Fostering the learning of subtraction concepts and the subtraction-as-addition reasoning strategy

• Published in: Early childhood research quarterly 2020-01, Vol.51, p.403-415
• Main Authors: Paliwal, Veena, Baroody, Arthur J.
• Format: Article
• Language: English
• Subjects: Basic facts; Fluency; Learning of subtraction concepts; Reasoning strategies; Strategy; Subtraction-as-addition
• ISSN: 0885-2006; 1873-7706
• DOI: 10.1016/j.ecresq.2019.05.008

•The efficacy of promoting the discovery of the subtraction-as-addition strategy in learning subtraction concepts and facts was evaluated.•Eighty-one participants received either structured-subtraction, unstructured subtraction drill, or unrelated addition instruction.•Testing involved assessing whether a child recognized that addition could be used to solve a related, unknown subtraction combination.•Most participants in the structured-subtraction intervention group had learned and reliably used the subtraction-as-addition strategy. The subtraction-as-addition strategy (e.g., using the known sum 7 + 4 = 11 to solve for the unknown difference of 11 − 4 = ?) is an important example of mathematical reasoning and can facilitate subtraction fluency. A 12-weeks long randomized control trial consisting of an experimental group (structured-subtraction instruction/practice on the strategy) and two comparison groups (unstructured practice of subtraction combinations and structured instruction/practice on a different reasoning strategy) served to evaluate whether conceptually based instruction was efficacious in promoting knowledge and reliable use of the subtraction-as-addition reasoning strategy. Eighty-one Grade K-3 students (mean age 7.9 years) participated. A computational shortcut task (presenting a related sum such as 7 + 7 = 14 before 14 − 7 = ?) was used to gauge whether participants recognized addition could be used to solve related, unpracticed, and unknown subtraction combinations. Significantly more participants in the structured-subtraction group than those in the comparison groups used a related sum to avoid computing a difference. A large majority of participants in the experimental group, but not in the comparison groups, exhibited knowledge and reliable use of the subtraction-as-addition strategy.