Study 2 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.

关联论文《提升算术运算中概念衍生策略的使用：借助反转问题（inversion problems）促进结合律（associativity）捷径的应用》的研究参与者手册。摘要：算术核心原理的概念性知识，是理解代数并在后续数学学习中取得成功的重要前置条件。其中一项核心原理为结合律（associativity），即个体可通过分解与重组子表达式（例如“a + b – c” = “b – c + a”），以多种路径求解算术问题。相较于其他算术原理，无论儿童还是成人都更难掌握结合律的内涵，教育工作者呼吁对此作出改进。本研究开展三项于大学课堂中实施的干预实验，旨在探究能否提升成人对结合律的应用能力。三项实验均发现，相较于对照组，先完成反转问题（例如“a + b – b”）求解的参与者，后续在解答“a + b – c”类问题时，更倾向于运用结合律策略。我们认为，“a + b – b”形式的反转问题，既可将空间注意力引导至结合律问题中“b – c”的位置，也可隐性传递从右至左求解策略的有效性与高效性。本研究结果可为旨在助力学习者理解算术原理与代数知识的简短教学活动设计者提供参考。