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.

与文章《通过概念推导策略提升算术应用：以逆运算问题促进结合律简算的使用》相关联的数据集：摘要：对算术基本原理的内在概念性知识是理解代数以及未来数学成功的重要先导。其中一项原则即为结合律，它使得个体能够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’）。相较于其他任何原则，无论是儿童还是成人，对结合律的理解都尤为困难，教育工作者亦呼吁这一状况的改变。本研究报告了在大学课堂中进行的三项干预研究，旨在探讨成人对结合律的应用是否能够得到改善。在所有三项研究中，我们发现，首先解决逆运算问题（例如：‘a + b – b’）的参与者，相较于对照组，在解决‘a + b – c’问题时更有可能应用结合律。我们提出，‘a + b – b’逆运算问题可能要么引导空间注意力指向结合律问题中‘b – c’的位置，要么隐含地传达了从右至左策略的有效性和效率。这些发现对于设计旨在辅助理解算术原理和代数的简短活动的设计者而言可能颇具裨益。