Geary David C, Hoard Mary K, Nugent Lara, Rouder Jeffrey N
Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA.
Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA.
J Exp Child Psychol. 2015 Dec;140:211-27. doi: 10.1016/j.jecp.2015.07.010. Epub 2015 Aug 7.
The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 ninth graders (92 girls) while controlling for parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation but not to schema memory. Frequency of fact retrieval errors was related to schema memory but not to coordinate plane or expression evaluation accuracy. The results suggest that the ANS may contribute to or be influenced by spatial-numerical and numerical-only quantity judgments in algebraic contexts, whereas difficulties in committing addition facts to long-term memory may presage slow formation of memories for the basic structure of algebra equations. More generally, the results suggest that different brain and cognitive systems are engaged during the learning of different components of algebraic competence while controlling for demographic and domain general abilities.
在控制父母教育程度、性别、阅读成绩、数字处理速度、符号数字处理流畅性、智力和工作记忆的中央执行成分的情况下，对171名九年级学生（92名女生）的代数认知测量表现与近似数字系统（ANS）的敏锐度以及加法事实记忆之间的关系进行了评估。代数任务评估了在坐标平面中放置x、y对的准确性、表达式求值的速度和准确性以及代数方程的模式记忆。ANS敏锐度与坐标平面中的放置准确性和表达式求值有关，但与模式记忆无关。事实检索错误的频率与模式记忆有关，但与坐标平面或表达式求值准确性无关。结果表明，ANS可能在代数情境中对空间数字和仅数字数量判断有贡献或受其影响，而将加法事实存储到长期记忆中的困难可能预示着代数方程基本结构记忆的缓慢形成。更普遍地说，结果表明在控制人口统计学和领域通用能力的同时，不同的大脑和认知系统在代数能力不同组成部分的学习过程中发挥作用。
