Study 1 booklet example

Booklet for participants in research 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“通过逆问题促进算术中概念导出策略的使用：提高算术的关联性简捷法使用”相关的参与者手册》：摘要：对算术基本原理的概念性知识是理解代数及其在数学学习后期成功的重要先导。其中一项原理即为结合律，它使得个人能够通过分解和重组子表达式以不同的方式解决问题（例如：‘a + b – c’ = ‘b – c + a’）。相较于其他原理，无论是儿童还是成人，对结合律的理解都尤为困难，教育工作者们呼吁这一状况得以改变。本研究报告了在大学课堂中进行的三个干预研究，旨在探究成人使用结合律的能力是否能够得到提升。在所有三个研究中，我们发现，首先解决逆问题（例如：‘a + b – b’）的参与者相较于对照组，在解决‘a + b – c’问题时更有可能使用结合律。我们推测，‘a + b – b’逆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。这些发现可能对设计旨在辅助理解算术原理和代数的简短活动的设计者有所帮助。