Department of Psychology and Human Development, Peabody College, Vanderbilt University, 230 Appleton Place, Nashville, TN, 37203, USA.
Division of Psychology, School of Social Sciences, Nanyang Technological University, 48 Nanyang Avenue, Singapore, 639818, Singapore.
Psychol Res. 2021 Apr;85(3):1248-1271. doi: 10.1007/s00426-020-01299-z. Epub 2020 Feb 14.
Numerosity estimation performance (e.g., how accurate, consistent, or proportionally spaced (linear) numerosity-numeral mappings are) has previously been associated with math competence. However, the specific mechanisms that underlie such a relation is unknown. One possible mechanism is the mapping process between numerical sets and symbolic numbers (e.g., Arabic numerals). The current study examined two hypothesized mechanisms of numerosity-numeral mappings (item-based "associative" and holistic "structural" mapping) and their roles in the estimation-and-math relation. Specifically, mappings for small numbers (e.g., 1-10) are thought to be associative and resistant to calibration (e.g., feedback on accuracy of estimates), whereas holistic "structural" mapping for larger numbers (e.g., beyond 10) may be supported by flexibly aligning a numeral "response grid" (akin to a ruler) to an analog "mental number line" upon calibration. In 57 adults, we used pre- and post-calibration estimates to measure the range of continuous associative mappings among small numbers (e.g., a base range of associative mappings from 1 to 10), and obtained measures of math competence and delayed multiple-choice strategy reports. Consistent with previous research, uncalibrated estimation performance correlated with calculation competence, controlling for reading fluency and working memory. However, having a higher base range of associative mappings was not related to estimation performance or any math competence measures. Critically, discontinuity in calibration effects was typical at the individual level, which calls into question the nature of "holistic structural mapping". A parsimonious explanation to integrate previous and current findings is that estimation performance is likely optimized by dynamically constructing numerosity-numeral mappings through the use of multiple strategies from trial to trial.
数值估计表现（例如，准确性、一致性或比例间隔（线性）的数值-数字映射如何）先前与数学能力相关。然而，支持这种关系的具体机制尚不清楚。一种可能的机制是数字集合和符号数字（例如，阿拉伯数字）之间的映射过程。本研究检验了数值-数字映射的两种假设机制（基于项目的“联想”和整体“结构”映射）及其在估计和数学关系中的作用。具体来说，对于较小的数字（例如，1-10）的映射被认为是联想的，并且不受校准（例如，对估计准确性的反馈）的影响，而对于较大的数字（例如，超过 10）的整体“结构”映射可能通过灵活地将数字“响应网格”（类似于标尺）与校准后的模拟“心理数字线”对齐来支持。在 57 名成年人中，我们使用校准前后的估计值来测量小数字之间连续联想映射的范围（例如，从 1 到 10 的联想映射的基本范围），并获得数学能力和延迟多项选择策略报告的测量值。与先前的研究一致，未经校准的估计表现与计算能力相关，控制了阅读流畅性和工作记忆。然而，较高的联想映射基本范围与估计表现或任何数学能力测量值都没有关系。关键的是，个体水平上校准效应的不连续性是典型的，这对“整体结构映射”的性质提出了质疑。一个简洁的解释是，通过从试验到试验使用多种策略动态构建数值-数字映射，估计表现可能得到优化。
