contributes to how well adult observers judge the <i>direction</i> and <i>magnitude</i> of symbolic math equation errors. We developed a novel task in which participants view symbolic equations with incorrect answers (e.g., 47 + 21 = 102), and indicate whether the provided answer was too high or too low. By varying the ratio between the correct and the provided answers, we measured individual differences in how well participants detect the <i>magnitude</i> and <i>direction</i> of symbolic equation errors. We find that individual differences in equation error detection were uniquely predicted by ANS acuity-that is, the precision of each participant's intuitive number representations-even when controlling for differences in surface area perception, working memory span, and operational span. This suggests that the ANS can act as a unique source of error detection variability for formal mathematics, providing a plausible mechanism for how our universally shared number sense might link with human-specific symbolic math abilities. (PsycInfo Database Record (c) 2021 APA, all rights reserved).</p>\",\"PeriodicalId\":504300,\"journal\":{\"name\":\"Journal of Experimental Psychology: Learning, Memory, and Cognition\",\"volume\":\" \",\"pages\":\"1-10\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Experimental Psychology: Learning, Memory, and Cognition\",\"FirstCategoryId\":\"102\",\"ListUrlMain\":\"https://doi.org/10.1037/xlm0000803\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2020/1/9 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Experimental Psychology: Learning, Memory, and Cognition","FirstCategoryId":"102","ListUrlMain":"https://doi.org/10.1037/xlm0000803","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2020/1/9 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
摘要
过去20年的研究表明,我们对数字的直觉——近似数字系统(ANS)——与个体在符号数学表现上的差异有关。然而,支持这种关系的机制尚不清楚。在这里,我们测试了ANS是否有助于成年观察者判断符号数学方程错误的方向和大小。我们开发了一个新颖的任务,在这个任务中,参与者观看具有不正确答案的符号方程(例如,47 + 21 = 102),并指出所提供的答案是太高还是太低。通过改变正确答案和提供答案之间的比例,我们测量了参与者在检测符号方程错误的大小和方向方面的个体差异。我们发现,即使在控制表面积感知、工作记忆广度和操作广度的差异时,方程错误检测的个体差异也是由ANS敏锐度(即每个参与者直观数字表示的精度)唯一预测的。这表明ANS可以作为形式数学错误检测可变性的独特来源,为我们普遍共享的数字感如何与人类特定的符号数学能力联系起来提供了一种合理的机制。(PsycInfo Database Record (c) 2021 APA,版权所有)。
The intuitive number sense contributes to symbolic equation error detection abilities.
Research over the past 20 years has suggested that our intuitive sense of number-the Approximate Number System (ANS)-is associated with individual differences in symbolic math performance. The mechanism supporting this relationship, however, remains unknown. Here, we test whether the ANS contributes to how well adult observers judge the direction and magnitude of symbolic math equation errors. We developed a novel task in which participants view symbolic equations with incorrect answers (e.g., 47 + 21 = 102), and indicate whether the provided answer was too high or too low. By varying the ratio between the correct and the provided answers, we measured individual differences in how well participants detect the magnitude and direction of symbolic equation errors. We find that individual differences in equation error detection were uniquely predicted by ANS acuity-that is, the precision of each participant's intuitive number representations-even when controlling for differences in surface area perception, working memory span, and operational span. This suggests that the ANS can act as a unique source of error detection variability for formal mathematics, providing a plausible mechanism for how our universally shared number sense might link with human-specific symbolic math abilities. (PsycInfo Database Record (c) 2021 APA, all rights reserved).