Study 1 stimuli

Dataset connected with article: 'Increasing the use of conceptually-derived strategies in arithmetic: using inversion problems to promote the use of associativity shortcuts.' Abstract: Conceptual knowledge of key principles underlying arithmetic is an important precursor to understanding algebra and later success in mathematics. One such principle is associativity, which allows individuals to solve problems in different ways by decomposing and recombining subexpressions (e.g. ‘a + b – c’ = ‘b – c + a’). More than any other principle, children and adults alike have difficulty understanding it, and educators have called for this to change. We report three intervention studies that were conducted in university classrooms to investigate whether adults’ use of associativity could be improved. In all three studies, it was found that those who first solved inversion problems (e.g. ‘a + b – b’) were more likely than controls to then use associativity on ‘a + b – c’ problems. We suggest that ‘a + b – b’ inversion problems may either direct spatial attention to the location of ‘b – c’ on associativity problems, or implicitly communicate the validity and efficiency of a right-to-left strategy. These findings may be helpful for those designing brief activities that aim to aid the understanding of arithmetic principles and algebra.

数据集关联的文章：《提升算术问题中概念衍生策略的应用：借助逆运算问题促进结合律捷径的使用》。摘要：算术核心原理的概念性知识是理解代数及后续数学学习成功的重要前提。其中一项关键原理为结合律（associativity），它允许个体通过分解与重组子表达式以不同方式解决问题（例如“a + b – c” = “b – c + a”）。无论是儿童还是成人，对结合律的理解都比对其他任何原理的理解更为困难，教育工作者呼吁改变这一现状。本文报告了三项在大学课堂开展的干预研究，旨在探究能否提升成人对结合律的应用能力。三项研究均发现，先解决逆运算问题（例如“a + b – b”）的被试，在后续解决“a + b – c”类问题时，比对照组更有可能运用结合律。我们推测，“a + b – b”这类逆运算问题可能要么引导空间注意力聚焦于结合律问题中“b – c”的位置，要么间接传递了从右至左策略的有效性与高效性。这些发现或许能为设计旨在帮助理解算术原理与代数的简短活动提供参考。