TY - JOUR

T1 - Increasing the use of conceptually-derived strategies in arithmetic

T2 - using inversion problems to promote the use of associativity shortcuts

AU - Attridge, Nina

AU - Eaves, Joanne

AU - Gilmore, Camilla

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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 sub-expressions (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.

AB - 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 sub-expressions (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.

UR - https://repository.lboro.ac.uk/articles/journal_contribution/Increasing_the_use_of_conceptually-derived_strategies_in_arithmetic_using_inversion_problems_to_promote_the_use_of_associativity_shortcuts/9367043

U2 - 10.1016/j.learninstruc.2019.01.004

DO - 10.1016/j.learninstruc.2019.01.004

M3 - Article

VL - 61

SP - 84

EP - 98

JO - Learning and Instruction

JF - Learning and Instruction

SN - 0959-4752

M1 - 0

ER -