Individual differences in cognitive arithmetic.
Individual differences in cognitive arithmetic.
复制标题
认知算术的个体差异。
DOI：
10.1037//0096-3445.116.2.154
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发表时间：
1987
期刊：
影响因子：
--
通讯作者：
Widaman,KF
中科院分区：
文献类型：
--
作者：
Geary,DC;Widaman,KF
同时使用因子分析和信息处理方法的研究表明，在解决各种运算的算术问题时所涉及的过程是统一的。我们设计这项研究是为了考察通过纸笔测量来评估的心理过程的趋同性，这些测量定义了认知算术的数值工具因子和成分加工，通过计时技术识别。对100名本科生在真假反应时(RT)验证范式下回答了320个算术问题，并对其进行了一系列能力测量，包括数字设备、知觉速度和空间关系因素。320个认知算术问题包括简单加法、复杂加法、简单乘法和复数乘法四种类型中的每一种的80个问题。信息处理结果表明，结构变量与算术事实记忆网络提取一致的回归模型对四类算术问题中的每一种都是最好的预测因子。结果还验证了心理解决算术问题的其他基本过程的影响，包括对单个数字进行编码，以及对复杂问题进行下一列编码。通过结构方程模型检验了过程成分与能力测量之间的关系。最终的结构模型揭示了包含算术事实检索和执行进位运算的效率的因子与传统的数值工具因子之间的强烈的直接关系。此外，编码速度因子与决策和反应时间以及传统的知觉速度因子之间也存在适度的直接关系。没有发现代表认知算术成分加工的结构变量与跨越空间关系因素的能力测量之间的关系。结构模型的结果支持这样的结论，即从算术事实网络中提取信息和执行进位运算是算术问题心理解决中唯一涉及的基本成分过程。此外，执行这两个基本成分过程的速度的个体差异似乎是传统上跨越数值工具因素的能力测量的个体差异的基础。更广泛地说，本研究提供了通过使用因素分析方法和通过使用反应时间技术分离的基本成分过程来确定智力能力的连续性的证据。
Unities in the processes involved in solving arithmetic problems of varying operations have been suggested by studies that have used both factor-analytic and information-processing methods. We designed the present study to investigate the convergence of mental processes assessed by paper-and-pencil measures defining the Numerical Facility factor and component processes for cognitive arithmetic identified by using chronometric techniques. A sample of 100 undergraduate students responded to 320 arithmetic problems in a true-false reaction-time (RT) verification paradigm and were administered a battery of ability measures spanning Numerical Facility, Perceptual Speed, and Spatial Relations factors. The 320 cognitive arithmetic problems comprised 80 problems of each of four types: simple addition, complex addition, simple multiplication, and complex multiplication. The information-processing results indicated that regression models that included a structural variable consistent with memory network retrieval of arithmetic facts were the best predictors of RT to each of the four types of arithmetic problems. The results also verified the effects of other elementary processes that are involved in the mental solving of arithmetic problems, including encoding of single digits and carrying to the next column for complex problems. The relation between process components and ability measures was examined by means of structural equation modeling. The final structural model revealed a strong direct relation between a factor subsuming efficiency of retrieval of arithmetic facts and of executing the carry operation and the traditional Numerical Facility factor. Furthermore, a moderate direct relation between a factor subsuming speed of encoding digits and decision and response times and the traditional Perceptual Speed factor was also found. No relation between structural variables representing cognitive arithmetic component processes and ability measures spanning the Spatial Relations factor was found. Results of the structural modeling support the conclusion that information retrieval from a network of arithmetic facts and execution of the carry operation are elementary component processes involved uniquely in the mental solving of arithmetic problems. Furthermore, individual differences in the speed of executing these two elementary component processes appear to underlie individual differences on ability measures that traditionally span the Numerical Facility factor. More generally, the present study provides evidence for continuity of intellectual abilities identified with the use of factor-analytic methods and elementary component processes isolated with the use of reaction-time techniques.